TPTP Problem File: SEV607+1.p
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%------------------------------------------------------------------------------
% File : SEV607+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - ArithCompl Zodd sqr2
% 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 : ArithCompl.Zodd.sqr2.p [Kal26]
% Status : Theorem
% Rating : 0.74 v9.3.0
% Syntax : Number of formulae : 2361 ( 767 unt; 0 def)
% Number of atoms : 8618 (2334 equ)
% Maximal formula atoms : 82 ( 3 avg)
% Number of connectives : 6409 ( 152 ~; 405 |;1272 &)
% ( 712 <=>;3868 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 351 ( 350 usr; 0 prp; 1-23 aty)
% Number of functors : 1069 (1069 usr; 617 con; 0-22 aty)
% Number of variables : 7756 (7271 !; 485 ?)
% 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.bool$66339',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$66341',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466341___24a1(Vv__CANONICAL__0) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(Vv__CANONICAL__0) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466341___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$32068',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__32069] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32069)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32069)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__32069)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$32090',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__32091] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32091)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32091)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__32091)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$16654',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__16659] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__16659)
& ? [Vvar__3___24Anonymous__16660] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__16660)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__16659,Vvar__3___24Anonymous__16660)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416654___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__1,Vvar__2___24Anonymous__16659),Vvar__3___24Anonymous__16660)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3___24Anonymous__16660))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3___24Anonymous__16660,Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$19767',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__19772] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19772)
& ? [Vvar__3___24Anonymous__19773] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19773)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19772,Vvar__3___24Anonymous__19773)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419767___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2___24Anonymous__19772,Vv__CANONICAL__1),Vvar__3___24Anonymous__19773) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$19795',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__19800] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19800)
& ? [Vvar__3___24Anonymous__19801] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__19801)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__19801)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),Vvar__2___24Anonymous__19800,Vvar__3___24Anonymous__19801)
& ? [Vvar__2___24Anonymous__19813] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19813)
& ? [Vvar__3___24Anonymous__19814] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19814)
& Vvar__3___24Anonymous__19801 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19813,Vvar__3___24Anonymous__19814)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419795___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2___24Anonymous__19800,Vvar__2___24Anonymous__19813)
& Vv__CANONICAL__1 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2___24Anonymous__19800,Vvar__3___24Anonymous__19814) ) ) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$32085',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__32086] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32086)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32086)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32086) )
| ? [Vvar__0___24Anonymous__32087] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32087)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32087)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32087) ) ) ) ).
fof('$_def_$_cast_16748',axiom,
c_24__cast__16748 = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24True,c_24False,cCoq_2eInit_2eLogic_2eI) ).
fof('$_def_$_cast_16749',axiom,
! [Vvar__0___24Anonymous__16740] : c_24__cast__16749___24a1(Vvar__0___24Anonymous__16740) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24False,c_24True,cCoq_2eInit_2eLogic_2eI) ).
fof('$_def_$_cast_16750',axiom,
! [Vvar__0___24Anonymous__16741] : c_24__cast__16750___24a1(Vvar__0___24Anonymous__16741) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24True,c_24False,cCoq_2eInit_2eLogic_2eI) ).
fof('$_def_$_cast_16751',axiom,
c_24__cast__16751 = cCoq_2eInit_2eSpecif_2eright___24a3(c_24False,c_24True,cCoq_2eInit_2eLogic_2eI) ).
fof('$_def_$_cast_16752',axiom,
! [Vvar__0___24Anonymous__16746] : c_24__cast__16752___24a1(Vvar__0___24Anonymous__16746) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24False,c_24True,cCoq_2eInit_2eLogic_2eI) ).
fof('$_def_$_cast_16753',axiom,
! [Vvar__0___24Anonymous__16747] : c_24__cast__16753___24a1(Vvar__0___24Anonymous__16747) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24True,c_24False,cCoq_2eInit_2eLogic_2eI) ).
fof('$_def_$_cast_16754',axiom,
c_24__cast__16754 = cCoq_2eInit_2eSpecif_2eright___24a3(c_24False,c_24True,cCoq_2eInit_2eLogic_2eI) ).
fof('$_def_$_let_11_subst_l_14524',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__14524___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_32944',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__32947] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32947)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32947)
& c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__32948] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32948)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32948)
& c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_32945',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__32945___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_32946',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__32946___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_2_s_19729',axiom,
! [V0__n] : c_24__let__2__s__19729___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) ).
fof('$_def_$_let_6_lmp_16424',axiom,
! [V2__lpe] : c_24__let__6__lmp__16424___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_var_6_p_14926_14929',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925] : c_24__let__var__6__p__14926__14929___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925) ).
fof('$_def_$_let_var_6_p_14928_14930',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927] : c_24__let__var__6__p__14928__14930___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927) ).
fof('$_def_ArithCompl.both_odd',axiom,
! [V0__x,V1__y] :
( cArithCompl_2eboth__odd___24a2(V0__x,V1__y)
<=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__x))
& p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__y)) ) ) ).
fof('$_def_ArithCompl.distinct_parity',axiom,
! [V0__a,V1__b] :
( cArithCompl_2edistinct__parity___24a2(V0__a,V1__b)
<=> ( ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__a))
& p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__b)) )
| ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a))
& p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V1__b)) ) ) ) ).
fof('$_def_Coq.Arith.Factorial.fact',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__19991] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19991)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19991)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19991),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__19991)) ) ) ) ).
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.Sumbool.bool_of_sumbool',axiom,
! [V0__A,V1__B,V2__H] : cCoq_2eBool_2eSumbool_2ebool__of__sumbool___24a3(V0__A,V1__B,V2__H) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(V0__A,V1__B,c_24__lam__59316___24a2(V0__A,V1__B),c_24__lam__59332___24a2(V0__A,V1__B),c_24__lam__59347___24a2(V0__A,V1__B),V2__H) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__69005] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__69005)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__69005) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__58728] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__58728)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__58728) ) ).
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.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('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__35244] :
( t(Vvar__1___24Anonymous__35244,V0__A)
& ? [Vvar__2___24Anonymous__35245] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35245)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35244,Vvar__2___24Anonymous__35245)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35244,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__35245,V3__m)) ) ) ) ) ) ).
fof('$_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__13297] :
( t(Vvar__2___24Anonymous__13297,V0__A)
& ? [Vvar__3___24Anonymous__13298] :
( t(Vvar__3___24Anonymous__13298,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__13297,Vvar__3___24Anonymous__13298)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__13297 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__13214___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__13212] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13212)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13212)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__13212),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__13212)) ) ) ) ) ).
fof('$_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__13309] :
( t(Vvar__2___24Anonymous__13309,V0__A)
& ? [Vvar__3___24Anonymous__13310] :
( t(Vvar__3___24Anonymous__13310,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__13309,Vvar__3___24Anonymous__13310)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__13310 ) ) ) ) ) ).
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__20894] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20894)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20894)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__20894,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__20903] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20903)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20903)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__20906] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20906)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20906)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__20903,Vvar__0___24Anonymous__20906)) ) ) ) ) ) ) ) ).
fof('$_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__13847] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13847)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13847)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__13847,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__64813] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64813)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64813)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__64813 ) ) ) ).
fof('$_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__20897] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20897)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20897)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__20900] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20900)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20900)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__20897,Vvar__0___24Anonymous__20900) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.sig_rec',axiom,
! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esig__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V0__A,V1__P,V2__P) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__19085] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19085)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19085)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__19088] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19088)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19088)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19085,Vvar__0___24Anonymous__19088)) ) ) ) ) ) ) ) ).
fof('$_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__31340] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31340)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31340)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__31341] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31341)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31341)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31344] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31344)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31344)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31341,Vvar__0___24Anonymous__31344) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__19092] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19092)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19092)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__19095] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19095)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19095)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__19092,Vvar__0___24Anonymous__19095)) ) ) ) ) ) ) ) ).
fof('$_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__31346] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31346)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31346)
& 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__31346)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__19155] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19155)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19155)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__19155,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__19159] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19159)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19159)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__19159) ) ) ) ).
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.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__414] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__414)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__414)
& ( ? [Vvar__0___24Anonymous__418] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__418)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__418)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__413__1__add__carry___24a2(Vvar__0___24Anonymous__414,Vvar__0___24Anonymous__418)) )
| ? [Vvar__0___24Anonymous__419] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__419)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__419)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__414,Vvar__0___24Anonymous__419)) )
| ( 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__414)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__420] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__420)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__420)
& ( ? [Vvar__0___24Anonymous__424] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__424)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__424)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__420,Vvar__0___24Anonymous__424)) )
| ? [Vvar__0___24Anonymous__425] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__425)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__425)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__420,Vvar__0___24Anonymous__425)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__420) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__426] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__426)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__426)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__426)) )
| ? [Vvar__0___24Anonymous__427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__427)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__427)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__427) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__19188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19188)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19188)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__19188),Vvar__0___24Anonymous__19188)) )
| ? [Vvar__0___24Anonymous__19189] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19189)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19189)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__19189),Vvar__0___24Anonymous__19189) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__452] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__452)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__452)
& 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__452,V2__y))) )
| ? [Vvar__0___24Anonymous__453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__453)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__453)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__453,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_N',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__19183] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19183)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19183)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19183)) )
| ? [Vvar__0___24Anonymous__19184] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19184)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19184)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__19184)) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__19181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19181)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19181)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19181)) )
| ? [Vvar__0___24Anonymous__19182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19182)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19182)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__19182)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__19185] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19185)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__19185)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__19185 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__19178] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19178)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19178)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__19178)) )
| ? [Vvar__0___24Anonymous__19179] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19179)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19179)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19179) )
| ( 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__19210] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19210)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19210)
& ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__19213] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19213)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19213)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__19210,cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__19213)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19214)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19214)
& ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__19217] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19217)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19217)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__19214,cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__19217)) ) ) ) ) )
| ( 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__19218] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19218)
& V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19218)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V1__p,V2__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
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('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__22005] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__22005)
& ? [Vvar__1__Qden__22006] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__22006)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__22005,Vvar__1__Qden__22006)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__22006 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq',axiom,
! [V0__p,V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__p,V1__q)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qmult',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y)),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__22000] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__22000)
& ? [Vvar__1__Qden__22001] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__22001)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__22000,Vvar__1__Qden__22001)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__22000 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.inject_Z',axiom,
! [V0__x] : cCoq_2eQArith_2eQArith__base_2einject__Z___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.Reals.NewtonInt.Newton_integrable',axiom,
! [V0__f,V1__a,V2__b] : cCoq_2eReals_2eNewtonInt_2eNewton__integrable___24a3(V0__f,V1__a,V2__b) = cCoq_2eInit_2eSpecif_2esig___24a2(c_24__type__13871,c_24__lam__36855___24a3(V0__f,V1__a,V2__b)) ).
fof('$_def_Coq.Reals.Ranalysis1.antiderivative',axiom,
! [V0__f,V1__g,V2__a,V3__b] :
( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V0__f,V1__g,V2__a,V3__b)
<=> ( ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V4__x)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__x,V3__b) )
=> ? [V6__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__g,V4__x,V6__pr)
& happ(V0__f,V4__x) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V4__x,V6__pr) ) ) )
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V3__b) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt',axiom,
! [V0__f,V1__x] : cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V0__f,V1__x) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__22033___24a2(V0__f,V1__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt_abs',axiom,
! [V0__f,V1__x,V2__l] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(V0__f,V1__x,V2__l)
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derive_pt',axiom,
! [V0__f,V1__x,V2__pr] : cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__22033___24a2(V0__f,V1__x),V2__pr) ).
fof('$_def_Coq.Reals.Ranalysis1.fct_cte',axiom,
! [V0__a,V1__x] : cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V0__a,V1__x) = V0__a ).
fof('$_def_Coq.Reals.Ranalysis1.mult_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.no_cond',axiom,
! [V0__x] :
( cCoq_2eReals_2eRanalysis1_2eno__cond___24a1(V0__x)
<=> p(c_24True) ) ).
fof('$_def_Coq.Reals.Ranalysis1.plus_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__13864] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13864)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13864)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13864)
& ( ( Vvar__0___24Anonymous__13864 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__13867] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13867)
& Vvar__0___24Anonymous__13864 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13867)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__13864),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Raxioms.bound',axiom,
! [V0__E] :
( cCoq_2eReals_2eRaxioms_2ebound___24a1(V0__E)
<=> ? [V1__m] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__m)
& cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m) ) ) ).
fof('$_def_Coq.Reals.Raxioms.is_upper_bound',axiom,
! [V0__E,V1__m] :
( cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m)
<=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(happ(V0__E,V2__x))
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__x,V1__m) ) ) ) ).
fof('$_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__13883] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13883)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13883)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__13883) )
| ? [Vvar__0___24Anonymous__13884] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13884)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13884)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__13884)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rfunctions.R_dist',axiom,
! [V0__x,V1__y] : cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__x,V1__y)) ).
fof('$_def_Coq.Reals.Rfunctions.sum_f_R0',axiom,
! [V1__f,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__13890] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13890)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13890)
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,Vvar__0___24Anonymous__13890),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13890))) ) ) ) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__31254] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31254)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31254)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__31254)) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.EUn',axiom,
! [V0__Un,V1__r] :
( cCoq_2eReals_2eRseries_2eEUn___24a2(V0__Un,V1__r)
<=> ? [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
& V1__r = happ(V0__Un,V2__i) ) ) ).
fof('$_def_Coq.Reals.Rseries.Un_growing',axiom,
! [V0__Un] :
( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V1__n),happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n))) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__399___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Bezout',axiom,
! [V0__n,V1__m,V2__p] :
( cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V0__n,V1__m,V2__p)
<=> ? [V3__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__a)
& ? [V4__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__b)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__a,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__b,V1__m)) = V2__p ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Even',axiom,
! [V0__a] :
( cCoq_2eZArith_2eBinInt_2eZ_2eEven___24a1(V0__a)
<=> ? [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Odd',axiom,
! [V0__a] :
( cCoq_2eZArith_2eBinInt_2eZ_2eOdd___24a1(V0__a)
<=> ? [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv = cCoq_2eZArith_2eBinIntDef_2eZ_2equot ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo = cCoq_2eZArith_2eBinIntDef_2eZ_2erem ).
fof('$_def_Coq.ZArith.BinInt.Z.b2z',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( p(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('$_def_Coq.ZArith.BinInt.Z.lcm',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinInt_2eZ_2elcm___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b)))) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.log2_up',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__a))) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.sqrt_up',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__a))) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__327)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__327)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__327) )
| ? [Vvar__0___24Anonymous__328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__328)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__328)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__328) ) ) ) ).
fof('$_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__19309] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19309)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19309)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19309) )
| ? [Vvar__0___24Anonymous__19310] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19310)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19310)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19310) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__19305] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19305)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19305)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__19305) )
| ? [Vvar__0___24Anonymous__19306] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19306)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19306)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__19306) ) ) ) ).
fof('$_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__32] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__36] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__36)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__32,Vvar__0___24Anonymous__36)) )
| ? [Vvar__0___24Anonymous__37] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__37)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__32,Vvar__0___24Anonymous__37) ) ) ) ) )
| ? [Vvar__0___24Anonymous__38] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__38)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__42] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__42,Vvar__0___24Anonymous__38) )
| ? [Vvar__0___24Anonymous__43] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__43)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__38,Vvar__0___24Anonymous__43)) ) ) ) ) ) ) ) ).
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__308] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__308)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__308)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__309] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__309)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__309)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__310] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__310)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__310)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__314] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__314)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__314)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__310,Vvar__0___24Anonymous__314) )
| ? [Vvar__0___24Anonymous__315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__315)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__315)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__316)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__316)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__320)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__320)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__321] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__321)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__321)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__316,Vvar__0___24Anonymous__321)) ) ) ) ) ) ) ) ).
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__333] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__333)
& ? [Vvar__3___24Anonymous__334] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__334)
& 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__333,Vvar__3___24Anonymous__334)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__333 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19551)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19551)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19551)
& ( ? [Vvar__0___24Anonymous__19555] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19555)
& Vvar__0___24Anonymous__19551 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19555)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(Vvar__0___24Anonymous__19551)) )
| ? [Vvar__0___24Anonymous__19556] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19556)
& Vvar__0___24Anonymous__19551 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19556)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(Vvar__0___24Anonymous__19551)) )
| ( Vvar__0___24Anonymous__19551 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__19557] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19557)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19557)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(Vvar__0___24Anonymous__19557)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19275] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19275)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19275)
& cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19275)) )
| ? [Vvar__0___24Anonymous__19276] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19276)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19276)
& cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19276)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__19527] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19527)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19527)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19527)
& ( ? [Vvar__0___24Anonymous__19531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19531)
& Vvar__0___24Anonymous__19527 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19531)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__19532] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19532)
& Vvar__0___24Anonymous__19527 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19532)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__19527 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__19533] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19533)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19533)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19533)
& ( ? [Vvar__0___24Anonymous__19537] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19537)
& Vvar__0___24Anonymous__19533 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19537)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__19538] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19538)
& Vvar__0___24Anonymous__19533 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19538)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__19533 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b) )
| ? [Vvar__0___24Anonymous__345] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__345)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__345)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__349] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__349)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__349)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__345,Vvar__0___24Anonymous__349)) )
| ? [Vvar__0___24Anonymous__350] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__350)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__350)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__345,Vvar__0___24Anonymous__350)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__351] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__351)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__351)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__355] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__355)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__355)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__351,Vvar__0___24Anonymous__355)) )
| ? [Vvar__0___24Anonymous__356] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__356)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__356)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__351,Vvar__0___24Anonymous__356)) ) ) ) ) ) ) ) ).
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.log2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__489] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__489)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__489)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__489)
& ( ? [Vvar__0___24Anonymous__493] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__493)
& Vvar__0___24Anonymous__489 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__493)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__493)) )
| ? [Vvar__0___24Anonymous__494] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__494)
& Vvar__0___24Anonymous__489 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__494)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__494)) )
| ( Vvar__0___24Anonymous__489 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__495] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__495)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__495)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.ltb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_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__341] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__341)
& ? [Vvar__3___24Anonymous__342] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__342)
& 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__341,Vvar__3___24Anonymous__342)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__342 ) ) ) ) ).
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__47] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__47)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__47)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__51] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__51)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__51)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__47,Vvar__0___24Anonymous__51)) )
| ? [Vvar__0___24Anonymous__52] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__52)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__52)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__47,Vvar__0___24Anonymous__52)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__53] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__53)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__57] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__57)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__57)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__53,Vvar__0___24Anonymous__57)) )
| ? [Vvar__0___24Anonymous__58] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__58)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__58)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__53,Vvar__0___24Anonymous__58)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__19539] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19539)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19539)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19539)
& ( ? [Vvar__0___24Anonymous__19543] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19543)
& Vvar__0___24Anonymous__19539 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19543)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__19544] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19544)
& Vvar__0___24Anonymous__19539 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19544)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__19539 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__19545] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19545)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19545)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19545)
& ( ? [Vvar__0___24Anonymous__19549] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19549)
& Vvar__0___24Anonymous__19545 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19549)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__19550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19550)
& Vvar__0___24Anonymous__19545 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19550)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__19545 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19320)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19320)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19320) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19317] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19317)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19317)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__19317)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__70] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__70)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__70)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__70) )
| ? [Vvar__0___24Anonymous__71] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__71)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__71)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__71) ) ) ) ).
fof('$_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__485] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__485)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__485)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__485) )
| ? [Vvar__0___24Anonymous__486] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__486)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__486)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow_pos',axiom,
! [V0__z] : cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a1(V0__z),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_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.quot2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35315)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35315)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35315)
& ( ? [Vvar__0___24Anonymous__35319] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35319)
& Vvar__0___24Anonymous__35315 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35319)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(Vvar__0___24Anonymous__35315)) )
| ? [Vvar__0___24Anonymous__35320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35320)
& Vvar__0___24Anonymous__35315 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35320)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(Vvar__0___24Anonymous__35315)) )
| ( Vvar__0___24Anonymous__35315 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__35321] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35321)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35321)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35321)
& ( ? [Vvar__0___24Anonymous__35325] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35325)
& Vvar__0___24Anonymous__35321 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35325)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(Vvar__0___24Anonymous__35321)) )
| ? [Vvar__0___24Anonymous__35326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35326)
& Vvar__0___24Anonymous__35321 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35326)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(Vvar__0___24Anonymous__35321)) )
| ( Vvar__0___24Anonymous__35321 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__19461] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19461)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19461)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__19471] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19471)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19461)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19471)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19471)
& ? [Vvar__2___24Anonymous__19479] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__19479)
& ? [Vvar__3___24Anonymous__19480] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__19480)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19461,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19471)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__19479,Vvar__3___24Anonymous__19480)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__19479),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__19480)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19482] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19482)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19461)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19482)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19482)
& ? [Vvar__2___24Anonymous__19490] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__19490)
& ? [Vvar__3___24Anonymous__19491] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__19491)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19461,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19482)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__19490,Vvar__3___24Anonymous__19491)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__19490)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__19491)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19493] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19493)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19493)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__19503] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19503)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19493)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19503)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19503)
& ? [Vvar__2___24Anonymous__19511] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__19511)
& ? [Vvar__3___24Anonymous__19512] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__19512)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19493,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19503)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__19511,Vvar__3___24Anonymous__19512)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__19511)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__19512))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19514)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19493)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19514)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19514)
& ? [Vvar__2___24Anonymous__19522] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__19522)
& ? [Vvar__3___24Anonymous__19523] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__19523)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19493,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19514)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__19522,Vvar__3___24Anonymous__19523)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__19522),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__19523))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__325] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__325)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__325)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__326)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__326)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.shiftl',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n) = V0__a )
| ? [Vvar__0___24Anonymous__19703] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19703)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19703)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V0__a,Vvar__0___24Anonymous__19703) )
| ? [Vvar__0___24Anonymous__19704] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19704)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19704)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2,V0__a,Vvar__0___24Anonymous__19704) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.shiftr',axiom,
! [V0__a,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19558] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19558)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19558)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__19558)) )
| ? [Vvar__0___24Anonymous__19559] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19559)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19559)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.square',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19300] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19300)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19300)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esquare___24a1(Vvar__0___24Anonymous__19300)) )
| ? [Vvar__0___24Anonymous__19301] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19301)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19301)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esquare___24a1(Vvar__0___24Anonymous__19301)) ) ) ) ).
fof('$_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.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__517] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__517)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__517)
& ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__521)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__521)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__521,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__517)) )
| ? [Vvar__0___24Anonymous__522] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__522)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__522)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__522),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__517))) ) ) ) ) )
| ? [Vvar__0___24Anonymous__523] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__523)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__523)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__19315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19315)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19315)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19315) )
| ? [Vvar__0___24Anonymous__19316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19316)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19316)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_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__19313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19313)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19313)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__19313) )
| ? [Vvar__0___24Anonymous__19314] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19314)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19314)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__19323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19323)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19323)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__19323 )
| ? [Vvar__0___24Anonymous__19324] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19324)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19324)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.ZArith_dec.Z_zerop',axiom,
! [V0__x] : cCoq_2eZArith_2eZArith__dec_2eZ__zerop___24a1(V0__x) = cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeven_odd_bool',axiom,
! [V0__x] : cCoq_2eZArith_2eZbool_2eZeven__odd__bool___24a1(V0__x) = cCoq_2eBool_2eSumbool_2ebool__of__sumbool___24a3(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__x),cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__x),cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__x)) ).
fof('$_def_Coq.ZArith.Zdiv.Remainder',axiom,
! [V0__r,V1__b] :
( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V0__r,V1__b)
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__r,V1__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('$_def_Coq.ZArith.Zdiv.eqm',axiom,
! [V0__N,V1__a,V2__b] :
( cCoq_2eZArith_2eZdiv_2eeqm___24a3(V0__N,V1__a,V2__b)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V1__a,V0__N) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V2__b,V0__N) ) ).
fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__16712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16712)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16712)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16712)
& ( ? [Vvar__0___24Anonymous__16716] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16716)
& Vvar__0___24Anonymous__16712 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16716)
& ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__16717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16717)
& Vvar__0___24Anonymous__16712 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16717)
& ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__16712 = cCoq_2eNumbers_2eBinNums_2exH
& ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__16718] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16718)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16718)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16718)
& ( ? [Vvar__0___24Anonymous__16722] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16722)
& Vvar__0___24Anonymous__16718 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16722)
& ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__16723] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16723)
& Vvar__0___24Anonymous__16718 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16723)
& ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__16718 = cCoq_2eNumbers_2eBinNums_2exH
& ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
<=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zeven_odd_dec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__n) = c_24__cast__16748 )
| ? [Vvar__0___24Anonymous__16736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16736)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16736)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16736)
& ( ? [Vvar__0___24Anonymous__16740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16740)
& Vvar__0___24Anonymous__16736 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16740)
& cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__n) = c_24__cast__16749___24a1(Vvar__0___24Anonymous__16740) )
| ? [Vvar__0___24Anonymous__16741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16741)
& Vvar__0___24Anonymous__16736 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16741)
& cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__n) = c_24__cast__16750___24a1(Vvar__0___24Anonymous__16741) )
| ( Vvar__0___24Anonymous__16736 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__n) = c_24__cast__16751 ) ) ) ) )
| ? [Vvar__0___24Anonymous__16742] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16742)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16742)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16742)
& ( ? [Vvar__0___24Anonymous__16746] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16746)
& Vvar__0___24Anonymous__16742 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16746)
& cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__n) = c_24__cast__16752___24a1(Vvar__0___24Anonymous__16746) )
| ? [Vvar__0___24Anonymous__16747] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16747)
& Vvar__0___24Anonymous__16742 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16747)
& cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__n) = c_24__cast__16753___24a1(Vvar__0___24Anonymous__16747) )
| ( Vvar__0___24Anonymous__16742 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V0__n) = c_24__cast__16754 ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__16724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16724)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16724)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__16724)
& ( ? [Vvar__0___24Anonymous__16728] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16728)
& Vvar__0___24Anonymous__16724 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16728)
& ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__16729] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16729)
& Vvar__0___24Anonymous__16724 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16729)
& ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__16724 = cCoq_2eNumbers_2eBinNums_2exH
& ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__16730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16730)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16730)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16730)
& ( ? [Vvar__0___24Anonymous__16734] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16734)
& Vvar__0___24Anonymous__16730 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__16734)
& ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__16735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16735)
& Vvar__0___24Anonymous__16730 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16735)
& ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__16730 = cCoq_2eNumbers_2eBinNums_2exH
& ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Znumtheory.Euclid_rect',axiom,
! [V0__a,V1__b,V2__P,V3__f,V4__e] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( c_24__type__16869___24t(V0__a,V1__b,V2__P,V2__P)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V0__a,V1__b,V4__e)
=> ? [Vvar__2__u__16859] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__16859)
& ? [Vvar__3__v__16860] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__16860)
& ? [Vvar__4__d__16861] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__16861)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__16859,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__16860,V1__b)) = Vvar__4__d__16861
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,Vvar__4__d__16861)
& V4__e = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V0__a,V1__b,Vvar__2__u__16859,Vvar__3__v__16860,Vvar__4__d__16861)
& cCoq_2eZArith_2eZnumtheory_2eEuclid__rect___24a5(V0__a,V1__b,V2__P,V3__f,V4__e) = happ(happ(happ(V3__f,Vvar__2__u__16859),Vvar__3__v__16860),Vvar__4__d__16861) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Znumtheory.rel_prime',axiom,
! [V0__a,V1__b] :
( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('$_def_Coq.ZArith.Zpower.Zpower_nat',axiom,
! [V0__z] : cCoq_2eZArith_2eZpower_2eZpower__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__18637,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),c_24__lam__18639___24a1(V0__z)) ).
fof('$_def_Coq.ZArith.Zpower.two_p',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__31337] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31337)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31337)
& cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__0___24Anonymous__31337) )
| ? [Vvar__0___24Anonymous__31338] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31338)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31338)
& cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.Zpower.two_power_pos',axiom,
! [V0__x] : cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eZArith_2eZpower_2eshift__pos___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.micromega.Env.jump',axiom,
! [V0__D,V1__j,V2__e,V3__x] : cCoq_2emicromega_2eEnv_2ejump___24a4(V0__D,V1__j,V2__e,V3__x) = happ(V2__e,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V3__x,V1__j)) ).
fof('$_def_Coq.micromega.Env.tail',axiom,
! [V0__D,V1__e] : cCoq_2emicromega_2eEnv_2etail___24a2(V0__D,V1__e) = cCoq_2emicromega_2eEnv_2ejump___24a3(V0__D,cCoq_2eNumbers_2eBinNums_2exH,V1__e) ).
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.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('$_def_Coq.micromega.RingMicromega.map_option',axiom,
! [V0__A,V1__B,V2__f,V3__o] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V3__o)
=> ( ? [Vvar__1___24Anonymous__13942] :
( t(Vvar__1___24Anonymous__13942,V0__A)
& V3__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__13942)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = happ(V2__f,Vvar__1___24Anonymous__13942) )
| ( V3__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option2',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V4__o)
=> ( ? [Vvar__1___24Anonymous__13960] :
( t(Vvar__1___24Anonymous__13960,V0__A)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V1__B,V5__o_27)
=> ( V4__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__13960)
& ( ? [Vvar__1___24Anonymous__13965] :
( t(Vvar__1___24Anonymous__13965,V1__B)
& V5__o_27 = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__1___24Anonymous__13965)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = happ(happ(V3__f,Vvar__1___24Anonymous__13960),Vvar__1___24Anonymous__13965) )
| ( V5__o_27 = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ) )
| ( V4__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.psubC',axiom,
! [V0__C,V1__cminus] : cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V0__C,V1__cminus) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V0__C,V1__cminus) ).
fof('$_def_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
! [V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp] : cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__31333] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__31333)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__31333) ) ).
fof('$_def_Coq.micromega.ZMicromega.ceiling',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__34442] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__34442)
& ? [Vvar__3___24Anonymous__34443] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__34443)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__34443)
=> ( 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__34442,Vvar__3___24Anonymous__34443)
& ( ( Vvar__3___24Anonymous__34443 = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__34442 )
| ? [Vvar__0___24Anonymous__34451] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34451)
& Vvar__3___24Anonymous__34443 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34451)
& cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(Vvar__2___24Anonymous__34442,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__34452] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34452)
& Vvar__3___24Anonymous__34443 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34452)
& cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(Vvar__2___24Anonymous__34442,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.omega.PreOmega.Zneg\'',axiom,
cCoq_2eomega_2ePreOmega_2eZneg_27 = cCoq_2eNumbers_2eBinNums_2eZneg ).
fof('$_def_Coq.omega.PreOmega.Zpos\'',axiom,
cCoq_2eomega_2ePreOmega_2eZpos_27 = cCoq_2eNumbers_2eBinNums_2eZpos ).
fof('$_def_Coq.setoid_ring.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__20324] :
( t(Vvar__1___24Anonymous__20324,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__20324)
& 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__20324) )
| ? [Vvar__1___24Anonymous__20326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20326)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__20326)
& 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__20326,V15__l) )
| ? [Vvar__1___24Anonymous__20328] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20328)
& ? [Vvar__2___24Anonymous__20329] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20329)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__20328,Vvar__2___24Anonymous__20329)
& 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__20328)),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__20329)) ) )
| ? [Vvar__1___24Anonymous__20332] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20332)
& ? [Vvar__2___24Anonymous__20333] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20333)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__20332,Vvar__2___24Anonymous__20333)
& 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__20332)),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__20333)) ) )
| ? [Vvar__1___24Anonymous__20336] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20336)
& ? [Vvar__2___24Anonymous__20337] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20337)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__20336,Vvar__2___24Anonymous__20337)
& 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__20336)),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__20337)) ) )
| ? [Vvar__1___24Anonymous__20340] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20340)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__20340)
& 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__20340)) )
| ? [Vvar__1___24Anonymous__20342] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20342)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__20342)
& 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__20342)) )
| ? [Vvar__1___24Anonymous__20344] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20344)
& ? [Vvar__2___24Anonymous__20345] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20345)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__20344,Vvar__2___24Anonymous__20345)
& 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__20344)),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__20345)) ) )
| ? [Vvar__1___24Anonymous__20348] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20348)
& ? [Vvar__2___24Anonymous__20349] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__20349)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__20348,Vvar__2___24Anonymous__20349)
& 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__20348)),happ(V12__Cp__phi,Vvar__2___24Anonymous__20349)) ) ) ) ) ) ) ) ).
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__36593] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36593)
& ? [Vvar__2___24Anonymous__36594] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__36594)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__36593,Vvar__2___24Anonymous__36594)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__36593),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__36594,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons2',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l] : cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e),V10__l) ).
fof('$_def_Coq.setoid_ring.Field_theory.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__20653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__20653)
& ? [Vvar__2___24Anonymous__20654] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__20654)
& ( 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__20654)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__20653,Vvar__2___24Anonymous__20654)
& ( ( Vvar__2___24Anonymous__20654 = 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__20653)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__20665] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__20665)
& ? [Vvar__2___24Anonymous__20666] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__20666)
& Vvar__2___24Anonymous__20654 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__20665,Vvar__2___24Anonymous__20666)
& ( 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__20653)),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__20654) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20640] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20640)
& ? [Vvar__2__denum__20641] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20641)
& ? [Vvar__3__condition__20642] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20642)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20640,Vvar__2__denum__20641,Vvar__3__condition__20642)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__20642 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20631] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20631)
& ? [Vvar__2__denum__20632] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20632)
& ? [Vvar__3__condition__20633] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20633)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20631,Vvar__2__denum__20632,Vvar__3__condition__20633)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__20632 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20620] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20620)
& ? [Vvar__2__denum__20621] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20621)
& ? [Vvar__3__condition__20622] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20622)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20620,Vvar__2__denum__20621,Vvar__3__condition__20622)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__20620 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__35343] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__35343)
& ? [Vvar__2__rsplit__common__35344] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__35344)
& ? [Vvar__3__rsplit__right__35345] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__35345)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__35343,Vvar__2__rsplit__common__35344,Vvar__3__rsplit__right__35345)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__35343 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__35354] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__35354)
& ? [Vvar__2__rsplit__common__35355] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__35355)
& ? [Vvar__3__rsplit__right__35356] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__35356)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__35354,Vvar__2__rsplit__common__35355,Vvar__3__rsplit__right__35356)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__35356 ) ) ) ) ) ).
fof('$_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__13678] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13678)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__13678)
& 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__13678))) )
| ? [Vvar__0___24Anonymous__13679] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13679)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__13679)
& 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__13679)) )
| ( 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('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__13763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13763)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13763)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__13763) )
| ? [Vvar__0___24Anonymous__13764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13764)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13764)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__13764)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ1',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__phiZ1___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__13710] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13710)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13710)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ1___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__13710) )
| ? [Vvar__0___24Anonymous__13711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13711)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13711)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ1___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__13711)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.get_signZ',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__31994] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31994)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31994)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__31995] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31995)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31995)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31995)) ) ) ) ).
fof('$_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__32311] :
( t(Vvar__1___24Anonymous__32311,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__32311)
& 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__32311) )
| ? [Vvar__1___24Anonymous__32313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32313)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__32313)
& 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__32313,V13__l) )
| ? [Vvar__1___24Anonymous__32315] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32315)
& ? [Vvar__2___24Anonymous__32316] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__32316)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__32315,Vvar__2___24Anonymous__32316)
& 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__32315)),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__32316)) ) )
| ? [Vvar__1___24Anonymous__32319] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32319)
& ? [Vvar__2___24Anonymous__32320] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__32320)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__32319,Vvar__2___24Anonymous__32320)
& 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__32319)),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__32320)) ) )
| ? [Vvar__1___24Anonymous__32323] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32323)
& ? [Vvar__2___24Anonymous__32324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__32324)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__32323,Vvar__2___24Anonymous__32324)
& 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__32323)),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__32324)) ) )
| ? [Vvar__1___24Anonymous__32327] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32327)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__32327)
& 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__32327)) )
| ? [Vvar__1___24Anonymous__32329] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32329)
& ? [Vvar__2___24Anonymous__32330] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__32330)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__32329,Vvar__2___24Anonymous__32330)
& 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__32329)),happ(V10__Cp__phi,Vvar__2___24Anonymous__32330)) ) ) ) ) ) ) ) ).
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__14128] :
( t(Vvar__1___24Anonymous__14128,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__14128)
& ( ? [Vvar__1___24Anonymous__14138] :
( t(Vvar__1___24Anonymous__14138,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__14138)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__14128),Vvar__1___24Anonymous__14138) )
| ? [Vvar__1___24Anonymous__14140] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14140)
& ? [Vvar__2___24Anonymous__14141] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14141)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__14140,Vvar__2___24Anonymous__14141)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__14144] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14144)
& ? [Vvar__2___24Anonymous__14145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14145)
& ? [Vvar__3___24Anonymous__14146] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14146)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__14144,Vvar__2___24Anonymous__14145,Vvar__3___24Anonymous__14146)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14151] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14151)
& ? [Vvar__2___24Anonymous__14152] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14152)
& ( 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__14151,Vvar__2___24Anonymous__14152)
& ( ? [Vvar__1___24Anonymous__14172] :
( t(Vvar__1___24Anonymous__14172,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__14172)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__14174] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14174)
& ? [Vvar__2___24Anonymous__14175] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14175)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14151)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14174)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__14174,Vvar__2___24Anonymous__14175)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__14151,Vvar__1___24Anonymous__14174) = 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__14152,Vvar__2___24Anonymous__14175) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__14151,Vvar__1___24Anonymous__14174) = 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__14151,Vvar__1___24Anonymous__14174) = 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__14180] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14180)
& ? [Vvar__2___24Anonymous__14181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14181)
& ? [Vvar__3___24Anonymous__14182] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14182)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__14180,Vvar__2___24Anonymous__14181,Vvar__3___24Anonymous__14182)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14187] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14187)
& ? [Vvar__2___24Anonymous__14188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14188)
& ? [Vvar__3___24Anonymous__14189] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14189)
& ( 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__14187,Vvar__2___24Anonymous__14188,Vvar__3___24Anonymous__14189)
& ( ? [Vvar__1___24Anonymous__14222] :
( t(Vvar__1___24Anonymous__14222,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__14222)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__14224] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14224)
& ? [Vvar__2___24Anonymous__14225] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14225)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__14224,Vvar__2___24Anonymous__14225)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__14228] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14228)
& ? [Vvar__2___24Anonymous__14229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14229)
& ? [Vvar__3___24Anonymous__14230] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14230)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14188)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14229)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__14228,Vvar__2___24Anonymous__14229,Vvar__3___24Anonymous__14230)
& ( ( cType___24t(V0__C)
=> ( c_24__type__14243___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14187)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14228)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__14188,Vvar__2___24Anonymous__14229) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__14187,Vvar__1___24Anonymous__14228) = 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__14189,Vvar__3___24Anonymous__14230) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__14187,Vvar__1___24Anonymous__14228) = 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__14188,Vvar__2___24Anonymous__14229) = 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__14188,Vvar__2___24Anonymous__14229) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__32944___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__32945___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__32946___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
=> ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__14752] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__14752)
& ? [Vvar__2___24Anonymous__14753] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__2___24Anonymous__14753)
& ( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__14752)
=> ( V10__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__1___24Anonymous__14752,Vvar__2___24Anonymous__14753)
& ? [Vvar__2___24Anonymous__14769] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14769)
& ? [Vvar__3___24Anonymous__14770] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__14770)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13636___24t(V0__C,V3__cadd)
=> ( c_24__type__13636___24t(V0__C,V4__cmul)
=> ( c_24__type__13636___24t(V0__C,V5__csub)
=> ( c_24__type__13657___24t(V0__C,V6__copp)
=> ( c_24__type__14243___24t(V0__C,V7__ceqb)
=> ( c_24__type__14746___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14769)
=> ( Vvar__1___24Anonymous__14752 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__14769,Vvar__3___24Anonymous__14770)
& ( ? [Vvar__1___24Anonymous__14778] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__14778)
& cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__14769)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__14778)
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C)),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C),Vvar__1___24Anonymous__14778,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__3___24Anonymous__14770)),cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__14753)) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__14769)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__14753) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__14596___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_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__14945] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14945)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__14945)
& 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__14945) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__14925] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14925)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__14925)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__14926__14929___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925)),c_24__let__var__6__p__14926__14929___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925))) )
| ? [Vvar__0___24Anonymous__14927] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14927)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__14927)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__14928__14930___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927)),c_24__let__var__6__p__14928__14930___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__13206] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13206) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__13241,Vvar__1___24Anonymous__13242,Vvar__0__A__13243] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13241,Vvar__1___24Anonymous__13242) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13243) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__13265,Vvar__1__B__13266,Vvar__2___24Anonymous__13267,Vvar__0__A__13268,Vvar__1__B__13269,Vvar__2___24Anonymous__13270] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__13265,Vvar__1__B__13266,Vvar__2___24Anonymous__13267) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__13268,Vvar__1__B__13269,Vvar__2___24Anonymous__13270) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__13323,Vvar__0__A__13324,Vvar__1___24Anonymous__13325,Vvar__2___24Anonymous__13326] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13323) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13324,Vvar__1___24Anonymous__13325,Vvar__2___24Anonymous__13326) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__19975,Vvar__1__f__19976,Vvar__0__i__19977,Vvar__1__f__19978,Vvar__2__e__19979] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__19975,Vvar__1__f__19976) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__19977,Vvar__1__f__19978,Vvar__2__e__19979) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__19937] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19937) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__19961,Vvar__0__d__19962] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19961) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19962) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__31273,Vvar__1__B__31274,Vvar__2___24Anonymous__31275,Vvar__0__A__31276,Vvar__1__B__31277,Vvar__2___24Anonymous__31278] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31273,Vvar__1__B__31274,Vvar__2___24Anonymous__31275) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31276,Vvar__1__B__31277) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__119,Vvar__1__B__120,Vvar__2___24Anonymous__121,Vvar__0__A__122,Vvar__1__B__123,Vvar__2___24Anonymous__124] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__119,Vvar__1__B__120) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__122,Vvar__1__B__123) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__13183] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13183) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__20] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__448] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__448) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__32108,Vvar__1___24Anonymous__32109,Vvar__0__x__32110,Vvar__1__n__32111,Vvar__2___24Anonymous__32112] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32108) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32110,Vvar__1__n__32111) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__13504,Vvar__1___24Anonymous__13505,Vvar__0__C__13506,Vvar__1___24Anonymous__13507] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13504,Vvar__1___24Anonymous__13505) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13506,Vvar__1___24Anonymous__13507) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__13568,Vvar__1___24Anonymous__13569,Vvar__0__C__13570,Vvar__1___24Anonymous__13571,Vvar__2___24Anonymous__13572] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13568,Vvar__1___24Anonymous__13569) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13570,Vvar__1___24Anonymous__13571,Vvar__2___24Anonymous__13572) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__27460,Vvar__1___24Anonymous__27461,Vvar__0__C__27462,Vvar__1___24Anonymous__27463] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27460,Vvar__1___24Anonymous__27461) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27462,Vvar__1___24Anonymous__27463) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__65456,Vvar__1__TX__65457,Vvar__2__AA__65458,Vvar__3__AF__65459,Vvar__0__TA__65460,Vvar__1__TX__65461,Vvar__2__AA__65462,Vvar__3__AF__65463] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65456,Vvar__1__TX__65457,Vvar__2__AA__65458,Vvar__3__AF__65459) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65460,Vvar__1__TX__65461,Vvar__2__AA__65462,Vvar__3__AF__65463) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__65587,Vvar__0__A__65588,Vvar__1___24Anonymous__65589] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65587) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65588,Vvar__1___24Anonymous__65589) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__58058,Vvar__1___24Anonymous__58059] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__58058,Vvar__1___24Anonymous__58059) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__20267,Vvar__0__C__20268] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20267) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20268) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__14460,Vvar__0__C__14461] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14460) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14461) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__14102,Vvar__1___24Anonymous__14103,Vvar__0__C__14104,Vvar__1___24Anonymous__14105,Vvar__2___24Anonymous__14106] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14102,Vvar__1___24Anonymous__14103) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14104,Vvar__1___24Anonymous__14105,Vvar__2___24Anonymous__14106) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__14270,Vvar__1___24Anonymous__14271] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14270,Vvar__1___24Anonymous__14271) ).
fof('$_fix_413_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__428)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__428)
& ( ? [Vvar__0___24Anonymous__432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__432)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__432)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__413__1__add__carry___24a2(Vvar__0___24Anonymous__428,Vvar__0___24Anonymous__432)) )
| ? [Vvar__0___24Anonymous__433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__433)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__433)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__413__1__add__carry___24a2(Vvar__0___24Anonymous__428,Vvar__0___24Anonymous__433)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__428)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__434)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__434)
& ( ? [Vvar__0___24Anonymous__438] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__438)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__438)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__413__1__add__carry___24a2(Vvar__0___24Anonymous__434,Vvar__0___24Anonymous__438)) )
| ? [Vvar__0___24Anonymous__439] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__439)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__439)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__434,Vvar__0___24Anonymous__439)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__434)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__440)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__440)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__440)) )
| ? [Vvar__0___24Anonymous__441] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__441)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__441)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__441)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__13248,Vvar__0__A__13249] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13248) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13249)
=> Vvar__0__A__13248 = Vvar__0__A__13249 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__13207,Vvar__0___24Anonymous__13208] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13207) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13208)
=> Vvar__0___24Anonymous__13207 = Vvar__0___24Anonymous__13208 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__13244,Vvar__0__A__13245,Vvar__1___24Anonymous__13246,Vvar__1___24Anonymous__13247] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13244,Vvar__1___24Anonymous__13246) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13245,Vvar__1___24Anonymous__13247)
=> ( Vvar__1___24Anonymous__13246 = Vvar__1___24Anonymous__13247
& Vvar__0__A__13244 = Vvar__0__A__13245 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__13329,Vvar__0__A__13330,Vvar__1___24Anonymous__13331,Vvar__1___24Anonymous__13332,Vvar__2___24Anonymous__13333,Vvar__2___24Anonymous__13334] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13329,Vvar__1___24Anonymous__13331,Vvar__2___24Anonymous__13333) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13330,Vvar__1___24Anonymous__13332,Vvar__2___24Anonymous__13334)
=> ( Vvar__2___24Anonymous__13333 = Vvar__2___24Anonymous__13334
& Vvar__1___24Anonymous__13331 = Vvar__1___24Anonymous__13332
& Vvar__0__A__13329 = Vvar__0__A__13330 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__13271,Vvar__0__A__13272,Vvar__1__B__13273,Vvar__1__B__13274,Vvar__2___24Anonymous__13275,Vvar__2___24Anonymous__13276] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__13271,Vvar__1__B__13273,Vvar__2___24Anonymous__13275) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__13272,Vvar__1__B__13274,Vvar__2___24Anonymous__13276)
=> ( Vvar__2___24Anonymous__13275 = Vvar__2___24Anonymous__13276
& Vvar__1__B__13273 = Vvar__1__B__13274
& Vvar__0__A__13271 = Vvar__0__A__13272 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__13277,Vvar__0__A__13278,Vvar__1__B__13279,Vvar__1__B__13280,Vvar__2___24Anonymous__13281,Vvar__2___24Anonymous__13282] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__13277,Vvar__1__B__13279,Vvar__2___24Anonymous__13281) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__13278,Vvar__1__B__13280,Vvar__2___24Anonymous__13282)
=> ( Vvar__2___24Anonymous__13281 = Vvar__2___24Anonymous__13282
& Vvar__1__B__13279 = Vvar__1__B__13280
& Vvar__0__A__13277 = Vvar__0__A__13278 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__13327,Vvar__0__A__13328] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13327) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13328)
=> Vvar__0__A__13327 = Vvar__0__A__13328 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__378,Vvar__0__A__379,Vvar__1__B__380,Vvar__1__B__381,Vvar__2___24Anonymous__382,Vvar__2___24Anonymous__383,Vvar__3___24Anonymous__384,Vvar__3___24Anonymous__385] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__378,Vvar__1__B__380,Vvar__2___24Anonymous__382,Vvar__3___24Anonymous__384) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__379,Vvar__1__B__381,Vvar__2___24Anonymous__383,Vvar__3___24Anonymous__385)
=> ( Vvar__3___24Anonymous__384 = Vvar__3___24Anonymous__385
& Vvar__2___24Anonymous__382 = Vvar__2___24Anonymous__383
& Vvar__1__B__380 = Vvar__1__B__381
& Vvar__0__A__378 = Vvar__0__A__379 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__19938,Vvar__0___24Anonymous__19939] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19938) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19939)
=> Vvar__0___24Anonymous__19938 = Vvar__0___24Anonymous__19939 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__19940,Vvar__0___24Anonymous__19941] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__19940) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__19941)
=> Vvar__0___24Anonymous__19940 = Vvar__0___24Anonymous__19941 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__19942,Vvar__0___24Anonymous__19943] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__19942) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__19943)
=> Vvar__0___24Anonymous__19942 = Vvar__0___24Anonymous__19943 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__19944,Vvar__0___24Anonymous__19945] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__19944) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__19945)
=> Vvar__0___24Anonymous__19944 = Vvar__0___24Anonymous__19945 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__19946,Vvar__0___24Anonymous__19947] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__19946) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__19947)
=> Vvar__0___24Anonymous__19946 = Vvar__0___24Anonymous__19947 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__19948,Vvar__0___24Anonymous__19949] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__19948) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__19949)
=> Vvar__0___24Anonymous__19948 = Vvar__0___24Anonymous__19949 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__19950,Vvar__0___24Anonymous__19951] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__19950) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__19951)
=> Vvar__0___24Anonymous__19950 = Vvar__0___24Anonymous__19951 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__19952,Vvar__0___24Anonymous__19953] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__19952) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__19953)
=> Vvar__0___24Anonymous__19952 = Vvar__0___24Anonymous__19953 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__19954,Vvar__0___24Anonymous__19955] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__19954) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__19955)
=> Vvar__0___24Anonymous__19954 = Vvar__0___24Anonymous__19955 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__19956,Vvar__0___24Anonymous__19957] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__19956) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__19957)
=> Vvar__0___24Anonymous__19956 = Vvar__0___24Anonymous__19957 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__19980,Vvar__0__i__19981,Vvar__1__f__19982,Vvar__1__f__19983] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__19980,Vvar__1__f__19982) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__19981,Vvar__1__f__19983)
=> ( Vvar__1__f__19982 = Vvar__1__f__19983
& Vvar__0__i__19980 = Vvar__0__i__19981 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__19984,Vvar__0__i__19985,Vvar__1__f__19986,Vvar__1__f__19987,Vvar__2__e__19988,Vvar__2__e__19989] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__19984,Vvar__1__f__19986,Vvar__2__e__19988) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__19985,Vvar__1__f__19987,Vvar__2__e__19989)
=> ( Vvar__2__e__19988 = Vvar__2__e__19989
& Vvar__1__f__19986 = Vvar__1__f__19987
& Vvar__0__i__19984 = Vvar__0__i__19985 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__19965,Vvar__0__d__19966] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19965) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19966)
=> Vvar__0__d__19965 = Vvar__0__d__19966 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__19963,Vvar__0__d__19964] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19963) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19964)
=> Vvar__0__d__19963 = Vvar__0__d__19964 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__99,Vvar__0__A__100,Vvar__1__P__101,Vvar__1__P__102,Vvar__2__x__103,Vvar__2__x__104,Vvar__3___24Anonymous__105,Vvar__3___24Anonymous__106] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__99,Vvar__1__P__101,Vvar__2__x__103) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__100,Vvar__1__P__102,Vvar__2__x__104)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__103 = Vvar__2__x__104
& Vvar__1__P__101 = Vvar__1__P__102
& Vvar__0__A__99 = Vvar__0__A__100 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__31279,Vvar__0__A__31280,Vvar__1__B__31281,Vvar__1__B__31282,Vvar__2___24Anonymous__31283,Vvar__2___24Anonymous__31284] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31279,Vvar__1__B__31281,Vvar__2___24Anonymous__31283) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31280,Vvar__1__B__31282,Vvar__2___24Anonymous__31284)
=> ( Vvar__2___24Anonymous__31283 = Vvar__2___24Anonymous__31284
& Vvar__1__B__31281 = Vvar__1__B__31282
& Vvar__0__A__31279 = Vvar__0__A__31280 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__31285,Vvar__0__A__31286,Vvar__1__B__31287,Vvar__1__B__31288,Vvar__2___24Anonymous__31289,Vvar__2___24Anonymous__31290] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31285,Vvar__1__B__31287) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31286,Vvar__1__B__31288)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__31287 = Vvar__1__B__31288
& Vvar__0__A__31285 = Vvar__0__A__31286 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__125,Vvar__0__A__126,Vvar__1__B__127,Vvar__1__B__128,Vvar__2___24Anonymous__129,Vvar__2___24Anonymous__130] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__125,Vvar__1__B__127) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__126,Vvar__1__B__128)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__127 = Vvar__1__B__128
& Vvar__0__A__125 = Vvar__0__A__126 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__131,Vvar__0__A__132,Vvar__1__B__133,Vvar__1__B__134,Vvar__2___24Anonymous__135,Vvar__2___24Anonymous__136] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__131,Vvar__1__B__133) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__132,Vvar__1__B__134)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__133 = Vvar__1__B__134
& Vvar__0__A__131 = Vvar__0__A__132 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__13184,Vvar__0___24Anonymous__13185] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13184) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13185)
=> Vvar__0___24Anonymous__13184 = Vvar__0___24Anonymous__13185 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__23,Vvar__0___24Anonymous__24] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__24)
=> Vvar__0___24Anonymous__23 = Vvar__0___24Anonymous__24 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__21,Vvar__0___24Anonymous__22] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22)
=> Vvar__0___24Anonymous__21 = Vvar__0___24Anonymous__22 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__8,Vvar__0___24Anonymous__9] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9)
=> Vvar__0___24Anonymous__8 = Vvar__0___24Anonymous__9 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__10,Vvar__0___24Anonymous__11] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11)
=> Vvar__0___24Anonymous__10 = Vvar__0___24Anonymous__11 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__449,Vvar__0___24Anonymous__450] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__449) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__450)
=> Vvar__0___24Anonymous__449 = Vvar__0___24Anonymous__450 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__13854,Vvar__0__Qnum__13855,Vvar__1__Qden__13856,Vvar__1__Qden__13857] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__13854,Vvar__1__Qden__13856) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__13855,Vvar__1__Qden__13857)
=> ( Vvar__1__Qden__13856 = Vvar__1__Qden__13857
& Vvar__0__Qnum__13854 = Vvar__0__Qnum__13855 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__77733,Vvar__0__nonneg__77734,Vvar__1__cond__nonneg__77735,Vvar__1__cond__nonneg__77736] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__77733) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__77734)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__77733 = Vvar__0__nonneg__77734 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__64821,Vvar__0__pos__64822,Vvar__1__cond__pos__64823,Vvar__1__cond__pos__64824] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__64821) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__64822)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__64821 = Vvar__0__pos__64822 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__32123,Vvar__0__x__32124,Vvar__1__n__32125,Vvar__1__n__32126,Vvar__2___24Anonymous__32127,Vvar__2___24Anonymous__32128] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32123,Vvar__1__n__32125) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32124,Vvar__1__n__32126)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__32125 = Vvar__1__n__32126
& Vvar__0__x__32123 = Vvar__0__x__32124 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__32113,Vvar__0__x__32114,Vvar__1___24Anonymous__32115,Vvar__1___24Anonymous__32116] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32113) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32114)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__32113 = Vvar__0__x__32114 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__32117,Vvar__0__x__32118,Vvar__1__n__32119,Vvar__1__n__32120,Vvar__2___24Anonymous__32121,Vvar__2___24Anonymous__32122] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32117,Vvar__1__n__32119) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32118,Vvar__1__n__32120)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__32119 = Vvar__1__n__32120
& Vvar__0__x__32117 = Vvar__0__x__32118 ) ) ).
fof('$_inj_Coq.Reals.Rlimit.Build_Metric_Space',axiom,
! [Vvar__0__Base__65055,Vvar__0__Base__65056,Vvar__1__dist__65057,Vvar__1__dist__65058,Vvar__2__dist__pos__65059,Vvar__2__dist__pos__65060,Vvar__3__dist__sym__65061,Vvar__3__dist__sym__65062,Vvar__4__dist__refl__65063,Vvar__4__dist__refl__65064,Vvar__5__dist__tri__65065,Vvar__5__dist__tri__65066] :
( cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__65055,Vvar__1__dist__65057) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__65056,Vvar__1__dist__65058)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__dist__65057 = Vvar__1__dist__65058
& Vvar__0__Base__65055 = Vvar__0__Base__65056 ) ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__16818,Vvar__0__a__16819,Vvar__1__b__16820,Vvar__1__b__16821,Vvar__2__u__16822,Vvar__2__u__16823,Vvar__3__v__16824,Vvar__3__v__16825,Vvar__4__d__16826,Vvar__4__d__16827,Vvar__5___24Anonymous__16828,Vvar__5___24Anonymous__16829,Vvar__6___24Anonymous__16830,Vvar__6___24Anonymous__16831] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16818,Vvar__1__b__16820,Vvar__2__u__16822,Vvar__3__v__16824,Vvar__4__d__16826) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16819,Vvar__1__b__16821,Vvar__2__u__16823,Vvar__3__v__16825,Vvar__4__d__16827)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__16826 = Vvar__4__d__16827
& Vvar__3__v__16824 = Vvar__3__v__16825
& Vvar__2__u__16822 = Vvar__2__u__16823
& Vvar__1__b__16820 = Vvar__1__b__16821
& Vvar__0__a__16818 = Vvar__0__a__16819 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__18837,Vvar__0__x__18838,Vvar__1__p__18839,Vvar__1__p__18840,Vvar__2__q__18841,Vvar__2__q__18842,Vvar__3__r__18843,Vvar__3__r__18844,Vvar__4___24Anonymous__18845,Vvar__4___24Anonymous__18846,Vvar__5___24Anonymous__18847,Vvar__5___24Anonymous__18848,Vvar__6___24Anonymous__18849,Vvar__6___24Anonymous__18850] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__18837,Vvar__1__p__18839,Vvar__2__q__18841,Vvar__3__r__18843) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__18838,Vvar__1__p__18840,Vvar__2__q__18842,Vvar__3__r__18844)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__18843 = Vvar__3__r__18844
& Vvar__2__q__18841 = Vvar__2__q__18842
& Vvar__1__p__18839 = Vvar__1__p__18840
& Vvar__0__x__18837 = Vvar__0__x__18838 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__13512,Vvar__0__C__13513,Vvar__1___24Anonymous__13514,Vvar__1___24Anonymous__13515] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13512,Vvar__1___24Anonymous__13514) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13513,Vvar__1___24Anonymous__13515)
=> ( Vvar__1___24Anonymous__13514 = Vvar__1___24Anonymous__13515
& Vvar__0__C__13512 = Vvar__0__C__13513 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__13516,Vvar__0__C__13517,Vvar__1___24Anonymous__13518,Vvar__1___24Anonymous__13519,Vvar__2___24Anonymous__13520,Vvar__2___24Anonymous__13521] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__13516,Vvar__1___24Anonymous__13518,Vvar__2___24Anonymous__13520) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__13517,Vvar__1___24Anonymous__13519,Vvar__2___24Anonymous__13521)
=> ( Vvar__2___24Anonymous__13520 = Vvar__2___24Anonymous__13521
& Vvar__1___24Anonymous__13518 = Vvar__1___24Anonymous__13519
& Vvar__0__C__13516 = Vvar__0__C__13517 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__13508,Vvar__0__C__13509,Vvar__1___24Anonymous__13510,Vvar__1___24Anonymous__13511] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13508,Vvar__1___24Anonymous__13510) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13509,Vvar__1___24Anonymous__13511)
=> ( Vvar__1___24Anonymous__13510 = Vvar__1___24Anonymous__13511
& Vvar__0__C__13508 = Vvar__0__C__13509 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__13528,Vvar__0__C__13529,Vvar__1___24Anonymous__13530,Vvar__1___24Anonymous__13531,Vvar__2___24Anonymous__13532,Vvar__2___24Anonymous__13533] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__13528,Vvar__1___24Anonymous__13530,Vvar__2___24Anonymous__13532) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__13529,Vvar__1___24Anonymous__13531,Vvar__2___24Anonymous__13533)
=> ( Vvar__2___24Anonymous__13532 = Vvar__2___24Anonymous__13533
& Vvar__1___24Anonymous__13530 = Vvar__1___24Anonymous__13531
& Vvar__0__C__13528 = Vvar__0__C__13529 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__13534,Vvar__0__C__13535,Vvar__1___24Anonymous__13536,Vvar__1___24Anonymous__13537] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__13534,Vvar__1___24Anonymous__13536) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__13535,Vvar__1___24Anonymous__13537)
=> ( Vvar__1___24Anonymous__13536 = Vvar__1___24Anonymous__13537
& Vvar__0__C__13534 = Vvar__0__C__13535 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__13538,Vvar__0__C__13539,Vvar__1___24Anonymous__13540,Vvar__1___24Anonymous__13541,Vvar__2___24Anonymous__13542,Vvar__2___24Anonymous__13543] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__13538,Vvar__1___24Anonymous__13540,Vvar__2___24Anonymous__13542) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__13539,Vvar__1___24Anonymous__13541,Vvar__2___24Anonymous__13543)
=> ( Vvar__2___24Anonymous__13542 = Vvar__2___24Anonymous__13543
& Vvar__1___24Anonymous__13540 = Vvar__1___24Anonymous__13541
& Vvar__0__C__13538 = Vvar__0__C__13539 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__13522,Vvar__0__C__13523,Vvar__1___24Anonymous__13524,Vvar__1___24Anonymous__13525,Vvar__2___24Anonymous__13526,Vvar__2___24Anonymous__13527] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__13522,Vvar__1___24Anonymous__13524,Vvar__2___24Anonymous__13526) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__13523,Vvar__1___24Anonymous__13525,Vvar__2___24Anonymous__13527)
=> ( Vvar__2___24Anonymous__13526 = Vvar__2___24Anonymous__13527
& Vvar__1___24Anonymous__13524 = Vvar__1___24Anonymous__13525
& Vvar__0__C__13522 = Vvar__0__C__13523 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__13583,Vvar__0__C__13584,Vvar__1___24Anonymous__13585,Vvar__1___24Anonymous__13586,Vvar__2___24Anonymous__13587,Vvar__2___24Anonymous__13588,Vvar__3___24Anonymous__13589,Vvar__3___24Anonymous__13590] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__13583,Vvar__1___24Anonymous__13585,Vvar__2___24Anonymous__13587,Vvar__3___24Anonymous__13589) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__13584,Vvar__1___24Anonymous__13586,Vvar__2___24Anonymous__13588,Vvar__3___24Anonymous__13590)
=> ( Vvar__3___24Anonymous__13589 = Vvar__3___24Anonymous__13590
& Vvar__2___24Anonymous__13587 = Vvar__2___24Anonymous__13588
& Vvar__1___24Anonymous__13585 = Vvar__1___24Anonymous__13586
& Vvar__0__C__13583 = Vvar__0__C__13584 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__13573,Vvar__0__C__13574,Vvar__1___24Anonymous__13575,Vvar__1___24Anonymous__13576] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13573,Vvar__1___24Anonymous__13575) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13574,Vvar__1___24Anonymous__13576)
=> ( Vvar__1___24Anonymous__13575 = Vvar__1___24Anonymous__13576
& Vvar__0__C__13573 = Vvar__0__C__13574 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__13577,Vvar__0__C__13578,Vvar__1___24Anonymous__13579,Vvar__1___24Anonymous__13580,Vvar__2___24Anonymous__13581,Vvar__2___24Anonymous__13582] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13577,Vvar__1___24Anonymous__13579,Vvar__2___24Anonymous__13581) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13578,Vvar__1___24Anonymous__13580,Vvar__2___24Anonymous__13582)
=> ( Vvar__2___24Anonymous__13581 = Vvar__2___24Anonymous__13582
& Vvar__1___24Anonymous__13579 = Vvar__1___24Anonymous__13580
& Vvar__0__C__13577 = Vvar__0__C__13578 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__64986,Vvar__0__r__64987] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__64986) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__64987)
=> Vvar__0__r__64986 = Vvar__0__r__64987 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__64974,Vvar__0__r1__64975,Vvar__1__r2__64976,Vvar__1__r2__64977] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__64974,Vvar__1__r2__64976) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__64975,Vvar__1__r2__64977)
=> ( Vvar__1__r2__64976 = Vvar__1__r2__64977
& Vvar__0__r1__64974 = Vvar__0__r1__64975 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__64978,Vvar__0__r1__64979,Vvar__1__r2__64980,Vvar__1__r2__64981] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__64978,Vvar__1__r2__64980) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__64979,Vvar__1__r2__64981)
=> ( Vvar__1__r2__64980 = Vvar__1__r2__64981
& Vvar__0__r1__64978 = Vvar__0__r1__64979 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__64988,Vvar__0__r__64989] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__64988) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__64989)
=> Vvar__0__r__64988 = Vvar__0__r__64989 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__64970,Vvar__0__r1__64971,Vvar__1__r2__64972,Vvar__1__r2__64973] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__64970,Vvar__1__r2__64972) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__64971,Vvar__1__r2__64973)
=> ( Vvar__1__r2__64972 = Vvar__1__r2__64973
& Vvar__0__r1__64970 = Vvar__0__r1__64971 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__64982,Vvar__0__r1__64983,Vvar__1__z__64984,Vvar__1__z__64985] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__64982,Vvar__1__z__64984) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__64983,Vvar__1__z__64985)
=> ( Vvar__1__z__64984 = Vvar__1__z__64985
& Vvar__0__r1__64982 = Vvar__0__r1__64983 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__64966,Vvar__0__r__64967] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__64966) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__64967)
=> Vvar__0__r__64966 = Vvar__0__r__64967 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__64968,Vvar__0__r__64969] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__64968) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__64969)
=> Vvar__0__r__64968 = Vvar__0__r__64969 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__27502,Vvar__0__T__27503,Vvar__1__Flhs__27504,Vvar__1__Flhs__27505,Vvar__2__Fop__27506,Vvar__2__Fop__27507,Vvar__3__Frhs__27508,Vvar__3__Frhs__27509] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27502,Vvar__1__Flhs__27504,Vvar__2__Fop__27506,Vvar__3__Frhs__27508) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27503,Vvar__1__Flhs__27505,Vvar__2__Fop__27507,Vvar__3__Frhs__27509)
=> ( Vvar__3__Frhs__27508 = Vvar__3__Frhs__27509
& Vvar__2__Fop__27506 = Vvar__2__Fop__27507
& Vvar__1__Flhs__27504 = Vvar__1__Flhs__27505
& Vvar__0__T__27502 = Vvar__0__T__27503 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__27484,Vvar__0__C__27485,Vvar__1___24Anonymous__27486,Vvar__1___24Anonymous__27487,Vvar__2___24Anonymous__27488,Vvar__2___24Anonymous__27489] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27484,Vvar__1___24Anonymous__27486,Vvar__2___24Anonymous__27488) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27485,Vvar__1___24Anonymous__27487,Vvar__2___24Anonymous__27489)
=> ( Vvar__2___24Anonymous__27488 = Vvar__2___24Anonymous__27489
& Vvar__1___24Anonymous__27486 = Vvar__1___24Anonymous__27487
& Vvar__0__C__27484 = Vvar__0__C__27485 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__27490,Vvar__0__C__27491,Vvar__1___24Anonymous__27492,Vvar__1___24Anonymous__27493] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27490,Vvar__1___24Anonymous__27492) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27491,Vvar__1___24Anonymous__27493)
=> ( Vvar__1___24Anonymous__27492 = Vvar__1___24Anonymous__27493
& Vvar__0__C__27490 = Vvar__0__C__27491 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__27464,Vvar__0__C__27465,Vvar__1___24Anonymous__27466,Vvar__1___24Anonymous__27467] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27464,Vvar__1___24Anonymous__27466) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27465,Vvar__1___24Anonymous__27467)
=> ( Vvar__1___24Anonymous__27466 = Vvar__1___24Anonymous__27467
& Vvar__0__C__27464 = Vvar__0__C__27465 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__27472,Vvar__0__C__27473,Vvar__1___24Anonymous__27474,Vvar__1___24Anonymous__27475,Vvar__2___24Anonymous__27476,Vvar__2___24Anonymous__27477] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27472,Vvar__1___24Anonymous__27474,Vvar__2___24Anonymous__27476) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27473,Vvar__1___24Anonymous__27475,Vvar__2___24Anonymous__27477)
=> ( Vvar__2___24Anonymous__27476 = Vvar__2___24Anonymous__27477
& Vvar__1___24Anonymous__27474 = Vvar__1___24Anonymous__27475
& Vvar__0__C__27472 = Vvar__0__C__27473 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__27478,Vvar__0__C__27479,Vvar__1___24Anonymous__27480,Vvar__1___24Anonymous__27481,Vvar__2___24Anonymous__27482,Vvar__2___24Anonymous__27483] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27478,Vvar__1___24Anonymous__27480,Vvar__2___24Anonymous__27482) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27479,Vvar__1___24Anonymous__27481,Vvar__2___24Anonymous__27483)
=> ( Vvar__2___24Anonymous__27482 = Vvar__2___24Anonymous__27483
& Vvar__1___24Anonymous__27480 = Vvar__1___24Anonymous__27481
& Vvar__0__C__27478 = Vvar__0__C__27479 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__27468,Vvar__0__C__27469,Vvar__1___24Anonymous__27470,Vvar__1___24Anonymous__27471] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27468,Vvar__1___24Anonymous__27470) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27469,Vvar__1___24Anonymous__27471)
=> ( Vvar__1___24Anonymous__27470 = Vvar__1___24Anonymous__27471
& Vvar__0__C__27468 = Vvar__0__C__27469 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__27494,Vvar__0__C__27495] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27494) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27495)
=> Vvar__0__C__27494 = Vvar__0__C__27495 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__65490,Vvar__0__TA__65491,Vvar__1__TX__65492,Vvar__1__TX__65493,Vvar__2__AA__65494,Vvar__2__AA__65495,Vvar__3__AF__65496,Vvar__3__AF__65497,Vvar__4___24Anonymous__65498,Vvar__4___24Anonymous__65499,Vvar__5___24Anonymous__65500,Vvar__5___24Anonymous__65501] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__65490,Vvar__1__TX__65492,Vvar__2__AA__65494,Vvar__3__AF__65496,Vvar__4___24Anonymous__65498,Vvar__5___24Anonymous__65500) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__65491,Vvar__1__TX__65493,Vvar__2__AA__65495,Vvar__3__AF__65497,Vvar__4___24Anonymous__65499,Vvar__5___24Anonymous__65501)
=> ( Vvar__5___24Anonymous__65500 = Vvar__5___24Anonymous__65501
& Vvar__4___24Anonymous__65498 = Vvar__4___24Anonymous__65499
& Vvar__3__AF__65496 = Vvar__3__AF__65497
& Vvar__2__AA__65494 = Vvar__2__AA__65495
& Vvar__1__TX__65492 = Vvar__1__TX__65493
& Vvar__0__TA__65490 = Vvar__0__TA__65491 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__65502,Vvar__0__TA__65503,Vvar__1__TX__65504,Vvar__1__TX__65505,Vvar__2__AA__65506,Vvar__2__AA__65507,Vvar__3__AF__65508,Vvar__3__AF__65509,Vvar__4___24Anonymous__65510,Vvar__4___24Anonymous__65511,Vvar__5___24Anonymous__65512,Vvar__5___24Anonymous__65513] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__65502,Vvar__1__TX__65504,Vvar__2__AA__65506,Vvar__3__AF__65508,Vvar__4___24Anonymous__65510,Vvar__5___24Anonymous__65512) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__65503,Vvar__1__TX__65505,Vvar__2__AA__65507,Vvar__3__AF__65509,Vvar__4___24Anonymous__65511,Vvar__5___24Anonymous__65513)
=> ( Vvar__5___24Anonymous__65512 = Vvar__5___24Anonymous__65513
& Vvar__4___24Anonymous__65510 = Vvar__4___24Anonymous__65511
& Vvar__3__AF__65508 = Vvar__3__AF__65509
& Vvar__2__AA__65506 = Vvar__2__AA__65507
& Vvar__1__TX__65504 = Vvar__1__TX__65505
& Vvar__0__TA__65502 = Vvar__0__TA__65503 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__65514,Vvar__0__TA__65515,Vvar__1__TX__65516,Vvar__1__TX__65517,Vvar__2__AA__65518,Vvar__2__AA__65519,Vvar__3__AF__65520,Vvar__3__AF__65521,Vvar__4___24Anonymous__65522,Vvar__4___24Anonymous__65523,Vvar__5___24Anonymous__65524,Vvar__5___24Anonymous__65525] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__65514,Vvar__1__TX__65516,Vvar__2__AA__65518,Vvar__3__AF__65520,Vvar__4___24Anonymous__65522,Vvar__5___24Anonymous__65524) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__65515,Vvar__1__TX__65517,Vvar__2__AA__65519,Vvar__3__AF__65521,Vvar__4___24Anonymous__65523,Vvar__5___24Anonymous__65525)
=> ( Vvar__5___24Anonymous__65524 = Vvar__5___24Anonymous__65525
& Vvar__4___24Anonymous__65522 = Vvar__4___24Anonymous__65523
& Vvar__3__AF__65520 = Vvar__3__AF__65521
& Vvar__2__AA__65518 = Vvar__2__AA__65519
& Vvar__1__TX__65516 = Vvar__1__TX__65517
& Vvar__0__TA__65514 = Vvar__0__TA__65515 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__65472,Vvar__0__TA__65473,Vvar__1__TX__65474,Vvar__1__TX__65475,Vvar__2__AA__65476,Vvar__2__AA__65477,Vvar__3__AF__65478,Vvar__3__AF__65479] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65472,Vvar__1__TX__65474,Vvar__2__AA__65476,Vvar__3__AF__65478) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65473,Vvar__1__TX__65475,Vvar__2__AA__65477,Vvar__3__AF__65479)
=> ( Vvar__3__AF__65478 = Vvar__3__AF__65479
& Vvar__2__AA__65476 = Vvar__2__AA__65477
& Vvar__1__TX__65474 = Vvar__1__TX__65475
& Vvar__0__TA__65472 = Vvar__0__TA__65473 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__65536,Vvar__0__TA__65537,Vvar__1__TX__65538,Vvar__1__TX__65539,Vvar__2__AA__65540,Vvar__2__AA__65541,Vvar__3__AF__65542,Vvar__3__AF__65543,Vvar__4___24Anonymous__65544,Vvar__4___24Anonymous__65545,Vvar__5___24Anonymous__65546,Vvar__5___24Anonymous__65547,Vvar__6___24Anonymous__65548,Vvar__6___24Anonymous__65549] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__65536,Vvar__1__TX__65538,Vvar__2__AA__65540,Vvar__3__AF__65542,Vvar__4___24Anonymous__65544,Vvar__5___24Anonymous__65546,Vvar__6___24Anonymous__65548) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__65537,Vvar__1__TX__65539,Vvar__2__AA__65541,Vvar__3__AF__65543,Vvar__4___24Anonymous__65545,Vvar__5___24Anonymous__65547,Vvar__6___24Anonymous__65549)
=> ( Vvar__6___24Anonymous__65548 = Vvar__6___24Anonymous__65549
& Vvar__5___24Anonymous__65546 = Vvar__5___24Anonymous__65547
& Vvar__4___24Anonymous__65544 = Vvar__4___24Anonymous__65545
& Vvar__3__AF__65542 = Vvar__3__AF__65543
& Vvar__2__AA__65540 = Vvar__2__AA__65541
& Vvar__1__TX__65538 = Vvar__1__TX__65539
& Vvar__0__TA__65536 = Vvar__0__TA__65537 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__65526,Vvar__0__TA__65527,Vvar__1__TX__65528,Vvar__1__TX__65529,Vvar__2__AA__65530,Vvar__2__AA__65531,Vvar__3__AF__65532,Vvar__3__AF__65533,Vvar__4___24Anonymous__65534,Vvar__4___24Anonymous__65535] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__65526,Vvar__1__TX__65528,Vvar__2__AA__65530,Vvar__3__AF__65532,Vvar__4___24Anonymous__65534) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__65527,Vvar__1__TX__65529,Vvar__2__AA__65531,Vvar__3__AF__65533,Vvar__4___24Anonymous__65535)
=> ( Vvar__4___24Anonymous__65534 = Vvar__4___24Anonymous__65535
& Vvar__3__AF__65532 = Vvar__3__AF__65533
& Vvar__2__AA__65530 = Vvar__2__AA__65531
& Vvar__1__TX__65528 = Vvar__1__TX__65529
& Vvar__0__TA__65526 = Vvar__0__TA__65527 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__65464,Vvar__0__TA__65465,Vvar__1__TX__65466,Vvar__1__TX__65467,Vvar__2__AA__65468,Vvar__2__AA__65469,Vvar__3__AF__65470,Vvar__3__AF__65471] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65464,Vvar__1__TX__65466,Vvar__2__AA__65468,Vvar__3__AF__65470) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65465,Vvar__1__TX__65467,Vvar__2__AA__65469,Vvar__3__AF__65471)
=> ( Vvar__3__AF__65470 = Vvar__3__AF__65471
& Vvar__2__AA__65468 = Vvar__2__AA__65469
& Vvar__1__TX__65466 = Vvar__1__TX__65467
& Vvar__0__TA__65464 = Vvar__0__TA__65465 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__65480,Vvar__0__TA__65481,Vvar__1__TX__65482,Vvar__1__TX__65483,Vvar__2__AA__65484,Vvar__2__AA__65485,Vvar__3__AF__65486,Vvar__3__AF__65487,Vvar__4___24Anonymous__65488,Vvar__4___24Anonymous__65489] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__65480,Vvar__1__TX__65482,Vvar__2__AA__65484,Vvar__3__AF__65486,Vvar__4___24Anonymous__65488) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__65481,Vvar__1__TX__65483,Vvar__2__AA__65485,Vvar__3__AF__65487,Vvar__4___24Anonymous__65489)
=> ( Vvar__4___24Anonymous__65488 = Vvar__4___24Anonymous__65489
& Vvar__3__AF__65486 = Vvar__3__AF__65487
& Vvar__2__AA__65484 = Vvar__2__AA__65485
& Vvar__1__TX__65482 = Vvar__1__TX__65483
& Vvar__0__TA__65480 = Vvar__0__TA__65481 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__65596,Vvar__0__A__65597,Vvar__1___24Anonymous__65598,Vvar__1___24Anonymous__65599,Vvar__2___24Anonymous__65600,Vvar__2___24Anonymous__65601,Vvar__3___24Anonymous__65602,Vvar__3___24Anonymous__65603] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__65596,Vvar__1___24Anonymous__65598,Vvar__2___24Anonymous__65600,Vvar__3___24Anonymous__65602) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__65597,Vvar__1___24Anonymous__65599,Vvar__2___24Anonymous__65601,Vvar__3___24Anonymous__65603)
=> ( Vvar__3___24Anonymous__65602 = Vvar__3___24Anonymous__65603
& Vvar__2___24Anonymous__65600 = Vvar__2___24Anonymous__65601
& Vvar__1___24Anonymous__65598 = Vvar__1___24Anonymous__65599
& Vvar__0__A__65596 = Vvar__0__A__65597 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__65592,Vvar__0__A__65593,Vvar__1___24Anonymous__65594,Vvar__1___24Anonymous__65595] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65592,Vvar__1___24Anonymous__65594) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65593,Vvar__1___24Anonymous__65595)
=> ( Vvar__1___24Anonymous__65594 = Vvar__1___24Anonymous__65595
& Vvar__0__A__65592 = Vvar__0__A__65593 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__65590,Vvar__0__A__65591] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65590) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65591)
=> Vvar__0__A__65590 = Vvar__0__A__65591 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__58064,Vvar__0___24Anonymous__58065,Vvar__1___24Anonymous__58066,Vvar__1___24Anonymous__58067] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__58064,Vvar__1___24Anonymous__58066) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__58065,Vvar__1___24Anonymous__58067)
=> ( Vvar__1___24Anonymous__58066 = Vvar__1___24Anonymous__58067
& Vvar__0___24Anonymous__58064 = Vvar__0___24Anonymous__58065 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__58068,Vvar__0___24Anonymous__58069,Vvar__1___24Anonymous__58070,Vvar__1___24Anonymous__58071,Vvar__2___24Anonymous__58072,Vvar__2___24Anonymous__58073] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__58068,Vvar__1___24Anonymous__58070,Vvar__2___24Anonymous__58072) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__58069,Vvar__1___24Anonymous__58071,Vvar__2___24Anonymous__58073)
=> ( Vvar__2___24Anonymous__58072 = Vvar__2___24Anonymous__58073
& Vvar__1___24Anonymous__58070 = Vvar__1___24Anonymous__58071
& Vvar__0___24Anonymous__58068 = Vvar__0___24Anonymous__58069 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__58060,Vvar__0___24Anonymous__58061,Vvar__1___24Anonymous__58062,Vvar__1___24Anonymous__58063] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__58060,Vvar__1___24Anonymous__58062) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__58061,Vvar__1___24Anonymous__58063)
=> ( Vvar__1___24Anonymous__58062 = Vvar__1___24Anonymous__58063
& Vvar__0___24Anonymous__58060 = Vvar__0___24Anonymous__58061 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__20271,Vvar__0__C__20272] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20271) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20272)
=> Vvar__0__C__20271 = Vvar__0__C__20272 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__20269,Vvar__0__C__20270] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20269) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20270)
=> Vvar__0__C__20269 = Vvar__0__C__20270 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__20277,Vvar__0__C__20278,Vvar__1___24Anonymous__20279,Vvar__1___24Anonymous__20280] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__20277,Vvar__1___24Anonymous__20279) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__20278,Vvar__1___24Anonymous__20280)
=> ( Vvar__1___24Anonymous__20279 = Vvar__1___24Anonymous__20280
& Vvar__0__C__20277 = Vvar__0__C__20278 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__20281,Vvar__0__C__20282,Vvar__1___24Anonymous__20283,Vvar__1___24Anonymous__20284,Vvar__2___24Anonymous__20285,Vvar__2___24Anonymous__20286] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__20281,Vvar__1___24Anonymous__20283,Vvar__2___24Anonymous__20285) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__20282,Vvar__1___24Anonymous__20284,Vvar__2___24Anonymous__20286)
=> ( Vvar__2___24Anonymous__20285 = Vvar__2___24Anonymous__20286
& Vvar__1___24Anonymous__20283 = Vvar__1___24Anonymous__20284
& Vvar__0__C__20281 = Vvar__0__C__20282 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__20273,Vvar__0__C__20274,Vvar__1___24Anonymous__20275,Vvar__1___24Anonymous__20276] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__20273,Vvar__1___24Anonymous__20275) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__20274,Vvar__1___24Anonymous__20276)
=> ( Vvar__1___24Anonymous__20275 = Vvar__1___24Anonymous__20276
& Vvar__0__C__20273 = Vvar__0__C__20274 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__20307,Vvar__0__C__20308,Vvar__1___24Anonymous__20309,Vvar__1___24Anonymous__20310,Vvar__2___24Anonymous__20311,Vvar__2___24Anonymous__20312] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__20307,Vvar__1___24Anonymous__20309,Vvar__2___24Anonymous__20311) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__20308,Vvar__1___24Anonymous__20310,Vvar__2___24Anonymous__20312)
=> ( Vvar__2___24Anonymous__20311 = Vvar__2___24Anonymous__20312
& Vvar__1___24Anonymous__20309 = Vvar__1___24Anonymous__20310
& Vvar__0__C__20307 = Vvar__0__C__20308 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__20303,Vvar__0__C__20304,Vvar__1___24Anonymous__20305,Vvar__1___24Anonymous__20306] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__20303,Vvar__1___24Anonymous__20305) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__20304,Vvar__1___24Anonymous__20306)
=> ( Vvar__1___24Anonymous__20305 = Vvar__1___24Anonymous__20306
& Vvar__0__C__20303 = Vvar__0__C__20304 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__20293,Vvar__0__C__20294,Vvar__1___24Anonymous__20295,Vvar__1___24Anonymous__20296,Vvar__2___24Anonymous__20297,Vvar__2___24Anonymous__20298] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__20293,Vvar__1___24Anonymous__20295,Vvar__2___24Anonymous__20297) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__20294,Vvar__1___24Anonymous__20296,Vvar__2___24Anonymous__20298)
=> ( Vvar__2___24Anonymous__20297 = Vvar__2___24Anonymous__20298
& Vvar__1___24Anonymous__20295 = Vvar__1___24Anonymous__20296
& Vvar__0__C__20293 = Vvar__0__C__20294 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__20299,Vvar__0__C__20300,Vvar__1___24Anonymous__20301,Vvar__1___24Anonymous__20302] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__20299,Vvar__1___24Anonymous__20301) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__20300,Vvar__1___24Anonymous__20302)
=> ( Vvar__1___24Anonymous__20301 = Vvar__1___24Anonymous__20302
& Vvar__0__C__20299 = Vvar__0__C__20300 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__20313,Vvar__0__C__20314,Vvar__1___24Anonymous__20315,Vvar__1___24Anonymous__20316,Vvar__2___24Anonymous__20317,Vvar__2___24Anonymous__20318] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__20313,Vvar__1___24Anonymous__20315,Vvar__2___24Anonymous__20317) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__20314,Vvar__1___24Anonymous__20316,Vvar__2___24Anonymous__20318)
=> ( Vvar__2___24Anonymous__20317 = Vvar__2___24Anonymous__20318
& Vvar__1___24Anonymous__20315 = Vvar__1___24Anonymous__20316
& Vvar__0__C__20313 = Vvar__0__C__20314 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__20287,Vvar__0__C__20288,Vvar__1___24Anonymous__20289,Vvar__1___24Anonymous__20290,Vvar__2___24Anonymous__20291,Vvar__2___24Anonymous__20292] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__20287,Vvar__1___24Anonymous__20289,Vvar__2___24Anonymous__20291) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__20288,Vvar__1___24Anonymous__20290,Vvar__2___24Anonymous__20292)
=> ( Vvar__2___24Anonymous__20291 = Vvar__2___24Anonymous__20292
& Vvar__1___24Anonymous__20289 = Vvar__1___24Anonymous__20290
& Vvar__0__C__20287 = Vvar__0__C__20288 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__20610,Vvar__0__C__20611,Vvar__1__num__20612,Vvar__1__num__20613,Vvar__2__denum__20614,Vvar__2__denum__20615,Vvar__3__condition__20616,Vvar__3__condition__20617] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20610,Vvar__1__num__20612,Vvar__2__denum__20614,Vvar__3__condition__20616) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20611,Vvar__1__num__20613,Vvar__2__denum__20615,Vvar__3__condition__20617)
=> ( Vvar__3__condition__20616 = Vvar__3__condition__20617
& Vvar__2__denum__20614 = Vvar__2__denum__20615
& Vvar__1__num__20612 = Vvar__1__num__20613
& Vvar__0__C__20610 = Vvar__0__C__20611 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__35333,Vvar__0__C__35334,Vvar__1__rsplit__left__35335,Vvar__1__rsplit__left__35336,Vvar__2__rsplit__common__35337,Vvar__2__rsplit__common__35338,Vvar__3__rsplit__right__35339,Vvar__3__rsplit__right__35340] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__35333,Vvar__1__rsplit__left__35335,Vvar__2__rsplit__common__35337,Vvar__3__rsplit__right__35339) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__35334,Vvar__1__rsplit__left__35336,Vvar__2__rsplit__common__35338,Vvar__3__rsplit__right__35340)
=> ( Vvar__3__rsplit__right__35339 = Vvar__3__rsplit__right__35340
& Vvar__2__rsplit__common__35337 = Vvar__2__rsplit__common__35338
& Vvar__1__rsplit__left__35335 = Vvar__1__rsplit__left__35336
& Vvar__0__C__35333 = Vvar__0__C__35334 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__14464,Vvar__0__C__14465] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14464) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14465)
=> Vvar__0__C__14464 = Vvar__0__C__14465 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__14462,Vvar__0__C__14463] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14462) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14463)
=> Vvar__0__C__14462 = Vvar__0__C__14463 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__14470,Vvar__0__C__14471,Vvar__1___24Anonymous__14472,Vvar__1___24Anonymous__14473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14470,Vvar__1___24Anonymous__14472) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14471,Vvar__1___24Anonymous__14473)
=> ( Vvar__1___24Anonymous__14472 = Vvar__1___24Anonymous__14473
& Vvar__0__C__14470 = Vvar__0__C__14471 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__14474,Vvar__0__C__14475,Vvar__1___24Anonymous__14476,Vvar__1___24Anonymous__14477,Vvar__2___24Anonymous__14478,Vvar__2___24Anonymous__14479] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14474,Vvar__1___24Anonymous__14476,Vvar__2___24Anonymous__14478) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14475,Vvar__1___24Anonymous__14477,Vvar__2___24Anonymous__14479)
=> ( Vvar__2___24Anonymous__14478 = Vvar__2___24Anonymous__14479
& Vvar__1___24Anonymous__14476 = Vvar__1___24Anonymous__14477
& Vvar__0__C__14474 = Vvar__0__C__14475 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__14466,Vvar__0__C__14467,Vvar__1___24Anonymous__14468,Vvar__1___24Anonymous__14469] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14466,Vvar__1___24Anonymous__14468) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14467,Vvar__1___24Anonymous__14469)
=> ( Vvar__1___24Anonymous__14468 = Vvar__1___24Anonymous__14469
& Vvar__0__C__14466 = Vvar__0__C__14467 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__14486,Vvar__0__C__14487,Vvar__1___24Anonymous__14488,Vvar__1___24Anonymous__14489,Vvar__2___24Anonymous__14490,Vvar__2___24Anonymous__14491] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14486,Vvar__1___24Anonymous__14488,Vvar__2___24Anonymous__14490) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14487,Vvar__1___24Anonymous__14489,Vvar__2___24Anonymous__14491)
=> ( Vvar__2___24Anonymous__14490 = Vvar__2___24Anonymous__14491
& Vvar__1___24Anonymous__14488 = Vvar__1___24Anonymous__14489
& Vvar__0__C__14486 = Vvar__0__C__14487 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__14492,Vvar__0__C__14493,Vvar__1___24Anonymous__14494,Vvar__1___24Anonymous__14495] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14492,Vvar__1___24Anonymous__14494) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14493,Vvar__1___24Anonymous__14495)
=> ( Vvar__1___24Anonymous__14494 = Vvar__1___24Anonymous__14495
& Vvar__0__C__14492 = Vvar__0__C__14493 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__14496,Vvar__0__C__14497,Vvar__1___24Anonymous__14498,Vvar__1___24Anonymous__14499,Vvar__2___24Anonymous__14500,Vvar__2___24Anonymous__14501] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14496,Vvar__1___24Anonymous__14498,Vvar__2___24Anonymous__14500) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14497,Vvar__1___24Anonymous__14499,Vvar__2___24Anonymous__14501)
=> ( Vvar__2___24Anonymous__14500 = Vvar__2___24Anonymous__14501
& Vvar__1___24Anonymous__14498 = Vvar__1___24Anonymous__14499
& Vvar__0__C__14496 = Vvar__0__C__14497 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__14480,Vvar__0__C__14481,Vvar__1___24Anonymous__14482,Vvar__1___24Anonymous__14483,Vvar__2___24Anonymous__14484,Vvar__2___24Anonymous__14485] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14480,Vvar__1___24Anonymous__14482,Vvar__2___24Anonymous__14484) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14481,Vvar__1___24Anonymous__14483,Vvar__2___24Anonymous__14485)
=> ( Vvar__2___24Anonymous__14484 = Vvar__2___24Anonymous__14485
& Vvar__1___24Anonymous__14482 = Vvar__1___24Anonymous__14483
& Vvar__0__C__14480 = Vvar__0__C__14481 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__14117,Vvar__0__C__14118,Vvar__1___24Anonymous__14119,Vvar__1___24Anonymous__14120,Vvar__2___24Anonymous__14121,Vvar__2___24Anonymous__14122,Vvar__3___24Anonymous__14123,Vvar__3___24Anonymous__14124] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__14117,Vvar__1___24Anonymous__14119,Vvar__2___24Anonymous__14121,Vvar__3___24Anonymous__14123) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__14118,Vvar__1___24Anonymous__14120,Vvar__2___24Anonymous__14122,Vvar__3___24Anonymous__14124)
=> ( Vvar__3___24Anonymous__14123 = Vvar__3___24Anonymous__14124
& Vvar__2___24Anonymous__14121 = Vvar__2___24Anonymous__14122
& Vvar__1___24Anonymous__14119 = Vvar__1___24Anonymous__14120
& Vvar__0__C__14117 = Vvar__0__C__14118 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__14107,Vvar__0__C__14108,Vvar__1___24Anonymous__14109,Vvar__1___24Anonymous__14110] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14107,Vvar__1___24Anonymous__14109) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14108,Vvar__1___24Anonymous__14110)
=> ( Vvar__1___24Anonymous__14109 = Vvar__1___24Anonymous__14110
& Vvar__0__C__14107 = Vvar__0__C__14108 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__14111,Vvar__0__C__14112,Vvar__1___24Anonymous__14113,Vvar__1___24Anonymous__14114,Vvar__2___24Anonymous__14115,Vvar__2___24Anonymous__14116] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14111,Vvar__1___24Anonymous__14113,Vvar__2___24Anonymous__14115) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14112,Vvar__1___24Anonymous__14114,Vvar__2___24Anonymous__14116)
=> ( Vvar__2___24Anonymous__14115 = Vvar__2___24Anonymous__14116
& Vvar__1___24Anonymous__14113 = Vvar__1___24Anonymous__14114
& Vvar__0__C__14111 = Vvar__0__C__14112 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__14276,Vvar__0___24Anonymous__14277,Vvar__1___24Anonymous__14278,Vvar__1___24Anonymous__14279] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__14276,Vvar__1___24Anonymous__14278) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__14277,Vvar__1___24Anonymous__14279)
=> ( Vvar__1___24Anonymous__14278 = Vvar__1___24Anonymous__14279
& Vvar__0___24Anonymous__14276 = Vvar__0___24Anonymous__14277 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__14272,Vvar__0___24Anonymous__14273,Vvar__1___24Anonymous__14274,Vvar__1___24Anonymous__14275] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14272,Vvar__1___24Anonymous__14274) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14273,Vvar__1___24Anonymous__14275)
=> ( Vvar__1___24Anonymous__14274 = Vvar__1___24Anonymous__14275
& Vvar__0___24Anonymous__14272 = Vvar__0___24Anonymous__14273 ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__13194,Vvar__1__Q__13195,Vvar__2___24Anonymous__13196] :
( cProp___24t(Vvar__0__P__13194)
=> ( cProp___24t(Vvar__1__Q__13195)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__13196)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__13194,Vvar__1__Q__13195,Vvar__2___24Anonymous__13196)
=> ( ( p(Vvar__0__P__13194)
& Vvar__2___24Anonymous__13196 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__13195)
& Vvar__2___24Anonymous__13196 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__13344,Vvar__1__Plt__13345,Vvar__2__Pgt__13346,Vvar__3___24Anonymous__13347] :
( cProp___24t(Vvar__0__Peq__13344)
=> ( cProp___24t(Vvar__1__Plt__13345)
=> ( cProp___24t(Vvar__2__Pgt__13346)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__13347)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__13344,Vvar__1__Plt__13345,Vvar__2__Pgt__13346,Vvar__3___24Anonymous__13347)
=> ( ( p(Vvar__0__Peq__13344)
& Vvar__3___24Anonymous__13347 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__13345)
& Vvar__3___24Anonymous__13347 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__13346)
& Vvar__3___24Anonymous__13347 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX367] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX367)
=> ( VX367 = cCoq_2eInit_2eDatatypes_2etrue
| VX367 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX394] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX394)
=> ( VX394 = cCoq_2eInit_2eDatatypes_2eEq
| VX394 = cCoq_2eInit_2eDatatypes_2eLt
| VX394 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__13317,VX13318] :
( cType___24t(Vvar__0__A__13317)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13317,VX13318)
=> ( VX13318 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13317)
| ? [Vvar__1___24Anonymous__13321] :
( t(Vvar__1___24Anonymous__13321,Vvar__0__A__13317)
& ? [Vvar__2___24Anonymous__13322] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13317,Vvar__2___24Anonymous__13322)
& VX13318 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13317,Vvar__1___24Anonymous__13321,Vvar__2___24Anonymous__13322) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX13204] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX13204)
=> ( VX13204 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__13205] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13205)
& VX13204 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13205) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__13236,VX13237] :
( cType___24t(Vvar__0__A__13236)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__13236,VX13237)
=> ( ? [Vvar__1___24Anonymous__13239] :
( t(Vvar__1___24Anonymous__13239,Vvar__0__A__13236)
& VX13237 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13236,Vvar__1___24Anonymous__13239) )
| VX13237 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13236) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__368,Vvar__1__B__369,VX370] :
( cType___24t(Vvar__0__A__368)
=> ( cType___24t(Vvar__1__B__369)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__368,Vvar__1__B__369,VX370)
=> ? [Vvar__2___24Anonymous__373] :
( t(Vvar__2___24Anonymous__373,Vvar__0__A__368)
& ? [Vvar__3___24Anonymous__374] :
( t(Vvar__3___24Anonymous__374,Vvar__1__B__369)
& VX370 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__368,Vvar__1__B__369,Vvar__2___24Anonymous__373,Vvar__3___24Anonymous__374) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__13255,Vvar__1__B__13256,VX13257] :
( cType___24t(Vvar__0__A__13255)
=> ( cType___24t(Vvar__1__B__13256)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__13255,Vvar__1__B__13256,VX13257)
=> ( ? [Vvar__2___24Anonymous__13260] :
( t(Vvar__2___24Anonymous__13260,Vvar__0__A__13255)
& VX13257 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__13255,Vvar__1__B__13256,Vvar__2___24Anonymous__13260) )
| ? [Vvar__2___24Anonymous__13263] :
( t(Vvar__2___24Anonymous__13263,Vvar__1__B__13256)
& VX13257 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__13255,Vvar__1__B__13256,Vvar__2___24Anonymous__13263) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX27] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX27)
=> VX27 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX19969] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX19969)
=> ( ? [Vvar__0__i__19970] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__19970)
& ? [Vvar__1__f__19971] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__19971)
& VX19969 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__19970,Vvar__1__f__19971) ) )
| ? [Vvar__0__i__19972] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__19972)
& ? [Vvar__1__f__19973] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__19973)
& ? [Vvar__2__e__19974] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__19974)
& VX19969 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__19972,Vvar__1__f__19973,Vvar__2__e__19974) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX19958] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX19958)
=> ( ? [Vvar__0__d__19959] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__19959)
& VX19958 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__19959) )
| ? [Vvar__0__d__19960] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__19960)
& VX19958 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__19960) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX19827] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX19827)
=> ( VX19827 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__19828] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19828)
& VX19827 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__19828) )
| ? [Vvar__0___24Anonymous__19829] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19829)
& VX19827 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__19829) )
| ? [Vvar__0___24Anonymous__19830] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19830)
& VX19827 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__19830) )
| ? [Vvar__0___24Anonymous__19831] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19831)
& VX19827 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__19831) )
| ? [Vvar__0___24Anonymous__19832] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19832)
& VX19827 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__19832) )
| ? [Vvar__0___24Anonymous__19833] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19833)
& VX19827 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__19833) )
| ? [Vvar__0___24Anonymous__19834] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19834)
& VX19827 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__19834) )
| ? [Vvar__0___24Anonymous__19835] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19835)
& VX19827 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__19835) )
| ? [Vvar__0___24Anonymous__19836] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19836)
& VX19827 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__19836) )
| ? [Vvar__0___24Anonymous__19837] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__19837)
& VX19827 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__19837) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__21986,Vvar__1___24Anonymous__21987] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__21986)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__21987)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__21986,Vvar__1___24Anonymous__21987)
=> ( Vvar__1___24Anonymous__21987 = Vvar__0__n__21986
| ? [Vvar__1__m__21991] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__21991)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__21986,Vvar__1__m__21991)
& Vvar__1___24Anonymous__21987 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__21991) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__76,Vvar__1__P__77,VX80] :
( cType___24t(Vvar__0__A__76)
=> ( c_24__type__90___24t(Vvar__0__A__76,Vvar__1__P__77,Vvar__1__P__77)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__76,Vvar__1__P__77,VX80)
=> ? [Vvar__2__x__85] :
( t(Vvar__2__x__85,Vvar__0__A__76)
& p(happ(Vvar__1__P__77,Vvar__2__x__85))
& VX80 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__76,Vvar__1__P__77,Vvar__2__x__85) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__107,Vvar__1__B__108,VX109] :
( cProp___24t(Vvar__0__A__107)
=> ( cProp___24t(Vvar__1__B__108)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__107,Vvar__1__B__108,VX109)
=> ( ( p(Vvar__0__A__107)
& VX109 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__107,Vvar__1__B__108) )
| ( p(Vvar__1__B__108)
& VX109 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__107,Vvar__1__B__108) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__31261,Vvar__1__B__31262,VX31263] :
( cType___24t(Vvar__0__A__31261)
=> ( cProp___24t(Vvar__1__B__31262)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__31261,Vvar__1__B__31262,VX31263)
=> ( ? [Vvar__2___24Anonymous__31266] :
( t(Vvar__2___24Anonymous__31266,Vvar__0__A__31261)
& VX31263 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31261,Vvar__1__B__31262,Vvar__2___24Anonymous__31266) )
| ( p(Vvar__1__B__31262)
& VX31263 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31261,Vvar__1__B__31262) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX13181] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX13181)
=> ( VX13181 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__13182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13182)
& VX13181 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13182) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX14] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX14)
=> ( VX14 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__15] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15)
& VX14 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15) )
| ? [Vvar__0___24Anonymous__16] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16)
& VX14 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1)
=> ( ? [Vvar__0___24Anonymous__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2) )
| ? [Vvar__0___24Anonymous__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3)
& VX1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3) )
| VX1 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SqrtSpec',axiom,
! [Vvar__0___24Anonymous__473,Vvar__1___24Anonymous__474] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0___24Anonymous__473)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__474)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec___24a2(Vvar__0___24Anonymous__473,Vvar__1___24Anonymous__474)
=> ( ? [Vvar__0__s__476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__s__476)
& ? [Vvar__1__x__477] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__x__477)
& Vvar__1__x__477 = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0__s__476,Vvar__0__s__476)
& Vvar__1___24Anonymous__474 = Vvar__1__x__477
& Vvar__0___24Anonymous__473 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0__s__476,cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ) )
| ? [Vvar__0__s__479] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__s__479)
& ? [Vvar__1__r__480] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__r__480)
& ? [Vvar__2__x__481] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__x__481)
& Vvar__2__x__481 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0__s__479,Vvar__0__s__479),Vvar__1__r__480)
& cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(Vvar__1__r__480,cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0__s__479))
& Vvar__1___24Anonymous__474 = Vvar__2__x__481
& Vvar__0___24Anonymous__473 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0__s__479,cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__1__r__480)) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX445] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX445)
=> ( VX445 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__446)
& VX445 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__446) )
| VX445 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX13851] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX13851)
=> ? [Vvar__0__Qnum__13852] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__13852)
& ? [Vvar__1__Qden__13853] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__13853)
& VX13851 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__13852,Vvar__1__Qden__13853) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX77730] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX77730)
=> ? [Vvar__0__nonneg__77731] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__77731)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__77731)
& VX77730 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__77731) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX64818] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX64818)
=> ? [Vvar__0__pos__64819] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__64819)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__64819)
& VX64818 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__64819) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__32042,Vvar__1___24Anonymous__32043,VX32044] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__32042)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__32043)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__32042,Vvar__1___24Anonymous__32043,VX32044)
=> ( ( Vvar__0__x__32042 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__32043 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX32044 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32042) )
| ? [Vvar__1__n__32048] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__32048)
& Vvar__0__x__32042 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__32048)
& Vvar__1___24Anonymous__32043 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068___24a3(Vvar__0__x__32042,Vvar__1___24Anonymous__32043,Vvar__1__n__32048)
& VX32044 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32042,Vvar__1__n__32048) )
| ? [Vvar__1__n__32053] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__32053)
& Vvar__0__x__32042 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__32053))
& Vvar__1___24Anonymous__32043 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vvar__0__x__32042,Vvar__1___24Anonymous__32043,Vvar__1__n__32053)
& VX32044 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32042,Vvar__1__n__32053) ) ) ) ) ) ).
fof('$_inversion_Coq.Reals.Rlimit.Metric_Space',axiom,
! [VX65012] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(VX65012)
=> ? [Vvar__0__Base__65013] :
( cType___24t(Vvar__0__Base__65013)
& ? [Vvar__1__dist__65014] :
( c_24__type__65044___24t(Vvar__0__Base__65013,Vvar__1__dist__65014)
& ! [Vvar__var__2__x__65020__65022] :
( t(Vvar__var__2__x__65020__65022,Vvar__0__Base__65013)
=> ! [Vvar__var__3__y__65021__65023] :
( t(Vvar__var__3__y__65021__65023,Vvar__0__Base__65013)
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__65014,Vvar__var__2__x__65020__65022),Vvar__var__3__y__65021__65023),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) )
& ! [Vvar__var__3__x__65025__65027] :
( t(Vvar__var__3__x__65025__65027,Vvar__0__Base__65013)
=> ! [Vvar__var__4__y__65026__65028] :
( t(Vvar__var__4__y__65026__65028,Vvar__0__Base__65013)
=> happ(happ(Vvar__1__dist__65014,Vvar__var__3__x__65025__65027),Vvar__var__4__y__65026__65028) = happ(happ(Vvar__1__dist__65014,Vvar__var__4__y__65026__65028),Vvar__var__3__x__65025__65027) ) )
& ! [Vvar__var__4__x__65030__65032] :
( t(Vvar__var__4__x__65030__65032,Vvar__0__Base__65013)
=> ! [Vvar__var__5__y__65031__65033] :
( t(Vvar__var__5__y__65031__65033,Vvar__0__Base__65013)
=> ( happ(happ(Vvar__1__dist__65014,Vvar__var__4__x__65030__65032),Vvar__var__5__y__65031__65033) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__65030__65032 = Vvar__var__5__y__65031__65033 ) ) )
& ! [Vvar__var__5__x__65035__65038] :
( t(Vvar__var__5__x__65035__65038,Vvar__0__Base__65013)
=> ! [Vvar__var__6__y__65036__65039] :
( t(Vvar__var__6__y__65036__65039,Vvar__0__Base__65013)
=> ! [Vvar__var__7__z__65037__65040] :
( t(Vvar__var__7__z__65037__65040,Vvar__0__Base__65013)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__65014,Vvar__var__5__x__65035__65038),Vvar__var__6__y__65036__65039),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__65014,Vvar__var__5__x__65035__65038),Vvar__var__7__z__65037__65040),happ(happ(Vvar__1__dist__65014,Vvar__var__7__z__65037__65040),Vvar__var__6__y__65036__65039))) ) ) )
& VX65012 = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__65013,Vvar__1__dist__65014) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX58788] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX58788)
=> ( VX58788 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX58788 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX58788 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__16996,Vvar__1__b__16997,Vvar__2__d__16998] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__16996)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__16997)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__16998)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__16996,Vvar__1__b__16997,Vvar__2__d__16998)
=> ? [Vvar__3__u__17003] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__17003)
& ? [Vvar__4__v__17004] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__17004)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__17003,Vvar__0__a__16996),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__17004,Vvar__1__b__16997)) = Vvar__2__d__16998
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__16805,Vvar__1__b__16806,VX16807] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__16805)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__16806)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__16805,Vvar__1__b__16806,VX16807)
=> ? [Vvar__2__u__16810] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__16810)
& ? [Vvar__3__v__16811] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__16811)
& ? [Vvar__4__d__16812] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__16812)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__16810,Vvar__0__a__16805),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__16811,Vvar__1__b__16806)) = Vvar__4__d__16812
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__16805,Vvar__1__b__16806,Vvar__4__d__16812)
& VX16807 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16805,Vvar__1__b__16806,Vvar__2__u__16810,Vvar__3__v__16811,Vvar__4__d__16812) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__16765,Vvar__1__b__16766,Vvar__2__g__16767] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__16765)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__16766)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__16767)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__16765,Vvar__1__b__16766,Vvar__2__g__16767)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__16767,Vvar__0__a__16765)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__16767,Vvar__1__b__16766)
& ! [Vvar__var__var__var__var__5__x__16775__16778__16781__16784__16787] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__16775__16778__16781__16784__16787)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__16775__16778__16781__16784__16787,Vvar__0__a__16765)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__16775__16778__16781__16784__16787,Vvar__1__b__16766)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__16775__16778__16781__16784__16787,Vvar__2__g__16767) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__17013] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__17013)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__17013)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__17013))
& ! [Vvar__var__var__2__n__17018__17020__17022] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__17018__17020__17022)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__17018__17020__17022))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__17018__17020__17022,Vvar__0__p__17013)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__17018__17020__17022,Vvar__0__p__17013) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__18813,Vvar__1__p__18814,VX18815] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__18813)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__18814)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__18813,Vvar__1__p__18814,VX18815)
=> ? [Vvar__2__q__18818] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__18818)
& ? [Vvar__3__r__18819] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__18819)
& Vvar__0__x__18813 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__18818,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__18814)),Vvar__3__r__18819)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__18819))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__18819,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__18814)))
& VX18815 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__18813,Vvar__1__p__18814,Vvar__2__q__18818,Vvar__3__r__18819) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__13380,VX13381] :
( cType___24t(Vvar__0__C__13380)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,VX13381)
=> ( ? [Vvar__1___24Anonymous__13383] :
( t(Vvar__1___24Anonymous__13383,Vvar__0__C__13380)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13380,Vvar__1___24Anonymous__13383) )
| ? [Vvar__1___24Anonymous__13385] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13385)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13380,Vvar__1___24Anonymous__13385) )
| ? [Vvar__1___24Anonymous__13387] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13387)
& ? [Vvar__2___24Anonymous__13388] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__2___24Anonymous__13388)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13387,Vvar__2___24Anonymous__13388) ) )
| ? [Vvar__1___24Anonymous__13390] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13390)
& ? [Vvar__2___24Anonymous__13391] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__2___24Anonymous__13391)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13390,Vvar__2___24Anonymous__13391) ) )
| ? [Vvar__1___24Anonymous__13393] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13393)
& ? [Vvar__2___24Anonymous__13394] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__2___24Anonymous__13394)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13393,Vvar__2___24Anonymous__13394) ) )
| ? [Vvar__1___24Anonymous__13396] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13396)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__13380,Vvar__1___24Anonymous__13396) )
| ? [Vvar__1___24Anonymous__13398] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13398)
& ? [Vvar__2___24Anonymous__13399] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13399)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13398,Vvar__2___24Anonymous__13399) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__13544,VX13545] :
( cType___24t(Vvar__0__C__13544)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,VX13545)
=> ( ? [Vvar__1___24Anonymous__13547] :
( t(Vvar__1___24Anonymous__13547,Vvar__0__C__13544)
& VX13545 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13544,Vvar__1___24Anonymous__13547) )
| ? [Vvar__1___24Anonymous__13549] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13549)
& ? [Vvar__2___24Anonymous__13550] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,Vvar__2___24Anonymous__13550)
& VX13545 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13544,Vvar__1___24Anonymous__13549,Vvar__2___24Anonymous__13550) ) )
| ? [Vvar__1___24Anonymous__13552] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,Vvar__1___24Anonymous__13552)
& ? [Vvar__2___24Anonymous__13553] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__13553)
& ? [Vvar__3___24Anonymous__13554] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,Vvar__3___24Anonymous__13554)
& VX13545 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__13544,Vvar__1___24Anonymous__13552,Vvar__2___24Anonymous__13553,Vvar__3___24Anonymous__13554) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939] :
( cType___24t(Vvar__0__R__20908)
=> ( t(Vvar__1__rO__20909,Vvar__0__R__20908)
=> ( t(Vvar__2__rI__20910,Vvar__0__R__20908)
=> ( c_24__type__21340___24t(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939,Vvar__3__rplus__20911)
=> ( c_24__type__21441___24t(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939,Vvar__4__rtimes__20916)
=> ( c_24__type__21542___24t(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939,Vvar__5__rminus__20921)
=> ( c_24__type__21632___24t(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939,Vvar__6__ropp__20926)
=> ( c_24__type__21733___24t(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939,Vvar__7__req__20929)
=> ( c_24__type__21834___24t(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939,Vvar__8__rle__20934)
=> ( c_24__type__21935___24t(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939,Vvar__9__rlt__20939)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929,Vvar__8__rle__20934,Vvar__9__rlt__20939)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__20908,Vvar__7__req__20929)
& ! [Vvar__var__var__var__var__11__x1__20983__20989__21094__21100__21106] :
( t(Vvar__var__var__var__var__11__x1__20983__20989__21094__21100__21106,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__12__x2__20984__20990__21095__21101__21107] :
( t(Vvar__var__var__var__var__12__x2__20984__20990__21095__21101__21107,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__11__x1__20983__20989__21094__21100__21106),Vvar__var__var__var__var__12__x2__20984__20990__21095__21101__21107))
=> ! [Vvar__var__var__var__var__14__y1__20985__20991__21096__21102__21108] :
( t(Vvar__var__var__var__var__14__y1__20985__20991__21096__21102__21108,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__15__y2__20986__20992__21097__21103__21109] :
( t(Vvar__var__var__var__var__15__y2__20986__20992__21097__21103__21109,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__14__y1__20985__20991__21096__21102__21108),Vvar__var__var__var__var__15__y2__20986__20992__21097__21103__21109))
=> p(happ(happ(Vvar__7__req__20929,happ(happ(Vvar__3__rplus__20911,Vvar__var__var__var__var__11__x1__20983__20989__21094__21100__21106),Vvar__var__var__var__var__14__y1__20985__20991__21096__21102__21108)),happ(happ(Vvar__3__rplus__20911,Vvar__var__var__var__var__12__x2__20984__20990__21095__21101__21107),Vvar__var__var__var__var__15__y2__20986__20992__21097__21103__21109))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__20996__21002__21112__21118__21124] :
( t(Vvar__var__var__var__var__12__x1__20996__21002__21112__21118__21124,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__13__x2__20997__21003__21113__21119__21125] :
( t(Vvar__var__var__var__var__13__x2__20997__21003__21113__21119__21125,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__12__x1__20996__21002__21112__21118__21124),Vvar__var__var__var__var__13__x2__20997__21003__21113__21119__21125))
=> ! [Vvar__var__var__var__var__15__y1__20998__21004__21114__21120__21126] :
( t(Vvar__var__var__var__var__15__y1__20998__21004__21114__21120__21126,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__16__y2__20999__21005__21115__21121__21127] :
( t(Vvar__var__var__var__var__16__y2__20999__21005__21115__21121__21127,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__15__y1__20998__21004__21114__21120__21126),Vvar__var__var__var__var__16__y2__20999__21005__21115__21121__21127))
=> p(happ(happ(Vvar__7__req__20929,happ(happ(Vvar__4__rtimes__20916,Vvar__var__var__var__var__12__x1__20996__21002__21112__21118__21124),Vvar__var__var__var__var__15__y1__20998__21004__21114__21120__21126)),happ(happ(Vvar__4__rtimes__20916,Vvar__var__var__var__var__13__x2__20997__21003__21113__21119__21125),Vvar__var__var__var__var__16__y2__20999__21005__21115__21121__21127))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__21009__21012__21130__21133__21136] :
( t(Vvar__var__var__var__var__13__x1__21009__21012__21130__21133__21136,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__14__x2__21010__21013__21131__21134__21137] :
( t(Vvar__var__var__var__var__14__x2__21010__21013__21131__21134__21137,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__13__x1__21009__21012__21130__21133__21136),Vvar__var__var__var__var__14__x2__21010__21013__21131__21134__21137))
=> p(happ(happ(Vvar__7__req__20929,happ(Vvar__6__ropp__20926,Vvar__var__var__var__var__13__x1__21009__21012__21130__21133__21136)),happ(Vvar__6__ropp__20926,Vvar__var__var__var__var__14__x2__21010__21013__21131__21134__21137))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__21016__21022__21139__21145__21151] :
( t(Vvar__var__var__var__var__14__x1__21016__21022__21139__21145__21151,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__15__x2__21017__21023__21140__21146__21152] :
( t(Vvar__var__var__var__var__15__x2__21017__21023__21140__21146__21152,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__14__x1__21016__21022__21139__21145__21151),Vvar__var__var__var__var__15__x2__21017__21023__21140__21146__21152))
=> ! [Vvar__var__var__var__var__17__y1__21018__21024__21141__21147__21153] :
( t(Vvar__var__var__var__var__17__y1__21018__21024__21141__21147__21153,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__18__y2__21019__21025__21142__21148__21154] :
( t(Vvar__var__var__var__var__18__y2__21019__21025__21142__21148__21154,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__17__y1__21018__21024__21141__21147__21153),Vvar__var__var__var__var__18__y2__21019__21025__21142__21148__21154))
=> ( p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__var__14__x1__21016__21022__21139__21145__21151),Vvar__var__var__var__var__17__y1__21018__21024__21141__21147__21153))
<=> p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__var__15__x2__21017__21023__21140__21146__21152),Vvar__var__var__var__var__18__y2__21019__21025__21142__21148__21154)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__21029__21035__21157__21163__21169] :
( t(Vvar__var__var__var__var__15__x1__21029__21035__21157__21163__21169,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__16__x2__21030__21036__21158__21164__21170] :
( t(Vvar__var__var__var__var__16__x2__21030__21036__21158__21164__21170,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__15__x1__21029__21035__21157__21163__21169),Vvar__var__var__var__var__16__x2__21030__21036__21158__21164__21170))
=> ! [Vvar__var__var__var__var__18__y1__21031__21037__21159__21165__21171] :
( t(Vvar__var__var__var__var__18__y1__21031__21037__21159__21165__21171,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__19__y2__21032__21038__21160__21166__21172] :
( t(Vvar__var__var__var__var__19__y2__21032__21038__21160__21166__21172,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__18__y1__21031__21037__21159__21165__21171),Vvar__var__var__var__var__19__y2__21032__21038__21160__21166__21172))
=> ( p(happ(happ(Vvar__9__rlt__20939,Vvar__var__var__var__var__15__x1__21029__21035__21157__21163__21169),Vvar__var__var__var__var__18__y1__21031__21037__21159__21165__21171))
<=> p(happ(happ(Vvar__9__rlt__20939,Vvar__var__var__var__var__16__x2__21030__21036__21158__21164__21170),Vvar__var__var__var__var__19__y2__21032__21038__21160__21166__21172)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__20908,Vvar__1__rO__20909,Vvar__2__rI__20910,Vvar__3__rplus__20911,Vvar__4__rtimes__20916,Vvar__5__rminus__20921,Vvar__6__ropp__20926,Vvar__7__req__20929)
& ! [Vvar__var__var__var__17__n__21043__21044__21175__21176] :
( t(Vvar__var__var__var__17__n__21043__21044__21175__21176,Vvar__0__R__20908)
=> p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__17__n__21043__21044__21175__21176),Vvar__var__var__var__17__n__21043__21044__21175__21176)) )
& ! [Vvar__var__var__var__var__18__n__21046__21050__21177__21181__21185] :
( t(Vvar__var__var__var__var__18__n__21046__21050__21177__21181__21185,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__19__m__21047__21051__21178__21182__21186] :
( t(Vvar__var__var__var__var__19__m__21047__21051__21178__21182__21186,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__var__18__n__21046__21050__21177__21181__21185),Vvar__var__var__var__var__19__m__21047__21051__21178__21182__21186))
=> ( p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__var__19__m__21047__21051__21178__21182__21186),Vvar__var__var__var__var__18__n__21046__21050__21177__21181__21185))
=> p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__18__n__21046__21050__21177__21181__21185),Vvar__var__var__var__var__19__m__21047__21051__21178__21182__21186)) ) ) ) )
& ! [Vvar__var__var__var__19__n__21055__21060__21189__21194] :
( t(Vvar__var__var__var__19__n__21055__21060__21189__21194,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__20__m__21056__21061__21190__21195] :
( t(Vvar__var__var__var__20__m__21056__21061__21190__21195,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__21__p__21057__21062__21191__21196] :
( t(Vvar__var__var__var__21__p__21057__21062__21191__21196,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__19__n__21055__21060__21189__21194),Vvar__var__var__var__20__m__21056__21061__21190__21195))
=> ( p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__20__m__21056__21061__21190__21195),Vvar__var__var__var__21__p__21057__21062__21191__21196))
=> p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__19__n__21055__21060__21189__21194),Vvar__var__var__var__21__p__21057__21062__21191__21196)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__21066__21068__21199__21201__21203__21205] :
( t(Vvar__var__var__var__var__var__20__n__21066__21068__21199__21201__21203__21205,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__var__21__m__21067__21069__21200__21202__21204__21206] :
( t(Vvar__var__var__var__var__var__21__m__21067__21069__21200__21202__21204__21206,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__9__rlt__20939,Vvar__var__var__var__var__var__20__n__21066__21068__21199__21201__21203__21205),Vvar__var__var__var__var__var__21__m__21067__21069__21200__21202__21204__21206))
<=> ( p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__var__var__20__n__21066__21068__21199__21201__21203__21205),Vvar__var__var__var__var__var__21__m__21067__21069__21200__21202__21204__21206))
& ~ p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__var__20__n__21066__21068__21199__21201__21203__21205),Vvar__var__var__var__var__var__21__m__21067__21069__21200__21202__21204__21206)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__21071__21073__21207__21209__21211] :
( t(Vvar__var__var__var__var__21__n__21071__21073__21207__21209__21211,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__22__m__21072__21074__21208__21210__21212] :
( t(Vvar__var__var__var__var__22__m__21072__21074__21208__21210__21212,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__9__rlt__20939,Vvar__var__var__var__var__21__n__21071__21073__21207__21209__21211),Vvar__var__var__var__var__22__m__21072__21074__21208__21210__21212))
| p(happ(happ(Vvar__7__req__20929,Vvar__var__var__var__var__21__n__21071__21073__21207__21209__21211),Vvar__var__var__var__var__22__m__21072__21074__21208__21210__21212))
| p(happ(happ(Vvar__9__rlt__20939,Vvar__var__var__var__var__22__m__21072__21074__21208__21210__21212),Vvar__var__var__var__var__21__n__21071__21073__21207__21209__21211)) ) ) )
& ! [Vvar__var__var__var__var__22__n__21076__21080__21213__21217__21221] :
( t(Vvar__var__var__var__var__22__n__21076__21080__21213__21217__21221,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__23__m__21077__21081__21214__21218__21222] :
( t(Vvar__var__var__var__var__23__m__21077__21081__21214__21218__21222,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__24__p__21078__21082__21215__21219__21223] :
( t(Vvar__var__var__var__var__24__p__21078__21082__21215__21219__21223,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__8__rle__20934,Vvar__var__var__var__var__22__n__21076__21080__21213__21217__21221),Vvar__var__var__var__var__23__m__21077__21081__21214__21218__21222))
=> p(happ(happ(Vvar__8__rle__20934,happ(happ(Vvar__3__rplus__20911,Vvar__var__var__var__var__24__p__21078__21082__21215__21219__21223),Vvar__var__var__var__var__22__n__21076__21080__21213__21217__21221)),happ(happ(Vvar__3__rplus__20911,Vvar__var__var__var__var__24__p__21078__21082__21215__21219__21223),Vvar__var__var__var__var__23__m__21077__21081__21214__21218__21222))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__21085__21089__21225__21229__21233__21237] :
( t(Vvar__var__var__var__var__var__23__n__21085__21089__21225__21229__21233__21237,Vvar__0__R__20908)
=> ! [Vvar__var__var__var__var__var__24__m__21086__21090__21226__21230__21234__21238] :
( t(Vvar__var__var__var__var__var__24__m__21086__21090__21226__21230__21234__21238,Vvar__0__R__20908)
=> ( p(happ(happ(Vvar__9__rlt__20939,Vvar__1__rO__20909),Vvar__var__var__var__var__var__23__n__21085__21089__21225__21229__21233__21237))
=> ( p(happ(happ(Vvar__9__rlt__20939,Vvar__1__rO__20909),Vvar__var__var__var__var__var__24__m__21086__21090__21226__21230__21234__21238))
=> p(happ(happ(Vvar__9__rlt__20939,Vvar__1__rO__20909),happ(happ(Vvar__4__rtimes__20916,Vvar__var__var__var__var__var__23__n__21085__21089__21225__21229__21233__21237),Vvar__var__var__var__var__var__24__m__21086__21090__21226__21230__21234__21238))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__20929,Vvar__1__rO__20909),Vvar__2__rI__20910))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX64845] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX64845)
=> ( VX64845 = cCoq_2emicromega_2eRMicromega_2eC0
| VX64845 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__64846] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__64846)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__64846) )
| ? [Vvar__0__r__64847] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__64847)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__64847) )
| ? [Vvar__0__r1__64848] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64848)
& ? [Vvar__1__r2__64849] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__64849)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__64848,Vvar__1__r2__64849) ) )
| ? [Vvar__0__r1__64850] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64850)
& ? [Vvar__1__r2__64851] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__64851)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__64850,Vvar__1__r2__64851) ) )
| ? [Vvar__0__r1__64852] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64852)
& ? [Vvar__1__r2__64853] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__64853)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__64852,Vvar__1__r2__64853) ) )
| ? [Vvar__0__r1__64854] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64854)
& ? [Vvar__1__z__64855] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__64855)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__64854,Vvar__1__z__64855) ) )
| ? [Vvar__0__r__64856] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__64856)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__64856) )
| ? [Vvar__0__r__64857] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__64857)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__64857) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__27496,VX27497] :
( cType___24t(Vvar__0__T__27496)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__27496,VX27497)
=> ? [Vvar__1__Flhs__27499] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__27496,Vvar__1__Flhs__27499)
& ? [Vvar__2__Fop__27500] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__27500)
& ? [Vvar__3__Frhs__27501] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__27496,Vvar__3__Frhs__27501)
& VX27497 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27496,Vvar__1__Flhs__27499,Vvar__2__Fop__27500,Vvar__3__Frhs__27501) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX32305] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX32305)
=> ( VX32305 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX32305 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX32305 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX32305 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX61428] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX61428)
=> ( VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__27350,VX27351] :
( cType___24t(Vvar__0__C__27350)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,VX27351)
=> ( ? [Vvar__1___24Anonymous__27353] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__27353)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27350,Vvar__1___24Anonymous__27353) )
| ? [Vvar__1___24Anonymous__27355] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27355)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27350,Vvar__1___24Anonymous__27355) )
| ? [Vvar__1___24Anonymous__27357] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27357)
& ? [Vvar__2___24Anonymous__27358] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__2___24Anonymous__27358)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27350,Vvar__1___24Anonymous__27357,Vvar__2___24Anonymous__27358) ) )
| ? [Vvar__1___24Anonymous__27360] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27360)
& ? [Vvar__2___24Anonymous__27361] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__2___24Anonymous__27361)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27350,Vvar__1___24Anonymous__27360,Vvar__2___24Anonymous__27361) ) )
| ? [Vvar__1___24Anonymous__27363] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27363)
& ? [Vvar__2___24Anonymous__27364] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__2___24Anonymous__27364)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27350,Vvar__1___24Anonymous__27363,Vvar__2___24Anonymous__27364) ) )
| ? [Vvar__1___24Anonymous__27366] :
( t(Vvar__1___24Anonymous__27366,Vvar__0__C__27350)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27350,Vvar__1___24Anonymous__27366) )
| VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27350) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126] :
( cType___24t(Vvar__0__R__22057)
=> ( t(Vvar__1__rO__22058,Vvar__0__R__22057)
=> ( t(Vvar__2__rI__22059,Vvar__0__R__22057)
=> ( c_24__type__22590___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__3__rplus__22060)
=> ( c_24__type__22936___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__4__rtimes__22065)
=> ( c_24__type__23282___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__5__rminus__22070)
=> ( c_24__type__23605___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__6__ropp__22075)
=> ( c_24__type__23951___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__7__req__22078)
=> ( c_24__type__24297___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__8__rle__22083)
=> ( cType___24t(Vvar__9__C__22088)
=> ( t(Vvar__10__cO__22089,Vvar__9__C__22088)
=> ( t(Vvar__11__cI__22090,Vvar__9__C__22088)
=> ( c_24__type__24643___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__12__cplus__22091)
=> ( c_24__type__24989___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__13__ctimes__22096)
=> ( c_24__type__25335___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__14__cminus__22101)
=> ( c_24__type__25658___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__15__copp__22106)
=> ( c_24__type__26004___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__16__ceqb__22109)
=> ( c_24__type__26350___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__17__cleb__22114)
=> ( c_24__type__26673___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__18__phi__22119)
=> ( cType___24t(Vvar__19__E__22122)
=> ( c_24__type__26996___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__20__pow__phi__22123)
=> ( c_24__type__27342___24t(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126,Vvar__21__rpow__22126)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__8__rle__22083,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__17__cleb__22114,Vvar__18__phi__22119,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__22057,Vvar__1__rO__22058,Vvar__2__rI__22059,Vvar__3__rplus__22060,Vvar__4__rtimes__22065,Vvar__5__rminus__22070,Vvar__6__ropp__22075,Vvar__7__req__22078,Vvar__9__C__22088,Vvar__10__cO__22089,Vvar__11__cI__22090,Vvar__12__cplus__22091,Vvar__13__ctimes__22096,Vvar__14__cminus__22101,Vvar__15__copp__22106,Vvar__16__ceqb__22109,Vvar__18__phi__22119)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__22057,Vvar__2__rI__22059,Vvar__4__rtimes__22065,Vvar__7__req__22078,Vvar__19__E__22122,Vvar__20__pow__phi__22123,Vvar__21__rpow__22126)
& ! [Vvar__var__var__var__var__var__24__x__22209__22212__22222__22225__22228__22231] :
( t(Vvar__var__var__var__var__var__24__x__22209__22212__22222__22225__22228__22231,Vvar__9__C__22088)
=> ! [Vvar__var__var__var__var__var__25__y__22210__22213__22223__22226__22229__22232] :
( t(Vvar__var__var__var__var__var__25__y__22210__22213__22223__22226__22229__22232,Vvar__9__C__22088)
=> ( happ(happ(Vvar__16__ceqb__22109,Vvar__var__var__var__var__var__24__x__22209__22212__22222__22225__22228__22231),Vvar__var__var__var__var__var__25__y__22210__22213__22223__22226__22229__22232) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__22078,happ(Vvar__18__phi__22119,Vvar__var__var__var__var__var__24__x__22209__22212__22222__22225__22228__22231)),happ(Vvar__18__phi__22119,Vvar__var__var__var__var__var__25__y__22210__22213__22223__22226__22229__22232))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__22216__22219__22234__22237__22240__22243] :
( t(Vvar__var__var__var__var__var__25__x__22216__22219__22234__22237__22240__22243,Vvar__9__C__22088)
=> ! [Vvar__var__var__var__var__var__26__y__22217__22220__22235__22238__22241__22244] :
( t(Vvar__var__var__var__var__var__26__y__22217__22220__22235__22238__22241__22244,Vvar__9__C__22088)
=> ( happ(happ(Vvar__17__cleb__22114,Vvar__var__var__var__var__var__25__x__22216__22219__22234__22237__22240__22243),Vvar__var__var__var__var__var__26__y__22217__22220__22235__22238__22241__22244) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__22083,happ(Vvar__18__phi__22119,Vvar__var__var__var__var__var__25__x__22216__22219__22234__22237__22240__22243)),happ(Vvar__18__phi__22119,Vvar__var__var__var__var__var__26__y__22217__22220__22235__22238__22241__22244))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,VX65111] :
( cType___24t(Vvar__0__TA__65107)
=> ( cType___24t(Vvar__1__TX__65108)
=> ( cType___24t(Vvar__2__AA__65109)
=> ( cType___24t(Vvar__3__AF__65110)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,VX65111)
=> ( VX65111 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110)
| VX65111 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110)
| ? [Vvar__4___24Anonymous__65124] :
( t(Vvar__4___24Anonymous__65124,Vvar__1__TX__65108)
& VX65111 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65124) )
| ? [Vvar__4___24Anonymous__65129] :
( t(Vvar__4___24Anonymous__65129,Vvar__0__TA__65107)
& ? [Vvar__5___24Anonymous__65130] :
( t(Vvar__5___24Anonymous__65130,Vvar__2__AA__65109)
& VX65111 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65129,Vvar__5___24Anonymous__65130) ) )
| ? [Vvar__4___24Anonymous__65135] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65135)
& ? [Vvar__5___24Anonymous__65136] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__5___24Anonymous__65136)
& VX65111 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65135,Vvar__5___24Anonymous__65136) ) )
| ? [Vvar__4___24Anonymous__65141] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65141)
& ? [Vvar__5___24Anonymous__65142] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__5___24Anonymous__65142)
& VX65111 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65141,Vvar__5___24Anonymous__65142) ) )
| ? [Vvar__4___24Anonymous__65147] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65147)
& VX65111 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65147) )
| ? [Vvar__4___24Anonymous__65152] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65152)
& ? [Vvar__5___24Anonymous__65153] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__65110,Vvar__5___24Anonymous__65153)
& ? [Vvar__6___24Anonymous__65154] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__6___24Anonymous__65154)
& VX65111 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65152,Vvar__5___24Anonymous__65153,Vvar__6___24Anonymous__65154) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__65567,VX65568] :
( cType___24t(Vvar__0__A__65567)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__65567,VX65568)
=> ( VX65568 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65567)
| ? [Vvar__1___24Anonymous__65571] :
( t(Vvar__1___24Anonymous__65571,Vvar__0__A__65567)
& VX65568 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65567,Vvar__1___24Anonymous__65571) )
| ? [Vvar__1___24Anonymous__65573] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__65567,Vvar__1___24Anonymous__65573)
& ? [Vvar__2___24Anonymous__65574] :
( t(Vvar__2___24Anonymous__65574,Vvar__0__A__65567)
& ? [Vvar__3___24Anonymous__65575] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__65567,Vvar__3___24Anonymous__65575)
& VX65568 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__65567,Vvar__1___24Anonymous__65573,Vvar__2___24Anonymous__65574,Vvar__3___24Anonymous__65575) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX58031] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX58031)
=> ( VX58031 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__58032] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__58032)
& ? [Vvar__1___24Anonymous__58033] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__58033)
& VX58031 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__58032,Vvar__1___24Anonymous__58033) ) )
| ? [Vvar__0___24Anonymous__58034] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__58034)
& ? [Vvar__1___24Anonymous__58035] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__58035)
& VX58031 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__58034,Vvar__1___24Anonymous__58035) ) )
| ? [Vvar__0___24Anonymous__58036] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__58036)
& ? [Vvar__1___24Anonymous__58037] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__58037)
& ? [Vvar__2___24Anonymous__58038] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__58038)
& VX58031 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__58036,Vvar__1___24Anonymous__58037,Vvar__2___24Anonymous__58038) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
! [Vvar__0__x__16600,Vvar__1___24Anonymous__16601] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__16600)
=> ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__16601)
=> ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__16600,Vvar__1___24Anonymous__16601)
=> ( ? [Vvar__1__c__16604] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__16604)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__16600,Vvar__1__c__16604)
& Vvar__1___24Anonymous__16601 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__16604) )
| ? [Vvar__1__p__16607] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__16607)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__16600,Vvar__1__p__16607)
& ? [Vvar__3__j__16609] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__16609)
& Vvar__1___24Anonymous__16601 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__16609,Vvar__1__p__16607) ) )
| ? [Vvar__1__p__16611] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__16611)
& ? [Vvar__2__q__16612] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__16612)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__16600,Vvar__1__p__16611)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__16600,Vvar__2__q__16612)
& ? [Vvar__5__j__16615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__16615)
& Vvar__1___24Anonymous__16601 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__16611,Vvar__5__j__16615,Vvar__2__q__16612) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__35270,Vvar__1__env__35271,Vvar__2__env_27__35274,Vvar__3__x__35277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__35270)
=> ( c_24__type__35298___24t(Vvar__0__fr__35270,Vvar__1__env__35271,Vvar__2__env_27__35274,Vvar__3__x__35277,Vvar__1__env__35271)
=> ( c_24__type__35307___24t(Vvar__0__fr__35270,Vvar__1__env__35271,Vvar__2__env_27__35274,Vvar__3__x__35277,Vvar__2__env_27__35274)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__35277)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__35270,Vvar__1__env__35271,Vvar__2__env_27__35274,Vvar__3__x__35277)
=> ( happ(Vvar__1__env__35271,Vvar__3__x__35277) = happ(Vvar__2__env_27__35274,Vvar__3__x__35277)
& happ(Vvar__1__env__35271,Vvar__3__x__35277) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__35274,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35270,Vvar__3__x__35277))),happ(Vvar__2__env_27__35274,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35270,Vvar__3__x__35277))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__35274,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35270,Vvar__3__x__35277))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__35274,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__35270,Vvar__3__x__35277))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__19992,VX19993] :
( cType___24t(Vvar__0__C__19992)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,VX19993)
=> ( VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19992)
| VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19992)
| ? [Vvar__1___24Anonymous__19997] :
( t(Vvar__1___24Anonymous__19997,Vvar__0__C__19992)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__19997) )
| ? [Vvar__1___24Anonymous__19999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__19999)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__19999) )
| ? [Vvar__1___24Anonymous__20001] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20001)
& ? [Vvar__2___24Anonymous__20002] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20002)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20001,Vvar__2___24Anonymous__20002) ) )
| ? [Vvar__1___24Anonymous__20004] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20004)
& ? [Vvar__2___24Anonymous__20005] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20005)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20004,Vvar__2___24Anonymous__20005) ) )
| ? [Vvar__1___24Anonymous__20007] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20007)
& ? [Vvar__2___24Anonymous__20008] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20008)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20007,Vvar__2___24Anonymous__20008) ) )
| ? [Vvar__1___24Anonymous__20010] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20010)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__20010) )
| ? [Vvar__1___24Anonymous__20012] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20012)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__20012) )
| ? [Vvar__1___24Anonymous__20014] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20014)
& ? [Vvar__2___24Anonymous__20015] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20015)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20014,Vvar__2___24Anonymous__20015) ) )
| ? [Vvar__1___24Anonymous__20017] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20017)
& ? [Vvar__2___24Anonymous__20018] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__20018)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20017,Vvar__2___24Anonymous__20018) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__20604,VX20605] :
( cType___24t(Vvar__0__C__20604)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__20604,VX20605)
=> ? [Vvar__1__num__20607] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20604,Vvar__1__num__20607)
& ? [Vvar__2__denum__20608] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20604,Vvar__2__denum__20608)
& ? [Vvar__3__condition__20609] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__20604),Vvar__3__condition__20609)
& VX20605 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20604,Vvar__1__num__20607,Vvar__2__denum__20608,Vvar__3__condition__20609) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__35327,VX35328] :
( cType___24t(Vvar__0__C__35327)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__35327,VX35328)
=> ? [Vvar__1__rsplit__left__35330] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__35327,Vvar__1__rsplit__left__35330)
& ? [Vvar__2__rsplit__common__35331] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__35327,Vvar__2__rsplit__common__35331)
& ? [Vvar__3__rsplit__right__35332] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__35327,Vvar__3__rsplit__right__35332)
& VX35328 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__35327,Vvar__1__rsplit__left__35330,Vvar__2__rsplit__common__35331,Vvar__3__rsplit__right__35332) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX14259] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX14259)
=> ( VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__14260] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14260)
& ? [Vvar__1___24Anonymous__14261] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__14261)
& VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14260,Vvar__1___24Anonymous__14261) ) )
| ? [Vvar__0___24Anonymous__14262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14262)
& ? [Vvar__1___24Anonymous__14263] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__14263)
& VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__14262,Vvar__1___24Anonymous__14263) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__14280,VX14281] :
( cType___24t(Vvar__0__C__14280)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,VX14281)
=> ( VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14280)
| VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14280)
| ? [Vvar__1___24Anonymous__14285] :
( t(Vvar__1___24Anonymous__14285,Vvar__0__C__14280)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14280,Vvar__1___24Anonymous__14285) )
| ? [Vvar__1___24Anonymous__14287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14287)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14280,Vvar__1___24Anonymous__14287) )
| ? [Vvar__1___24Anonymous__14289] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14289)
& ? [Vvar__2___24Anonymous__14290] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__2___24Anonymous__14290)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14289,Vvar__2___24Anonymous__14290) ) )
| ? [Vvar__1___24Anonymous__14292] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14292)
& ? [Vvar__2___24Anonymous__14293] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__2___24Anonymous__14293)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14292,Vvar__2___24Anonymous__14293) ) )
| ? [Vvar__1___24Anonymous__14295] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14295)
& ? [Vvar__2___24Anonymous__14296] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__2___24Anonymous__14296)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14295,Vvar__2___24Anonymous__14296) ) )
| ? [Vvar__1___24Anonymous__14298] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14298)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14280,Vvar__1___24Anonymous__14298) )
| ? [Vvar__1___24Anonymous__14300] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14300)
& ? [Vvar__2___24Anonymous__14301] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14301)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14300,Vvar__2___24Anonymous__14301) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__14078,VX14079] :
( cType___24t(Vvar__0__C__14078)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,VX14079)
=> ( ? [Vvar__1___24Anonymous__14081] :
( t(Vvar__1___24Anonymous__14081,Vvar__0__C__14078)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14078,Vvar__1___24Anonymous__14081) )
| ? [Vvar__1___24Anonymous__14083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14083)
& ? [Vvar__2___24Anonymous__14084] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__2___24Anonymous__14084)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14078,Vvar__1___24Anonymous__14083,Vvar__2___24Anonymous__14084) ) )
| ? [Vvar__1___24Anonymous__14086] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__1___24Anonymous__14086)
& ? [Vvar__2___24Anonymous__14087] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14087)
& ? [Vvar__3___24Anonymous__14088] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__3___24Anonymous__14088)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__14078,Vvar__1___24Anonymous__14086,Vvar__2___24Anonymous__14087,Vvar__3___24Anonymous__14088) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__14966,Vvar__1__rO__14967,Vvar__2__rI__14968,Vvar__3__radd__14969,Vvar__4__rmul__14974,Vvar__5__rsub__14979,Vvar__6__ropp__14984,Vvar__7__req__14987] :
( cType___24t(Vvar__0__R__14966)
=> ( t(Vvar__1__rO__14967,Vvar__0__R__14966)
=> ( t(Vvar__2__rI__14968,Vvar__0__R__14966)
=> ( c_24__type__15215___24t(Vvar__0__R__14966,Vvar__1__rO__14967,Vvar__2__rI__14968,Vvar__3__radd__14969,Vvar__4__rmul__14974,Vvar__5__rsub__14979,Vvar__6__ropp__14984,Vvar__7__req__14987,Vvar__3__radd__14969)
=> ( c_24__type__15278___24t(Vvar__0__R__14966,Vvar__1__rO__14967,Vvar__2__rI__14968,Vvar__3__radd__14969,Vvar__4__rmul__14974,Vvar__5__rsub__14979,Vvar__6__ropp__14984,Vvar__7__req__14987,Vvar__4__rmul__14974)
=> ( c_24__type__15341___24t(Vvar__0__R__14966,Vvar__1__rO__14967,Vvar__2__rI__14968,Vvar__3__radd__14969,Vvar__4__rmul__14974,Vvar__5__rsub__14979,Vvar__6__ropp__14984,Vvar__7__req__14987,Vvar__5__rsub__14979)
=> ( c_24__type__15395___24t(Vvar__0__R__14966,Vvar__1__rO__14967,Vvar__2__rI__14968,Vvar__3__radd__14969,Vvar__4__rmul__14974,Vvar__5__rsub__14979,Vvar__6__ropp__14984,Vvar__7__req__14987,Vvar__6__ropp__14984)
=> ( c_24__type__15458___24t(Vvar__0__R__14966,Vvar__1__rO__14967,Vvar__2__rI__14968,Vvar__3__radd__14969,Vvar__4__rmul__14974,Vvar__5__rsub__14979,Vvar__6__ropp__14984,Vvar__7__req__14987,Vvar__7__req__14987)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__14966,Vvar__1__rO__14967,Vvar__2__rI__14968,Vvar__3__radd__14969,Vvar__4__rmul__14974,Vvar__5__rsub__14979,Vvar__6__ropp__14984,Vvar__7__req__14987)
=> ( ! [Vvar__var__var__var__var__var__8__x__15020__15021__15074__15075__15076__15077] :
( t(Vvar__var__var__var__var__var__8__x__15020__15021__15074__15075__15076__15077,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__3__radd__14969,Vvar__1__rO__14967),Vvar__var__var__var__var__var__8__x__15020__15021__15074__15075__15076__15077)),Vvar__var__var__var__var__var__8__x__15020__15021__15074__15075__15076__15077)) )
& ! [Vvar__var__var__var__var__9__x__15023__15025__15078__15080__15082] :
( t(Vvar__var__var__var__var__9__x__15023__15025__15078__15080__15082,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__10__y__15024__15026__15079__15081__15083] :
( t(Vvar__var__var__var__var__10__y__15024__15026__15079__15081__15083,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__9__x__15023__15025__15078__15080__15082),Vvar__var__var__var__var__10__y__15024__15026__15079__15081__15083)),happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__10__y__15024__15026__15079__15081__15083),Vvar__var__var__var__var__9__x__15023__15025__15078__15080__15082))) ) )
& ! [Vvar__var__var__var__var__10__x__15028__15031__15084__15087__15090] :
( t(Vvar__var__var__var__var__10__x__15028__15031__15084__15087__15090,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__11__y__15029__15032__15085__15088__15091] :
( t(Vvar__var__var__var__var__11__y__15029__15032__15085__15088__15091,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__12__z__15030__15033__15086__15089__15092] :
( t(Vvar__var__var__var__var__12__z__15030__15033__15086__15089__15092,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__10__x__15028__15031__15084__15087__15090),happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__11__y__15029__15032__15085__15088__15091),Vvar__var__var__var__var__12__z__15030__15033__15086__15089__15092))),happ(happ(Vvar__3__radd__14969,happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__10__x__15028__15031__15084__15087__15090),Vvar__var__var__var__var__11__y__15029__15032__15085__15088__15091)),Vvar__var__var__var__var__12__z__15030__15033__15086__15089__15092))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__15035__15036__15093__15094__15095__15096] :
( t(Vvar__var__var__var__var__var__11__x__15035__15036__15093__15094__15095__15096,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__4__rmul__14974,Vvar__2__rI__14968),Vvar__var__var__var__var__var__11__x__15035__15036__15093__15094__15095__15096)),Vvar__var__var__var__var__var__11__x__15035__15036__15093__15094__15095__15096)) )
& ! [Vvar__var__var__var__var__var__12__x__15038__15039__15097__15098__15099__15100] :
( t(Vvar__var__var__var__var__var__12__x__15038__15039__15097__15098__15099__15100,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__4__rmul__14974,Vvar__1__rO__14967),Vvar__var__var__var__var__var__12__x__15038__15039__15097__15098__15099__15100)),Vvar__1__rO__14967)) )
& ! [Vvar__var__var__var__var__13__x__15041__15043__15101__15103__15105] :
( t(Vvar__var__var__var__var__13__x__15041__15043__15101__15103__15105,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__14__y__15042__15044__15102__15104__15106] :
( t(Vvar__var__var__var__var__14__y__15042__15044__15102__15104__15106,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__13__x__15041__15043__15101__15103__15105),Vvar__var__var__var__var__14__y__15042__15044__15102__15104__15106)),happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__14__y__15042__15044__15102__15104__15106),Vvar__var__var__var__var__13__x__15041__15043__15101__15103__15105))) ) )
& ! [Vvar__var__var__var__var__14__x__15046__15049__15107__15110__15113] :
( t(Vvar__var__var__var__var__14__x__15046__15049__15107__15110__15113,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__15__y__15047__15050__15108__15111__15114] :
( t(Vvar__var__var__var__var__15__y__15047__15050__15108__15111__15114,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__16__z__15048__15051__15109__15112__15115] :
( t(Vvar__var__var__var__var__16__z__15048__15051__15109__15112__15115,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__14__x__15046__15049__15107__15110__15113),happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__15__y__15047__15050__15108__15111__15114),Vvar__var__var__var__var__16__z__15048__15051__15109__15112__15115))),happ(happ(Vvar__4__rmul__14974,happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__14__x__15046__15049__15107__15110__15113),Vvar__var__var__var__var__15__y__15047__15050__15108__15111__15114)),Vvar__var__var__var__var__16__z__15048__15051__15109__15112__15115))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__15053__15056__15116__15119__15122__15125] :
( t(Vvar__var__var__var__var__var__15__x__15053__15056__15116__15119__15122__15125,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__var__16__y__15054__15057__15117__15120__15123__15126] :
( t(Vvar__var__var__var__var__var__16__y__15054__15057__15117__15120__15123__15126,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__var__17__z__15055__15058__15118__15121__15124__15127] :
( t(Vvar__var__var__var__var__var__17__z__15055__15058__15118__15121__15124__15127,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__4__rmul__14974,happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__var__15__x__15053__15056__15116__15119__15122__15125),Vvar__var__var__var__var__var__16__y__15054__15057__15117__15120__15123__15126)),Vvar__var__var__var__var__var__17__z__15055__15058__15118__15121__15124__15127)),happ(happ(Vvar__3__radd__14969,happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__var__15__x__15053__15056__15116__15119__15122__15125),Vvar__var__var__var__var__var__17__z__15055__15058__15118__15121__15124__15127)),happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__var__16__y__15054__15057__15117__15120__15123__15126),Vvar__var__var__var__var__var__17__z__15055__15058__15118__15121__15124__15127)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__15060__15062__15128__15130__15132__15134] :
( t(Vvar__var__var__var__var__var__16__x__15060__15062__15128__15130__15132__15134,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__var__17__y__15061__15063__15129__15131__15133__15135] :
( t(Vvar__var__var__var__var__var__17__y__15061__15063__15129__15131__15133__15135,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(Vvar__6__ropp__14984,happ(happ(Vvar__4__rmul__14974,Vvar__var__var__var__var__var__16__x__15060__15062__15128__15130__15132__15134),Vvar__var__var__var__var__var__17__y__15061__15063__15129__15131__15133__15135))),happ(happ(Vvar__4__rmul__14974,happ(Vvar__6__ropp__14984,Vvar__var__var__var__var__var__16__x__15060__15062__15128__15130__15132__15134)),Vvar__var__var__var__var__var__17__y__15061__15063__15129__15131__15133__15135))) ) )
& ! [Vvar__var__var__var__var__var__17__x__15065__15067__15136__15138__15140__15142] :
( t(Vvar__var__var__var__var__var__17__x__15065__15067__15136__15138__15140__15142,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__var__18__y__15066__15068__15137__15139__15141__15143] :
( t(Vvar__var__var__var__var__var__18__y__15066__15068__15137__15139__15141__15143,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(Vvar__6__ropp__14984,happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__var__17__x__15065__15067__15136__15138__15140__15142),Vvar__var__var__var__var__var__18__y__15066__15068__15137__15139__15141__15143))),happ(happ(Vvar__3__radd__14969,happ(Vvar__6__ropp__14984,Vvar__var__var__var__var__var__17__x__15065__15067__15136__15138__15140__15142)),happ(Vvar__6__ropp__14984,Vvar__var__var__var__var__var__18__y__15066__15068__15137__15139__15141__15143)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__15070__15072__15144__15146__15148__15150__15152] :
( t(Vvar__var__var__var__var__var__var__18__x__15070__15072__15144__15146__15148__15150__15152,Vvar__0__R__14966)
=> ! [Vvar__var__var__var__var__var__var__19__y__15071__15073__15145__15147__15149__15151__15153] :
( t(Vvar__var__var__var__var__var__var__19__y__15071__15073__15145__15147__15149__15151__15153,Vvar__0__R__14966)
=> p(happ(happ(Vvar__7__req__14987,happ(happ(Vvar__5__rsub__14979,Vvar__var__var__var__var__var__var__18__x__15070__15072__15144__15146__15148__15150__15152),Vvar__var__var__var__var__var__var__19__y__15071__15073__15145__15147__15149__15151__15153)),happ(happ(Vvar__3__radd__14969,Vvar__var__var__var__var__var__var__18__x__15070__15072__15144__15146__15148__15150__15152),happ(Vvar__6__ropp__14984,Vvar__var__var__var__var__var__var__19__y__15071__15073__15145__15147__15149__15151__15153)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032] :
( cType___24t(Vvar__0__R__31016)
=> ( t(Vvar__1__rI__31017,Vvar__0__R__31016)
=> ( c_24__type__31118___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__2__rmul__31018)
=> ( c_24__type__31162___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__3__req__31023)
=> ( cType___24t(Vvar__4__Cpow__31028)
=> ( c_24__type__31198___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__5__Cp__phi__31029)
=> ( c_24__type__31242___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__6__rpow__31032)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074] :
( t(Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074,Vvar__0__R__31016)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075)
=> p(happ(happ(Vvar__3__req__31023,happ(happ(Vvar__6__rpow__31032,Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074),happ(Vvar__5__Cp__phi__31029,Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074,Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009] :
( cType___24t(Vvar__0__R__15995)
=> ( c_24__type__16100___24t(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009,Vvar__1__radd__15996)
=> ( c_24__type__16130___24t(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009,Vvar__2__rmul__16001)
=> ( c_24__type__16154___24t(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009,Vvar__3__ropp__16006)
=> ( c_24__type__16184___24t(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009,Vvar__4__req__16009)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__16214___24a5(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__15995,c_24__type__16238___24a5(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009),Vvar__4__req__16009,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__15995,Vvar__0__R__15995,Vvar__4__req__16009,Vvar__4__req__16009)),Vvar__1__radd__15996)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__16271___24a5(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__15995,c_24__type__16295___24a5(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009),Vvar__4__req__16009,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__15995,Vvar__0__R__15995,Vvar__4__req__16009,Vvar__4__req__16009)),Vvar__2__rmul__16001)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__16322___24a5(Vvar__0__R__15995,Vvar__1__radd__15996,Vvar__2__rmul__16001,Vvar__3__ropp__16006,Vvar__4__req__16009),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__15995,Vvar__0__R__15995,Vvar__4__req__16009,Vvar__4__req__16009),Vvar__3__ropp__16006)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581] :
( cType___24t(Vvar__0__R__28529)
=> ( t(Vvar__1__rO__28530,Vvar__0__R__28529)
=> ( t(Vvar__2__rI__28531,Vvar__0__R__28529)
=> ( c_24__type__28925___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__3__radd__28532)
=> ( c_24__type__29138___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__4__rmul__28537)
=> ( c_24__type__29351___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__5__rsub__28542)
=> ( c_24__type__29546___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__6__ropp__28547)
=> ( c_24__type__29759___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__7__req__28550)
=> ( cType___24t(Vvar__8__C__28555)
=> ( t(Vvar__9__cO__28556,Vvar__8__C__28555)
=> ( t(Vvar__10__cI__28557,Vvar__8__C__28555)
=> ( c_24__type__29972___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__11__cadd__28558)
=> ( c_24__type__30185___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__12__cmul__28563)
=> ( c_24__type__30398___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__13__csub__28568)
=> ( c_24__type__30593___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__14__copp__28573)
=> ( c_24__type__30806___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__15__ceqb__28576)
=> ( c_24__type__31001___24t(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581,Vvar__16__phi__28581)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__28529,Vvar__1__rO__28530,Vvar__2__rI__28531,Vvar__3__radd__28532,Vvar__4__rmul__28537,Vvar__5__rsub__28542,Vvar__6__ropp__28547,Vvar__7__req__28550,Vvar__8__C__28555,Vvar__9__cO__28556,Vvar__10__cI__28557,Vvar__11__cadd__28558,Vvar__12__cmul__28563,Vvar__13__csub__28568,Vvar__14__copp__28573,Vvar__15__ceqb__28576,Vvar__16__phi__28581)
=> ( p(happ(happ(Vvar__7__req__28550,happ(Vvar__16__phi__28581,Vvar__9__cO__28556)),Vvar__1__rO__28530))
& p(happ(happ(Vvar__7__req__28550,happ(Vvar__16__phi__28581,Vvar__10__cI__28557)),Vvar__2__rI__28531))
& ! [Vvar__var__var__var__var__var__var__19__x__28643__28645__28667__28669__28671__28673__28675] :
( t(Vvar__var__var__var__var__var__var__19__x__28643__28645__28667__28669__28671__28673__28675,Vvar__8__C__28555)
=> ! [Vvar__var__var__var__var__var__var__20__y__28644__28646__28668__28670__28672__28674__28676] :
( t(Vvar__var__var__var__var__var__var__20__y__28644__28646__28668__28670__28672__28674__28676,Vvar__8__C__28555)
=> p(happ(happ(Vvar__7__req__28550,happ(Vvar__16__phi__28581,happ(happ(Vvar__11__cadd__28558,Vvar__var__var__var__var__var__var__19__x__28643__28645__28667__28669__28671__28673__28675),Vvar__var__var__var__var__var__var__20__y__28644__28646__28668__28670__28672__28674__28676))),happ(happ(Vvar__3__radd__28532,happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__var__19__x__28643__28645__28667__28669__28671__28673__28675)),happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__var__20__y__28644__28646__28668__28670__28672__28674__28676)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__28648__28650__28677__28679__28681__28683__28685] :
( t(Vvar__var__var__var__var__var__var__20__x__28648__28650__28677__28679__28681__28683__28685,Vvar__8__C__28555)
=> ! [Vvar__var__var__var__var__var__var__21__y__28649__28651__28678__28680__28682__28684__28686] :
( t(Vvar__var__var__var__var__var__var__21__y__28649__28651__28678__28680__28682__28684__28686,Vvar__8__C__28555)
=> p(happ(happ(Vvar__7__req__28550,happ(Vvar__16__phi__28581,happ(happ(Vvar__13__csub__28568,Vvar__var__var__var__var__var__var__20__x__28648__28650__28677__28679__28681__28683__28685),Vvar__var__var__var__var__var__var__21__y__28649__28651__28678__28680__28682__28684__28686))),happ(happ(Vvar__5__rsub__28542,happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__var__20__x__28648__28650__28677__28679__28681__28683__28685)),happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__var__21__y__28649__28651__28678__28680__28682__28684__28686)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__28653__28655__28687__28689__28691__28693__28695] :
( t(Vvar__var__var__var__var__var__var__21__x__28653__28655__28687__28689__28691__28693__28695,Vvar__8__C__28555)
=> ! [Vvar__var__var__var__var__var__var__22__y__28654__28656__28688__28690__28692__28694__28696] :
( t(Vvar__var__var__var__var__var__var__22__y__28654__28656__28688__28690__28692__28694__28696,Vvar__8__C__28555)
=> p(happ(happ(Vvar__7__req__28550,happ(Vvar__16__phi__28581,happ(happ(Vvar__12__cmul__28563,Vvar__var__var__var__var__var__var__21__x__28653__28655__28687__28689__28691__28693__28695),Vvar__var__var__var__var__var__var__22__y__28654__28656__28688__28690__28692__28694__28696))),happ(happ(Vvar__4__rmul__28537,happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__var__21__x__28653__28655__28687__28689__28691__28693__28695)),happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__var__22__y__28654__28656__28688__28690__28692__28694__28696)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__28658__28659__28697__28698__28699__28700__28701] :
( t(Vvar__var__var__var__var__var__var__22__x__28658__28659__28697__28698__28699__28700__28701,Vvar__8__C__28555)
=> p(happ(happ(Vvar__7__req__28550,happ(Vvar__16__phi__28581,happ(Vvar__14__copp__28573,Vvar__var__var__var__var__var__var__22__x__28658__28659__28697__28698__28699__28700__28701))),happ(Vvar__6__ropp__28547,happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__var__22__x__28658__28659__28697__28698__28699__28700__28701)))) )
& ! [Vvar__var__var__var__var__var__23__x__28661__28664__28702__28705__28708__28711] :
( t(Vvar__var__var__var__var__var__23__x__28661__28664__28702__28705__28708__28711,Vvar__8__C__28555)
=> ! [Vvar__var__var__var__var__var__24__y__28662__28665__28703__28706__28709__28712] :
( t(Vvar__var__var__var__var__var__24__y__28662__28665__28703__28706__28709__28712,Vvar__8__C__28555)
=> ( happ(happ(Vvar__15__ceqb__28576,Vvar__var__var__var__var__var__23__x__28661__28664__28702__28705__28708__28711),Vvar__var__var__var__var__var__24__y__28662__28665__28703__28706__28709__28712) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__28550,happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__23__x__28661__28664__28702__28705__28708__28711)),happ(Vvar__16__phi__28581,Vvar__var__var__var__var__var__24__y__28662__28665__28703__28706__28709__28712))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__15508,Vvar__1__rO__15509,Vvar__2__rI__15510,Vvar__3__radd__15511,Vvar__4__rmul__15516,Vvar__5__rsub__15521,Vvar__6__ropp__15526,Vvar__7__req__15529] :
( cType___24t(Vvar__0__R__15508)
=> ( t(Vvar__1__rO__15509,Vvar__0__R__15508)
=> ( t(Vvar__2__rI__15510,Vvar__0__R__15508)
=> ( c_24__type__15732___24t(Vvar__0__R__15508,Vvar__1__rO__15509,Vvar__2__rI__15510,Vvar__3__radd__15511,Vvar__4__rmul__15516,Vvar__5__rsub__15521,Vvar__6__ropp__15526,Vvar__7__req__15529,Vvar__3__radd__15511)
=> ( c_24__type__15795___24t(Vvar__0__R__15508,Vvar__1__rO__15509,Vvar__2__rI__15510,Vvar__3__radd__15511,Vvar__4__rmul__15516,Vvar__5__rsub__15521,Vvar__6__ropp__15526,Vvar__7__req__15529,Vvar__4__rmul__15516)
=> ( c_24__type__15858___24t(Vvar__0__R__15508,Vvar__1__rO__15509,Vvar__2__rI__15510,Vvar__3__radd__15511,Vvar__4__rmul__15516,Vvar__5__rsub__15521,Vvar__6__ropp__15526,Vvar__7__req__15529,Vvar__5__rsub__15521)
=> ( c_24__type__15912___24t(Vvar__0__R__15508,Vvar__1__rO__15509,Vvar__2__rI__15510,Vvar__3__radd__15511,Vvar__4__rmul__15516,Vvar__5__rsub__15521,Vvar__6__ropp__15526,Vvar__7__req__15529,Vvar__6__ropp__15526)
=> ( c_24__type__15975___24t(Vvar__0__R__15508,Vvar__1__rO__15509,Vvar__2__rI__15510,Vvar__3__radd__15511,Vvar__4__rmul__15516,Vvar__5__rsub__15521,Vvar__6__ropp__15526,Vvar__7__req__15529,Vvar__7__req__15529)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__15508,Vvar__1__rO__15509,Vvar__2__rI__15510,Vvar__3__radd__15511,Vvar__4__rmul__15516,Vvar__5__rsub__15521,Vvar__6__ropp__15526,Vvar__7__req__15529)
=> ( ! [Vvar__var__var__var__var__var__8__x__15562__15563__15606__15607__15608__15609] :
( t(Vvar__var__var__var__var__var__8__x__15562__15563__15606__15607__15608__15609,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__3__radd__15511,Vvar__1__rO__15509),Vvar__var__var__var__var__var__8__x__15562__15563__15606__15607__15608__15609)),Vvar__var__var__var__var__var__8__x__15562__15563__15606__15607__15608__15609)) )
& ! [Vvar__var__var__var__var__9__x__15565__15567__15610__15612__15614] :
( t(Vvar__var__var__var__var__9__x__15565__15567__15610__15612__15614,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__10__y__15566__15568__15611__15613__15615] :
( t(Vvar__var__var__var__var__10__y__15566__15568__15611__15613__15615,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__9__x__15565__15567__15610__15612__15614),Vvar__var__var__var__var__10__y__15566__15568__15611__15613__15615)),happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__10__y__15566__15568__15611__15613__15615),Vvar__var__var__var__var__9__x__15565__15567__15610__15612__15614))) ) )
& ! [Vvar__var__var__var__var__10__x__15570__15573__15616__15619__15622] :
( t(Vvar__var__var__var__var__10__x__15570__15573__15616__15619__15622,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__11__y__15571__15574__15617__15620__15623] :
( t(Vvar__var__var__var__var__11__y__15571__15574__15617__15620__15623,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__12__z__15572__15575__15618__15621__15624] :
( t(Vvar__var__var__var__var__12__z__15572__15575__15618__15621__15624,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__10__x__15570__15573__15616__15619__15622),happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__11__y__15571__15574__15617__15620__15623),Vvar__var__var__var__var__12__z__15572__15575__15618__15621__15624))),happ(happ(Vvar__3__radd__15511,happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__10__x__15570__15573__15616__15619__15622),Vvar__var__var__var__var__11__y__15571__15574__15617__15620__15623)),Vvar__var__var__var__var__12__z__15572__15575__15618__15621__15624))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__15577__15578__15625__15626__15627__15628] :
( t(Vvar__var__var__var__var__var__11__x__15577__15578__15625__15626__15627__15628,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__4__rmul__15516,Vvar__2__rI__15510),Vvar__var__var__var__var__var__11__x__15577__15578__15625__15626__15627__15628)),Vvar__var__var__var__var__var__11__x__15577__15578__15625__15626__15627__15628)) )
& ! [Vvar__var__var__var__var__12__x__15580__15582__15629__15631__15633] :
( t(Vvar__var__var__var__var__12__x__15580__15582__15629__15631__15633,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__13__y__15581__15583__15630__15632__15634] :
( t(Vvar__var__var__var__var__13__y__15581__15583__15630__15632__15634,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__4__rmul__15516,Vvar__var__var__var__var__12__x__15580__15582__15629__15631__15633),Vvar__var__var__var__var__13__y__15581__15583__15630__15632__15634)),happ(happ(Vvar__4__rmul__15516,Vvar__var__var__var__var__13__y__15581__15583__15630__15632__15634),Vvar__var__var__var__var__12__x__15580__15582__15629__15631__15633))) ) )
& ! [Vvar__var__var__var__var__13__x__15585__15588__15635__15638__15641] :
( t(Vvar__var__var__var__var__13__x__15585__15588__15635__15638__15641,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__14__y__15586__15589__15636__15639__15642] :
( t(Vvar__var__var__var__var__14__y__15586__15589__15636__15639__15642,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__15__z__15587__15590__15637__15640__15643] :
( t(Vvar__var__var__var__var__15__z__15587__15590__15637__15640__15643,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__4__rmul__15516,Vvar__var__var__var__var__13__x__15585__15588__15635__15638__15641),happ(happ(Vvar__4__rmul__15516,Vvar__var__var__var__var__14__y__15586__15589__15636__15639__15642),Vvar__var__var__var__var__15__z__15587__15590__15637__15640__15643))),happ(happ(Vvar__4__rmul__15516,happ(happ(Vvar__4__rmul__15516,Vvar__var__var__var__var__13__x__15585__15588__15635__15638__15641),Vvar__var__var__var__var__14__y__15586__15589__15636__15639__15642)),Vvar__var__var__var__var__15__z__15587__15590__15637__15640__15643))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__15592__15595__15644__15647__15650__15653] :
( t(Vvar__var__var__var__var__var__14__x__15592__15595__15644__15647__15650__15653,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__var__15__y__15593__15596__15645__15648__15651__15654] :
( t(Vvar__var__var__var__var__var__15__y__15593__15596__15645__15648__15651__15654,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__var__16__z__15594__15597__15646__15649__15652__15655] :
( t(Vvar__var__var__var__var__var__16__z__15594__15597__15646__15649__15652__15655,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__4__rmul__15516,happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__var__14__x__15592__15595__15644__15647__15650__15653),Vvar__var__var__var__var__var__15__y__15593__15596__15645__15648__15651__15654)),Vvar__var__var__var__var__var__16__z__15594__15597__15646__15649__15652__15655)),happ(happ(Vvar__3__radd__15511,happ(happ(Vvar__4__rmul__15516,Vvar__var__var__var__var__var__14__x__15592__15595__15644__15647__15650__15653),Vvar__var__var__var__var__var__16__z__15594__15597__15646__15649__15652__15655)),happ(happ(Vvar__4__rmul__15516,Vvar__var__var__var__var__var__15__y__15593__15596__15645__15648__15651__15654),Vvar__var__var__var__var__var__16__z__15594__15597__15646__15649__15652__15655)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__15599__15601__15656__15658__15660__15662__15664] :
( t(Vvar__var__var__var__var__var__var__15__x__15599__15601__15656__15658__15660__15662__15664,Vvar__0__R__15508)
=> ! [Vvar__var__var__var__var__var__var__16__y__15600__15602__15657__15659__15661__15663__15665] :
( t(Vvar__var__var__var__var__var__var__16__y__15600__15602__15657__15659__15661__15663__15665,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__5__rsub__15521,Vvar__var__var__var__var__var__var__15__x__15599__15601__15656__15658__15660__15662__15664),Vvar__var__var__var__var__var__var__16__y__15600__15602__15657__15659__15661__15663__15665)),happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__var__var__15__x__15599__15601__15656__15658__15660__15662__15664),happ(Vvar__6__ropp__15526,Vvar__var__var__var__var__var__var__16__y__15600__15602__15657__15659__15661__15663__15665)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__15604__15605__15666__15667__15668__15669__15670] :
( t(Vvar__var__var__var__var__var__var__16__x__15604__15605__15666__15667__15668__15669__15670,Vvar__0__R__15508)
=> p(happ(happ(Vvar__7__req__15529,happ(happ(Vvar__3__radd__15511,Vvar__var__var__var__var__var__var__16__x__15604__15605__15666__15667__15668__15669__15670),happ(Vvar__6__ropp__15526,Vvar__var__var__var__var__var__var__16__x__15604__15605__15666__15667__15668__15669__15670))),Vvar__1__rO__15509)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567] :
( cType___24t(Vvar__0__R__27531)
=> ( t(Vvar__1__rO__27532,Vvar__0__R__27531)
=> ( t(Vvar__2__rI__27533,Vvar__0__R__27531)
=> ( c_24__type__27784___24t(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567,Vvar__3__radd__27534)
=> ( c_24__type__27909___24t(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567,Vvar__4__rmul__27539)
=> ( c_24__type__28034___24t(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567,Vvar__5__req__27544)
=> ( cType___24t(Vvar__6__C__27549)
=> ( t(Vvar__7__cO__27550,Vvar__6__C__27549)
=> ( t(Vvar__8__cI__27551,Vvar__6__C__27549)
=> ( c_24__type__28159___24t(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567,Vvar__9__cadd__27552)
=> ( c_24__type__28284___24t(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567,Vvar__10__cmul__27557)
=> ( c_24__type__28409___24t(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567,Vvar__11__ceqb__27562)
=> ( c_24__type__28520___24t(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567,Vvar__12__phi__27567)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__27531,Vvar__1__rO__27532,Vvar__2__rI__27533,Vvar__3__radd__27534,Vvar__4__rmul__27539,Vvar__5__req__27544,Vvar__6__C__27549,Vvar__7__cO__27550,Vvar__8__cI__27551,Vvar__9__cadd__27552,Vvar__10__cmul__27557,Vvar__11__ceqb__27562,Vvar__12__phi__27567)
=> ( p(happ(happ(Vvar__5__req__27544,happ(Vvar__12__phi__27567,Vvar__7__cO__27550)),Vvar__1__rO__27532))
& p(happ(happ(Vvar__5__req__27544,happ(Vvar__12__phi__27567,Vvar__8__cI__27551)),Vvar__2__rI__27533))
& ! [Vvar__var__var__var__var__var__var__15__x__27613__27615__27629__27631__27633__27635__27637] :
( t(Vvar__var__var__var__var__var__var__15__x__27613__27615__27629__27631__27633__27635__27637,Vvar__6__C__27549)
=> ! [Vvar__var__var__var__var__var__var__16__y__27614__27616__27630__27632__27634__27636__27638] :
( t(Vvar__var__var__var__var__var__var__16__y__27614__27616__27630__27632__27634__27636__27638,Vvar__6__C__27549)
=> p(happ(happ(Vvar__5__req__27544,happ(Vvar__12__phi__27567,happ(happ(Vvar__9__cadd__27552,Vvar__var__var__var__var__var__var__15__x__27613__27615__27629__27631__27633__27635__27637),Vvar__var__var__var__var__var__var__16__y__27614__27616__27630__27632__27634__27636__27638))),happ(happ(Vvar__3__radd__27534,happ(Vvar__12__phi__27567,Vvar__var__var__var__var__var__var__15__x__27613__27615__27629__27631__27633__27635__27637)),happ(Vvar__12__phi__27567,Vvar__var__var__var__var__var__var__16__y__27614__27616__27630__27632__27634__27636__27638)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__27618__27620__27639__27641__27643__27645__27647] :
( t(Vvar__var__var__var__var__var__var__16__x__27618__27620__27639__27641__27643__27645__27647,Vvar__6__C__27549)
=> ! [Vvar__var__var__var__var__var__var__17__y__27619__27621__27640__27642__27644__27646__27648] :
( t(Vvar__var__var__var__var__var__var__17__y__27619__27621__27640__27642__27644__27646__27648,Vvar__6__C__27549)
=> p(happ(happ(Vvar__5__req__27544,happ(Vvar__12__phi__27567,happ(happ(Vvar__10__cmul__27557,Vvar__var__var__var__var__var__var__16__x__27618__27620__27639__27641__27643__27645__27647),Vvar__var__var__var__var__var__var__17__y__27619__27621__27640__27642__27644__27646__27648))),happ(happ(Vvar__4__rmul__27539,happ(Vvar__12__phi__27567,Vvar__var__var__var__var__var__var__16__x__27618__27620__27639__27641__27643__27645__27647)),happ(Vvar__12__phi__27567,Vvar__var__var__var__var__var__var__17__y__27619__27621__27640__27642__27644__27646__27648)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__27623__27626__27649__27652__27655__27658] :
( t(Vvar__var__var__var__var__var__17__x__27623__27626__27649__27652__27655__27658,Vvar__6__C__27549)
=> ! [Vvar__var__var__var__var__var__18__y__27624__27627__27650__27653__27656__27659] :
( t(Vvar__var__var__var__var__var__18__y__27624__27627__27650__27653__27656__27659,Vvar__6__C__27549)
=> ( happ(happ(Vvar__11__ceqb__27562,Vvar__var__var__var__var__var__17__x__27623__27626__27649__27652__27655__27658),Vvar__var__var__var__var__var__18__y__27624__27627__27650__27653__27656__27659) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__27544,happ(Vvar__12__phi__27567,Vvar__var__var__var__var__var__17__x__27623__27626__27649__27652__27655__27658)),happ(Vvar__12__phi__27567,Vvar__var__var__var__var__var__18__y__27624__27627__27650__27653__27656__27659))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_14596',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__14596___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__14524___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_18637',axiom,
! [Vv__CANONICAL__0] : c_24__lam__18637___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ ).
fof('$_lam_18639',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__18639___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a1(Vv__CANONICAL__0) ).
fof('$_lam_22033',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__22033___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_36855',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__36855___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2)
| cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__2,Vv__CANONICAL__1) ) ) ).
fof('$_lam_59316',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__59316___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2ebool,c_24__lam__59322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_59322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2etrue
& ( c_24__lam__59322___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(Vv__CANONICAL__0) ) )
| ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2efalse
& ( c_24__lam__59322___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(Vv__CANONICAL__1) ) ) ) ) ).
fof('$_lam_59332',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__59332___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2ebool,c_24__lam__59322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_lam_59347',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__59347___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2ebool,c_24__lam__59322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_lam_78226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
& ( c_24__lam__78226___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(Vv__CANONICAL__0)) ) )
| ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
& ( c_24__lam__78226___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_prop_13363',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__13363___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_19713',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__19713___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_34425',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__34425___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_34426',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__34426___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_35312',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__35312___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_type_117',axiom,
! [Vvar__118] :
( c_24__type__117___24t(Vvar__118)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__118,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12',axiom,
! [Vvar__13] :
( c_24__type__12___24t(Vvar__13)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__13,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12714',axiom,
! [Vvar__12715] :
( c_24__type__12714___24t(Vvar__12715)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__12715,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13175',axiom,
! [Vvar__13176] :
( c_24__type__13175___24t(Vvar__13176)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__13176,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13186',axiom,
! [Vvar__13187] :
( c_24__type__13186___24t(Vvar__13187)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__13187,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13189',axiom,
! [Vvar__13190] :
( c_24__type__13189___24t(Vvar__13190)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__13190,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13192',axiom,
! [Vvar__13193] :
( c_24__type__13192___24t(Vvar__13193)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__13193,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13209',axiom,
! [Vvar__13210] :
( c_24__type__13209___24t(Vvar__13210)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__13210,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13214',axiom,
! [Vv__CANONICAL__0,Vvar__13215] :
( c_24__type__13214___24t(Vv__CANONICAL__0,Vvar__13215)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__13215,Vv__CANONICAL__1)) ) ) ).
fof('$_type_13227',axiom,
! [Vvar__13228] :
( c_24__type__13227___24t(Vvar__13228)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13229___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__13234___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__13228,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13229',axiom,
! [Vvar__13230] :
( c_24__type__13229___24t(Vvar__13230)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__13230,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13234',axiom,
! [Vv__CANONICAL__0,Vvar__13235] :
( c_24__type__13234___24t(Vv__CANONICAL__0,Vvar__13235)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__13235,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_13251',axiom,
! [Vvar__13252] :
( c_24__type__13251___24t(Vvar__13252)
<=> ! [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__13252,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13253',axiom,
! [Vvar__13254] :
( c_24__type__13253___24t(Vvar__13254)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__13254,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13286',axiom,
! [Vvar__13287] :
( c_24__type__13286___24t(Vvar__13287)
<=> ! [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__13287,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13291',axiom,
! [Vvar__13292] :
( c_24__type__13291___24t(Vvar__13292)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__13292,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13303',axiom,
! [Vvar__13304] :
( c_24__type__13303___24t(Vvar__13304)
<=> ! [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__13304,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_13315',axiom,
! [Vvar__13316] :
( c_24__type__13315___24t(Vvar__13316)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__13316,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_13335',axiom,
! [Vvar__13336] :
( c_24__type__13335___24t(Vvar__13336)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__13336,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13340',axiom,
! [Vvar__13341] :
( c_24__type__13340___24t(Vvar__13341)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__13341,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13342',axiom,
! [Vvar__13343] :
( c_24__type__13342___24t(Vvar__13343)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__13343,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13361',axiom,
! [Vvar__13362] :
( c_24__type__13361___24t(Vvar__13362)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__13362,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13370',axiom,
! [Vvar__13371] :
( c_24__type__13370___24t(Vvar__13371)
<=> ! [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)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__13371,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_13378',axiom,
! [Vvar__13379] :
( c_24__type__13378___24t(Vvar__13379)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__13379,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_13592',axiom,
! [Vvar__13593] :
( c_24__type__13592___24t(Vvar__13593)
<=> ! [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__13593,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13597',axiom,
! [Vvar__13598] :
( c_24__type__13597___24t(Vvar__13598)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__13598,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13605',axiom,
! [Vvar__13606] :
( c_24__type__13605___24t(Vvar__13606)
<=> ! [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__13606,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13631',axiom,
! [Vvar__13632] :
( c_24__type__13631___24t(Vvar__13632)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__13632,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13636',axiom,
! [Vv__CANONICAL__0,Vvar__13637] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vvar__13637)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13637,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13657',axiom,
! [Vv__CANONICAL__0,Vvar__13658] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vvar__13658)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__13658,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_13702',axiom,
! [Vvar__13703] :
( c_24__type__13702___24t(Vvar__13703)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___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__13703,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_13754',axiom,
! [Vvar__13755] :
( c_24__type__13754___24t(Vvar__13755)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__13755,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_13849',axiom,
! [Vvar__13850] :
( c_24__type__13849___24t(Vvar__13850)
<=> ! [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__13850,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13858',axiom,
! [Vvar__13859] :
( c_24__type__13858___24t(Vvar__13859)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(Vvar__13859,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13861',axiom,
! [Vvar__13862] :
( c_24__type__13861___24t(Vvar__13862)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__13862,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13869',axiom,
! [Vvar__13870] :
( c_24__type__13869___24t(Vvar__13870)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__13870,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13871',axiom,
! [Vvar__13872] :
( c_24__type__13871___24t(Vvar__13872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__13872,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13874',axiom,
! [Vvar__13875] :
( c_24__type__13874___24t(Vvar__13875)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__13875,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13885',axiom,
! [Vvar__13886] :
( c_24__type__13885___24t(Vvar__13886)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__13886,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13892',axiom,
! [Vvar__13893] :
( c_24__type__13892___24t(Vvar__13893)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__13893,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13928',axiom,
! [Vvar__13929] :
( c_24__type__13928___24t(Vvar__13929)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13938___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__13929,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('$_type_13938',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13939] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13939)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__13939,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_13952',axiom,
! [Vvar__13953] :
( c_24__type__13952___24t(Vvar__13953)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13956___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__13953,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13956',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13957] :
( c_24__type__13956___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13957)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__13957,Vv__CANONICAL__2)) ) ) ).
fof('$_type_13990',axiom,
! [Vvar__13991] :
( c_24__type__13990___24t(Vvar__13991)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13999___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__13991,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_13999',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14000] :
( c_24__type__13999___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14000)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(Vvar__14000,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_14055',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14056] :
( c_24__type__14055___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14056)
<=> ! [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__14056,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_14067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14068] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14068)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__14068,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_14076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14077] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14077)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__14077,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_14243',axiom,
! [Vv__CANONICAL__0,Vvar__14244] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vvar__14244)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14244,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_14254',axiom,
! [Vvar__14255] :
( c_24__type__14254___24t(Vvar__14255)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14243___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__14255,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_14503',axiom,
! [Vvar__14504] :
( c_24__type__14503___24t(Vvar__14504)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__14504,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14506',axiom,
! [Vvar__14507] :
( c_24__type__14506___24t(Vvar__14507)
<=> ! [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__14507,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14511',axiom,
! [Vvar__14512] :
( c_24__type__14511___24t(Vvar__14512)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__14512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14520',axiom,
! [Vvar__14521] :
( c_24__type__14520___24t(Vvar__14521)
<=> ! [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__14521,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14728',axiom,
! [Vvar__14729] :
( c_24__type__14728___24t(Vvar__14729)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14729,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_14746',axiom,
! [Vv__CANONICAL__0,Vvar__14747] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vvar__14747)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__14747,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_14906',axiom,
! [Vvar__14907] :
( c_24__type__14906___24t(Vvar__14907)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14907,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_14940',axiom,
! [Vvar__14941] :
( c_24__type__14940___24t(Vvar__14941)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13636___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__14941,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_14961',axiom,
! [Vvar__14962] :
( c_24__type__14961___24t(Vvar__14962)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__14962,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_15215',axiom,
! [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__15216] :
( c_24__type__15215___24t(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__15216)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15216,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15278',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15279] :
( c_24__type__15278___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15279)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15279,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15341',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15342] :
( c_24__type__15341___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15342)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15342,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15395',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15396] :
( c_24__type__15395___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15396)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__15396,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_15458',axiom,
! [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__15459] :
( c_24__type__15458___24t(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__15459)
<=> ! [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__15459,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_15732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15733] :
( c_24__type__15732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15733)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15733,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15795',axiom,
! [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__15796] :
( c_24__type__15795___24t(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__15796)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15796,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15858',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15859] :
( c_24__type__15858___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15859)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15859,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15912',axiom,
! [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__15913] :
( c_24__type__15912___24t(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__15913)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__15913,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_15975',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15976] :
( c_24__type__15975___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__15976)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__15976,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_16100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16101] :
( c_24__type__16100___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16101)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16101,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16131] :
( c_24__type__16130___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16131)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16131,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16154',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16155] :
( c_24__type__16154___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16155)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__16155,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_16184',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16185] :
( c_24__type__16184___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16185)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__16185,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_16214',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16215] :
( c_24__type__16214___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16215)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16215,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16238',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16239] :
( c_24__type__16238___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16239)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__16239,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_16271',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16272] :
( c_24__type__16271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16272)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16272,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16295',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16296] :
( c_24__type__16295___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16296)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__16296,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_16322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16323] :
( c_24__type__16322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__16323)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__16323,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_16378',axiom,
! [Vvar__16379] :
( c_24__type__16378___24t(Vvar__16379)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__16379,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16381',axiom,
! [Vvar__16382] :
( c_24__type__16381___24t(Vvar__16382)
<=> ! [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__16382,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16386',axiom,
! [Vvar__16387] :
( c_24__type__16386___24t(Vvar__16387)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__16387,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_16391',axiom,
! [Vvar__16392] :
( c_24__type__16391___24t(Vvar__16392)
<=> ! [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__16392,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_16412',axiom,
! [Vvar__16413] :
( c_24__type__16412___24t(Vvar__16413)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__16414___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__16422___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__16413,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_16414',axiom,
! [Vvar__16415] :
( c_24__type__16414___24t(Vvar__16415)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__16415,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16422',axiom,
! [Vv__CANONICAL__0,Vvar__16423] :
( c_24__type__16422___24t(Vv__CANONICAL__0,Vvar__16423)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__16423,Vv__CANONICAL__1),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ) ).
fof('$_type_16755',axiom,
! [Vvar__16756] :
( c_24__type__16755___24t(Vvar__16756)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eZeven_2eZeven___24a1(Vv__CANONICAL__0),cCoq_2eZArith_2eZeven_2eZodd___24a1(Vv__CANONICAL__0),happ(Vvar__16756,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16816',axiom,
! [Vvar__16817] :
( c_24__type__16816___24t(Vvar__16817)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__16817,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16853',axiom,
! [Vvar__16854] :
( c_24__type__16853___24t(Vvar__16854)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__2,Vv__CANONICAL__0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__3,Vv__CANONICAL__1)) = Vv__CANONICAL__4
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(happ(Vvar__16854,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ) ).
fof('$_type_16869',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16870] :
( c_24__type__16869___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16870)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cType___24t(happ(Vvar__16870,Vv__CANONICAL__3)) ) ) ).
fof('$_type_16908',axiom,
! [Vvar__16909] :
( c_24__type__16908___24t(Vvar__16909)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__16912___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__16941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__16909,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_16912',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16913] :
( c_24__type__16912___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16913)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__16913,Vv__CANONICAL__2)) ) ) ).
fof('$_type_16941',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16942] :
( c_24__type__16941___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__16942)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__5)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__3,Vv__CANONICAL__0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__4,Vv__CANONICAL__1)) = Vv__CANONICAL__5
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(Vvar__16942,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5))) ) ) ) ) ) ) ).
fof('$_type_16945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16946] :
( c_24__type__16945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16946)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__16946,Vv__CANONICAL__2)) ) ) ).
fof('$_type_18641',axiom,
! [Vvar__18642] :
( c_24__type__18641___24t(Vvar__18642)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__18642,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18835',axiom,
! [Vvar__18836] :
( c_24__type__18835___24t(Vvar__18836)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__18836,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18872',axiom,
! [Vvar__18873] :
( c_24__type__18872___24t(Vvar__18873)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ( Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__2,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vv__CANONICAL__1)),Vv__CANONICAL__3)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__3))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__3,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vv__CANONICAL__1)))
=> cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__18873,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ) ).
fof('$_type_19090',axiom,
! [Vvar__19091] :
( c_24__type__19090___24t(Vvar__19091)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__19091,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19157',axiom,
! [Vvar__19158] :
( c_24__type__19157___24t(Vvar__19158)
<=> ! [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__19158,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19160',axiom,
! [Vvar__19161] :
( c_24__type__19160___24t(Vvar__19161)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__19161,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19197',axiom,
! [Vvar__19198] :
( c_24__type__19197___24t(Vvar__19198)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13657___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__19198,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_19204',axiom,
! [Vvar__19205] :
( c_24__type__19204___24t(Vvar__19205)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__19205,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19220',axiom,
! [Vvar__19221] :
( c_24__type__19220___24t(Vvar__19221)
<=> ! [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__19221,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19222',axiom,
! [Vvar__19223] :
( c_24__type__19222___24t(Vvar__19223)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__19223,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19298',axiom,
! [Vvar__19299] :
( c_24__type__19298___24t(Vvar__19299)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__19299,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19307',axiom,
! [Vvar__19308] :
( c_24__type__19307___24t(Vvar__19308)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__19308,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19311',axiom,
! [Vvar__19312] :
( c_24__type__19311___24t(Vvar__19312)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__19312,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19318',axiom,
! [Vvar__19319] :
( c_24__type__19318___24t(Vvar__19319)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__19319,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19321',axiom,
! [Vvar__19322] :
( c_24__type__19321___24t(Vvar__19322)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__19322,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19325',axiom,
! [Vvar__19326] :
( c_24__type__19325___24t(Vvar__19326)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__19326,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19459',axiom,
! [Vvar__19460] :
( c_24__type__19459___24t(Vvar__19460)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__19460,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19818',axiom,
! [Vvar__19819] :
( c_24__type__19818___24t(Vvar__19819)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__19819,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19822',axiom,
! [Vvar__19823] :
( c_24__type__19822___24t(Vvar__19823)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__19823,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19967',axiom,
! [Vvar__19968] :
( c_24__type__19967___24t(Vvar__19968)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__19968,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20576',axiom,
! [Vvar__20577] :
( c_24__type__20576___24t(Vvar__20577)
<=> ! [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__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__14076___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__20577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__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('$_type_20627',axiom,
! [Vvar__20628] :
( c_24__type__20627___24t(Vvar__20628)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__20628,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20647',axiom,
! [Vvar__20648] :
( c_24__type__20647___24t(Vvar__20648)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__20648,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20866',axiom,
! [Vvar__20867] :
( c_24__type__20866___24t(Vvar__20867)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__399___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__20867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_21340',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__21341] :
( c_24__type__21340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__21341)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21341,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21441',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21442] :
( c_24__type__21441___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21442)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21442,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21542',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__21543] :
( c_24__type__21542___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__21543)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21543,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21632',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21633] :
( c_24__type__21632___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21633)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__21633,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_21733',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__21734] :
( c_24__type__21733___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__21734)
<=> ! [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__21734,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_21834',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21835] :
( c_24__type__21834___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21835)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21835,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_21935',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__21936] :
( c_24__type__21935___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__21936)
<=> ! [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__21936,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_21994',axiom,
! [Vvar__21995] :
( c_24__type__21994___24t(Vvar__21995)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21995,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21998',axiom,
! [Vvar__21999] :
( c_24__type__21998___24t(Vvar__21999)
<=> ! [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__21999,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22003',axiom,
! [Vvar__22004] :
( c_24__type__22003___24t(Vvar__22004)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__22004,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22008',axiom,
! [Vvar__22009] :
( c_24__type__22008___24t(Vvar__22009)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__22009,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22011',axiom,
! [Vvar__22012] :
( c_24__type__22011___24t(Vvar__22012)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22012,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22019',axiom,
! [Vvar__22020] :
( c_24__type__22019___24t(Vvar__22020)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13871___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__22020,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22029',axiom,
! [Vvar__22030] :
( c_24__type__22029___24t(Vvar__22030)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__22030,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22035',axiom,
! [Vvar__22036] :
( c_24__type__22035___24t(Vvar__22036)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22036,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22038',axiom,
! [Vvar__22039] :
( c_24__type__22038___24t(Vvar__22039)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22040___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22039,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22040',axiom,
! [Vvar__22041] :
( c_24__type__22040___24t(Vvar__22041)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22041,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22042',axiom,
! [Vvar__22043] :
( c_24__type__22042___24t(Vvar__22043)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22040___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22043,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22590',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__22591] :
( c_24__type__22590___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__22591)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22591,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22936',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22937] :
( c_24__type__22936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22937)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22937,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23282',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23283] :
( c_24__type__23282___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23283)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23283,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23606] :
( c_24__type__23605___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23606)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__23606,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_23951',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23952] :
( c_24__type__23951___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23952)
<=> ! [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__23952,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_24297',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24298] :
( c_24__type__24297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24298)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24298,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_24643',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__24644] :
( c_24__type__24643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__24644)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__24644,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_24989',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24990] :
( c_24__type__24989___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24990)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__24990,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_25',axiom,
! [Vvar__26] :
( c_24__type__25___24t(Vvar__26)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__26,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25335',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25336] :
( c_24__type__25335___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25336)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__25336,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_25658',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25659] :
( c_24__type__25658___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25659)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__25659,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_26004',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26005] :
( c_24__type__26004___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26005)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26005,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_26350',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26351] :
( c_24__type__26350___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26351)
<=> ! [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__26351,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_26673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26674] :
( c_24__type__26673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26674)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__26674,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_26996',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26997] :
( c_24__type__26996___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26997)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__26997,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_27342',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27343] :
( c_24__type__27342___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27343)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__27343,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27511',axiom,
! [Vvar__27512] :
( c_24__type__27511___24t(Vvar__27512)
<=> ! [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__27512,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27516',axiom,
! [Vvar__27517] :
( c_24__type__27516___24t(Vvar__27517)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__27517,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27524',axiom,
! [Vvar__27525] :
( c_24__type__27524___24t(Vvar__27525)
<=> ! [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__27525,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27529',axiom,
! [Vvar__27530] :
( c_24__type__27529___24t(Vvar__27530)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__27530,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27784',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__27785] :
( c_24__type__27784___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__27785)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27785,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__27910] :
( c_24__type__27909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__27910)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27910,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28034',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28035] :
( c_24__type__28034___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28035)
<=> ! [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__28035,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_28159',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28160] :
( c_24__type__28159___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28160)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__28160,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_28284',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28285] :
( c_24__type__28284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28285)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__28285,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_28409',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28410] :
( c_24__type__28409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__28410)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__28410,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_28520',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28521] :
( c_24__type__28520___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28521)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__28521,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_28925',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28926] :
( c_24__type__28925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28926)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28926,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29138',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29139] :
( c_24__type__29138___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29139)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29139,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29351',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__29352] :
( c_24__type__29351___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__29352)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29352,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29546',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29547] :
( c_24__type__29546___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29547)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__29547,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_29759',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__29760] :
( c_24__type__29759___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__29760)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29760,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_29972',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29973] :
( c_24__type__29972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29973)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__29973,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_30',axiom,
! [Vvar__31] :
( c_24__type__30___24t(Vvar__31)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30185',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30186] :
( c_24__type__30185___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30186)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__30186,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_30398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30399] :
( c_24__type__30398___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30399)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__30399,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_30593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30594] :
( c_24__type__30593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30594)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__30594,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_30806',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30807] :
( c_24__type__30806___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30807)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__30807,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_31001',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31002] :
( c_24__type__31001___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31002)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__31002,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_31014',axiom,
! [Vvar__31015] :
( c_24__type__31014___24t(Vvar__31015)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31015,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31119] :
( c_24__type__31118___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31119)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31119,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31163] :
( c_24__type__31162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31163)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31163,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_31198',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31199] :
( c_24__type__31198___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31199)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__31199,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_31242',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31243] :
( c_24__type__31242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31243)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__31243,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31256',axiom,
! [Vvar__31257] :
( c_24__type__31256___24t(Vvar__31257)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__31257,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31259',axiom,
! [Vvar__31260] :
( c_24__type__31259___24t(Vvar__31260)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31260,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31271',axiom,
! [Vvar__31272] :
( c_24__type__31271___24t(Vvar__31272)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__31272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31347',axiom,
! [Vvar__31348] :
( c_24__type__31347___24t(Vvar__31348)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__31348,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31442',axiom,
! [Vvar__31443] :
( c_24__type__31442___24t(Vvar__31443)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__2))
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__8)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__4,Vv__CANONICAL__0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__5,Vv__CANONICAL__1)) = Vv__CANONICAL__6
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__7,Vv__CANONICAL__0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__8,Vv__CANONICAL__1)) = Vv__CANONICAL__2
=> ( ! [Vv__CANONICAL__11] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__11)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vv__CANONICAL__6,Vv__CANONICAL__2,Vv__CANONICAL__11)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__11) ) )
=> cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(happ(happ(happ(happ(Vvar__31443,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_31996',axiom,
! [Vvar__31997] :
( c_24__type__31996___24t(Vvar__31997)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__31997,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32002',axiom,
! [Vv__CANONICAL__0,Vvar__32003] :
( c_24__type__32002___24t(Vv__CANONICAL__0,Vvar__32003)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__32003,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_323',axiom,
! [Vvar__324] :
( c_24__type__323___24t(Vvar__324)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__324,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32497',axiom,
! [Vvar__32498] :
( c_24__type__32497___24t(Vvar__32498)
<=> ! [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__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__14076___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__32498,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__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_33224',axiom,
! [Vvar__33225] :
( c_24__type__33224___24t(Vvar__33225)
<=> ! [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__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__14055___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__33256___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__17)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__33225,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_33256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33257] :
( c_24__type__33256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33257)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__33257,Vv__CANONICAL__3)) ) ) ).
fof('$_type_34423',axiom,
! [Vvar__34424] :
( c_24__type__34423___24t(Vvar__34424)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__34425___24a1(Vv__CANONICAL__0),c_24__prop__34426___24a1(Vv__CANONICAL__0),happ(Vvar__34424,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35250',axiom,
! [Vvar__35251] :
( c_24__type__35250___24t(Vvar__35251)
<=> ! [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__35251,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35298',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35299] :
( c_24__type__35298___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35299)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__35299,Vv__CANONICAL__4)) ) ) ).
fof('$_type_35307',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35308] :
( c_24__type__35307___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__35308)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__35308,Vv__CANONICAL__4)) ) ) ).
fof('$_type_35350',axiom,
! [Vvar__35351] :
( c_24__type__35350___24t(Vvar__35351)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35351,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36605',axiom,
! [Vvar__36606] :
( c_24__type__36605___24t(Vvar__36606)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36610___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__36606,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36610',axiom,
! [Vv__CANONICAL__0,Vvar__36611] :
( c_24__type__36610___24t(Vv__CANONICAL__0,Vvar__36611)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__36611,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_36732',axiom,
! [Vvar__36733] :
( c_24__type__36732___24t(Vvar__36733)
<=> ! [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__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__10)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__36733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_36859',axiom,
! [Vvar__36860] :
( c_24__type__36859___24t(Vvar__36860)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__36860,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_376',axiom,
! [Vvar__377] :
( c_24__type__376___24t(Vvar__377)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__377,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_392',axiom,
! [Vvar__393] :
( c_24__type__392___24t(Vvar__393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_399',axiom,
! [Vv__CANONICAL__0,Vvar__400] :
( c_24__type__399___24t(Vv__CANONICAL__0,Vvar__400)
<=> ! [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__400,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_401',axiom,
! [Vvar__402] :
( c_24__type__401___24t(Vvar__402)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__402,Vv__CANONICAL__0)) ) ) ).
fof('$_type_410',axiom,
! [Vvar__411] :
( c_24__type__410___24t(Vvar__411)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__97___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__411,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_443',axiom,
! [Vvar__444] :
( c_24__type__443___24t(Vvar__444)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__444,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45',axiom,
! [Vvar__46] :
( c_24__type__45___24t(Vvar__46)
<=> ! [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__46,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_471',axiom,
! [Vvar__472] :
( c_24__type__471___24t(Vvar__472)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__472,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_525',axiom,
! [Vvar__526] :
( c_24__type__525___24t(Vvar__526)
<=> ! [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__526,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57068',axiom,
! [Vvar__57069] :
( c_24__type__57068___24t(Vvar__57069)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__57069,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_57077',axiom,
! [Vvar__57078] :
( c_24__type__57077___24t(Vvar__57078)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13871___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__57078,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_57106',axiom,
! [Vvar__57107] :
( c_24__type__57106___24t(Vvar__57107)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,happ(happ(Vvar__57107,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57851',axiom,
! [Vvar__57852] :
( c_24__type__57851___24t(Vvar__57852)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__57852,Vv__CANONICAL__0)) ) ) ).
fof('$_type_58002',axiom,
! [Vvar__58003] :
( c_24__type__58002___24t(Vvar__58003)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__97___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__58008___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__58020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__58003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_58008',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58009] :
( c_24__type__58008___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58009)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__58009,Vv__CANONICAL__2)) ) ) ).
fof('$_type_58020',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__58021] :
( c_24__type__58020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__58021)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(Vvar__58021,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).
fof('$_type_59363',axiom,
! [Vvar__59364] :
( c_24__type__59363___24t(Vvar__59364)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2ebool,c_24__lam__59322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(Vvar__59364,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_61',axiom,
! [Vvar__62] :
( c_24__type__61___24t(Vvar__62)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__62,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_65004',axiom,
! [Vvar__65005] :
( c_24__type__65004___24t(Vvar__65005)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__65005,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65044',axiom,
! [Vv__CANONICAL__0,Vvar__65045] :
( c_24__type__65044___24t(Vv__CANONICAL__0,Vvar__65045)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__65045,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_65103',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__65104] :
( c_24__type__65103___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__65104)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__65104,Vv__CANONICAL__2)) ) ) ).
fof('$_type_65161',axiom,
! [Vvar__65162] :
( c_24__type__65161___24t(Vvar__65162)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__65162,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_65878',axiom,
! [Vvar__65879] :
( c_24__type__65878___24t(Vvar__65879)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__65879,Vv__CANONICAL__0)) ) ) ).
fof('$_type_68',axiom,
! [Vvar__69] :
( c_24__type__68___24t(Vvar__69)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__69,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_74',axiom,
! [Vvar__75] :
( c_24__type__74___24t(Vvar__75)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__75,Vv__CANONICAL__0)) ) ) ).
fof('$_type_78221',axiom,
! [Vvar__78222] :
( c_24__type__78221___24t(Vvar__78222)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2ebool,c_24__lam__78226___24a1(Vv__CANONICAL__0),happ(Vvar__78222,Vv__CANONICAL__0)) ) ) ).
fof('$_type_90',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__91] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__91)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__91,Vv__CANONICAL__2)) ) ) ).
fof('$_type_94',axiom,
! [Vvar__95] :
( c_24__type__94___24t(Vvar__95)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__97___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__95,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_956',axiom,
! [Vvar__957] :
( c_24__type__956___24t(Vvar__957)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__957,Vv__CANONICAL__0)) ) ) ).
fof('$_type_97',axiom,
! [Vv__CANONICAL__0,Vvar__98] :
( c_24__type__97___24t(Vv__CANONICAL__0,Vvar__98)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__98,Vv__CANONICAL__1)) ) ) ).
fof('$_typeof_ArithCompl.both_odd',axiom,
c_24__type__61___24t(cArithCompl_2eboth__odd) ).
fof('$_typeof_ArithCompl.distinct_parity',axiom,
c_24__type__61___24t(cArithCompl_2edistinct__parity) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__13209___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__13189___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Sumbool.bool_of_sumbool',axiom,
c_24__type__59363___24t(cCoq_2eBool_2eSumbool_2ebool__of__sumbool) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__13342___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__13253___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__13209___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__13251___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__13189___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__35250___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__13340___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__13303___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__13286___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__13291___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__401___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__13227___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__13192___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__13335___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__401___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__13189___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__392___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__376___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__13315___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__376___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__13189___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
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__19967___24t(cCoq_2eInit_2eDecimal_2ePos) ).
fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__13849___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__13849___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__13849___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__13209___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__13849___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__21994___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__21994___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__410___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__16386___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__16391___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__94___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
c_24__type__58002___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__117___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__31271___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__13361___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__19090___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__19157___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__19090___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__31347___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__19157___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__19160___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__13186___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__25___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__25___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__12___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__12___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__471___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__471___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__443___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__19204___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__19197___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
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__443___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_N',axiom,
c_24__type__13186___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__12___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__443___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__12___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit',axiom,
c_24__type__19220___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__19222___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.Qden',axiom,
c_24__type__22008___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__22011___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__21998___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__13861___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__22003___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.QArith.QArith_base.inject_Z',axiom,
c_24__type__13858___24t(cCoq_2eQArith_2eQArith__base_2einject__Z) ).
fof('$_typeof_Coq.Reals.NewtonInt.Newton_integrable',axiom,
c_24__type__36859___24t(cCoq_2eReals_2eNewtonInt_2eNewton__integrable) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.Ranalysis1.antiderivative',axiom,
c_24__type__57077___24t(cCoq_2eReals_2eRanalysis1_2eantiderivative) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt',axiom,
c_24__type__22035___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_abs',axiom,
c_24__type__22029___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_const',axiom,
c_24__type__57106___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__const) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derive_pt',axiom,
c_24__type__57068___24t(cCoq_2eReals_2eRanalysis1_2ederive__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.fct_cte',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRanalysis1_2efct__cte) ).
fof('$_typeof_Coq.Reals.Ranalysis1.mult_fct',axiom,
c_24__type__22019___24t(cCoq_2eReals_2eRanalysis1_2emult__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.no_cond',axiom,
c_24__type__22040___24t(cCoq_2eReals_2eRanalysis1_2eno__cond) ).
fof('$_typeof_Coq.Reals.Ranalysis1.plus_fct',axiom,
c_24__type__22019___24t(cCoq_2eReals_2eRanalysis1_2eplus__fct) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__12714___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Raxioms.bound',axiom,
c_24__type__22042___24t(cCoq_2eReals_2eRaxioms_2ebound) ).
fof('$_typeof_Coq.Reals.Raxioms.is_upper_bound',axiom,
c_24__type__22038___24t(cCoq_2eReals_2eRaxioms_2eis__upper__bound) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__13885___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__13874___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__13874___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__13874___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__65004___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.R_dist',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRfunctions_2eR__dist) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__16816___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_f_R0',axiom,
c_24__type__13892___24t(cCoq_2eReals_2eRfunctions_2esum__f__R0) ).
fof('$_typeof_Coq.Reals.Rlimit.Metric_Space',axiom,
cType___24t(cCoq_2eReals_2eRlimit_2eMetric__Space) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__31256___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Reals.Rseries.EUn',axiom,
c_24__type__16378___24t(cCoq_2eReals_2eRseries_2eEUn) ).
fof('$_typeof_Coq.Reals.Rseries.Un_growing',axiom,
c_24__type__31259___24t(cCoq_2eReals_2eRseries_2eUn__growing) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__401___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__16381___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__61___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Bezout',axiom,
c_24__type__68___24t(cCoq_2eZArith_2eBinInt_2eZ_2eBezout) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Even',axiom,
c_24__type__74___24t(cCoq_2eZArith_2eBinInt_2eZ_2eEven) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Odd',axiom,
c_24__type__74___24t(cCoq_2eZArith_2eBinInt_2eZ_2eOdd) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__19818___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lcm',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinInt_2eZ_2elcm) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.log2_up',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.sqrt_up',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
c_24__type__19311___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__19307___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__323___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div2',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.double',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2edouble) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__956___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__525___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
c_24__type__525___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__956___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__19321___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__19318___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow_pos',axiom,
c_24__type__19298___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot2',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__19459___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.shiftl',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.shiftr',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.square',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.testbit',axiom,
c_24__type__525___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__19311___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__19307___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__19325___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.Wf_Z.natlike_rec',axiom,
c_24__type__16412___24t(cCoq_2eZArith_2eWf__Z_2enatlike__rec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_zerop',axiom,
c_24__type__34423___24t(cCoq_2eZArith_2eZArith__dec_2eZ__zerop) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__525___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeven_odd_bool',axiom,
c_24__type__78221___24t(cCoq_2eZArith_2eZbool_2eZeven__odd__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Zdiv.eqm',axiom,
c_24__type__68___24t(cCoq_2eZArith_2eZdiv_2eeqm) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__74___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven_odd_dec',axiom,
c_24__type__16755___24t(cCoq_2eZArith_2eZeven_2eZeven__odd__dec) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__74___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__16816___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
c_24__type__16853___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid_rect',axiom,
c_24__type__16908___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid__rect) ).
fof('$_typeof_Coq.ZArith.Znumtheory.euclid_rec',axiom,
c_24__type__31442___24t(cCoq_2eZArith_2eZnumtheory_2eeuclid__rec) ).
fof('$_typeof_Coq.ZArith.Znumtheory.rel_prime',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eZnumtheory_2erel__prime) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
c_24__type__18872___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__18835___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.ZArith.Zpower.Zpower_nat',axiom,
c_24__type__18641___24t(cCoq_2eZArith_2eZpower_2eZpower__nat) ).
fof('$_typeof_Coq.ZArith.Zpower.two_p',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eZpower_2etwo__p) ).
fof('$_typeof_Coq.ZArith.Zpower.two_power_pos',axiom,
c_24__type__25___24t(cCoq_2eZArith_2eZpower_2etwo__power__pos) ).
fof('$_typeof_Coq.micromega.Env.jump',axiom,
c_24__type__13370___24t(cCoq_2emicromega_2eEnv_2ejump) ).
fof('$_typeof_Coq.micromega.Env.tail',axiom,
c_24__type__13378___24t(cCoq_2emicromega_2eEnv_2etail) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__13605___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__13592___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__13597___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__65878___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_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.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_pol',axiom,
c_24__type__13928___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pol) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option',axiom,
c_24__type__13952___24t(cCoq_2emicromega_2eRingMicromega_2emap__option) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option2',axiom,
c_24__type__13990___24t(cCoq_2emicromega_2eRingMicromega_2emap__option2) ).
fof('$_typeof_Coq.micromega.RingMicromega.psubC',axiom,
c_24__type__13631___24t(cCoq_2emicromega_2eRingMicromega_2epsubC) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__65161___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
c_24__type__13754___24t(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).
fof('$_typeof_Coq.micromega.ZMicromega.ceiling',axiom,
c_24__type__45___24t(cCoq_2emicromega_2eZMicromega_2eceiling) ).
fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
c_24__type__25___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
c_24__type__25___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__20576___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__36605___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__36732___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__20866___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__20647___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__20627___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__20627___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__35350___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__35350___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__13702___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__13754___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ1',axiom,
c_24__type__13754___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__31996___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__14506___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__14511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__14503___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__32497___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__14511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__14520___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__27529___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__14511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__27524___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__27511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__14254___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__27516___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__33224___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__14906___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__14728___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__31014___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__57851___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__14961___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__14940___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('ArithCompl.Zeven_def1',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
=> ? [V2__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__k)
& V0__z = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V2__k) ) ) ) ).
fof('ArithCompl.Zeven_def2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ? [V1__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__k)
& V0__z = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__k) )
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)) ) ) ).
fof('ArithCompl.Zeven_sqr1',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V0__z))) ) ) ).
fof('ArithCompl.Zeven_sqr2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n)))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) ) ) ).
fof('ArithCompl.Zle_square_simpl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ) ) ).
fof('ArithCompl.Zmult_eq_reg_l',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ! [V1__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z1)
=> ! [V2__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z2)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V1__z1) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V2__z2)
=> ( V0__z != cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__z1 = V2__z2 ) ) ) ) ) ).
fof('ArithCompl.Zmult_neq_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
& V1__b != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('ArithCompl.Zodd_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> V0__n != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('ArithCompl.Zodd_def1',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
=> ? [V2__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__k)
& V0__z = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V2__k),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('ArithCompl.Zodd_def2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ? [V1__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__k)
& V0__z = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__k),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)) ) ) ).
fof('ArithCompl.Zodd_mult',axiom,
! [V0__u] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__u)
=> ! [V1__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__v)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__u))
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__v))
=> ? [V4__s] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__s)
& ? [V5__w] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__w)
& ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__u,V1__v) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V4__s)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__u,V1__v) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V5__w) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__u,V1__v) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V5__w)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__u,V1__v) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V4__s) ) ) ) ) ) ) ) ) ).
fof('ArithCompl.Zodd_opp1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a)))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a)) ) ) ).
fof('ArithCompl.Zodd_opp2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a))) ) ) ).
fof('ArithCompl.Zodd_sqr1',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V0__z))) ) ) ).
fof('ArithCompl.Zodd_sum1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a))
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__b))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('ArithCompl.Zodd_sum2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a))
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__b))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('ArithCompl.Zodd_sum3',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b))))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a)) ) ) ) ).
fof('ArithCompl.is_sqr_mult',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q)
=> ( cArithCompl_2eis__sqr___24a1(V0__p)
=> ( cArithCompl_2eis__sqr___24a1(V1__q)
=> cArithCompl_2eis__sqr___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__p,V1__q)) ) ) ) ) ).
fof('ArithCompl.ndistp_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ~ cArithCompl_2edistinct__parity___24a2(V0__a,V0__a) ) ).
fof('ArithCompl.neq_1',axiom,
! [V0__u] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__u)
=> ! [V1__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__v)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( V2__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V3__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__u,V0__u) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__m,V2__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__n,V3__n))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__v,V1__v) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__n,V3__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__m,V2__m))
=> ( V0__u != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
& V1__v != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ) ) ) ).
fof('ArithCompl.sqr_0',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__z = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('ArithCompl.sqr_2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a)))) ) ).
fof('ArithCompl.sqr_compat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)
=> ( V0__a = V1__b
| V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b) ) ) ) ) ).
fof('ArithCompl.sqr_ge',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b))) ) ) ) ) ).
fof('ArithCompl.sqr_gt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b))) ) ) ) ) ).
fof('ArithCompl.sqr_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a))) ) ).
fof('ArithCompl.sqr_lt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a))) ) ) ) ).
fof('ArithCompl.sqr_poss',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V0__z)))
=> V0__z != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('ArithCompl.sqr_spos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( V0__z != cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V0__z),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('ArithCompl.sqr_sub1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)))) ) ) ) ) ).
fof('ArithCompl.sqr_sub2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)))) ) ) ) ) ).
fof('ArithCompl.sqr_sub3',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b))))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__a)) ) ) ) ) ) ).
fof('ArithCompl.sqr_sum',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('ArithCompl.sqr_sum2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)))) ) ) ).
fof('ArithCompl.sqr_sum3',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('ArithCompl.sqr_sum4',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& V1__b = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Bool.Bool.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Bool.Bool.negb_true_iff',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__19822___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.mult_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__65103___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__13363___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.dec_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__35312___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Numbers.BinNums.Z_ind',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V2__p))) )
=> ( ! [V3__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__p))) )
=> ! [V4__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__z)
=> p(happ(V0__P,V4__z)) ) ) ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__13175___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_1_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__p) ) ).
fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.PArith.BinPos.Pos.iter_invariant',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__f] :
( c_24__type__13657___24t(V1__A,V2__f)
=> ! [V3__Inv] :
( c_24__type__97___24t(V1__A,V3__Inv)
=> ( ! [V4__x] :
( t(V4__x,V1__A)
=> ( p(happ(V3__Inv,V4__x))
=> p(happ(V3__Inv,happ(V2__f,V4__x))) ) )
=> ! [V5__x] :
( t(V5__x,V1__A)
=> ( p(happ(V3__Inv,V5__x))
=> p(happ(V3__Inv,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__A,V2__f,V5__x,V0__p))) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.le_1_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(cCoq_2eNumbers_2eBinNums_2exH,V0__p) ) ).
fof('Coq.PArith.BinPos.Pos.le_antisym',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V1__q)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__q,V0__p)
=> V0__p = V1__q ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.mul_1_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2exH) = V0__p ) ).
fof('Coq.Reals.DiscrR.IZR_eq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 = V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_neq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 != V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_0_lt_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) ) ) ).
fof('Coq.Reals.RIneq.Rle_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_0_1',axiom,
cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r) ) ).
fof('Coq.Reals.RIneq.Rlt_le_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_1_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = V0__r ) ).
fof('Coq.Reals.RIneq.Rmult_eq_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V1__r1 = V2__r2 ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0',axiom,
cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.Rplus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4)) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.eq_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.mult_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.not_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Ranalysis1.pr_nu',axiom,
! [V0__f] :
( c_24__type__13871___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V2__pr1)
=> ! [V3__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V3__pr2)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr1) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V3__pr2) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_lt_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)) ) ) ) ) ).
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.ZArith.BinInt.Pos2Z.is_nonneg',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p))) ) ).
fof('Coq.ZArith.BinInt.Z.Even_or_Odd',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2eEven___24a1(V0__x)
| cCoq_2eZArith_2eBinInt_2eZ_2eOdd___24a1(V0__x) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_BootStrap.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.Private_BootStrap.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.Private_BootStrap.mul_add_distr_pos',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__n,V2__m),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__m,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_BootStrap.mul_add_distr_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_BootStrap.mul_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_BootStrap.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.add_mod_idemp_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V2__n),V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c))))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V2__c),V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_add_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__c)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__c),V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V2__c,V1__b)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_le_lower_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__q,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V1__b,V2__c))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_le_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_lt_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_mod_unique',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ! [V1__q1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q1)
=> ! [V2__q2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q2)
=> ! [V3__r1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r1)
=> ! [V4__r2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r2)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r1,V0__b)) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V4__r2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__r2,V0__b)) )
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V1__q1),V3__r1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V2__q2),V4__r2)
=> ( V1__q1 = V2__q2
& V3__r1 = V4__r2 ) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = V0__a ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_mul_cancel_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_unique_exact',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mod_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c))))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V2__c) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mod_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mul_div_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ))),cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.mod_bound_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b),V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c))))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V2__c),V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_add_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__c)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__c),V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V2__c,V1__b)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_le_lower_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__q,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,V2__c))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_le_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_lt_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_mod_unique',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ! [V1__q1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q1)
=> ! [V2__q2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q2)
=> ! [V3__r1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r1)
=> ! [V4__r2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r2)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r1,V0__b)) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V4__r2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__r2,V0__b)) )
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V1__q1),V3__r1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V2__q2),V4__r2)
=> ( V1__q1 = V2__q2
& V3__r1 = V4__r2 ) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = V0__a ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_mul_cancel_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_mul_cancel_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_unique_exact',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.mod_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c))))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V2__c) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.mod_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.mul_div_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_le',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)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_lt',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)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',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)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_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)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',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)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.abs_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.abs_0_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_mul',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n))) ) ).
fof('Coq.ZArith.BinInt.Z.abs_opp',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.abs_sgn',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.abs_square',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.abs_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.add_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_lt_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_lt_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_lt_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_move_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = V2__p
<=> V1__m = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__p,V0__n) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_neg_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_nonneg_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_nonpos_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_opp_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.add_opp_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.add_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_rem',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( V2__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V2__n),cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V1__b,V2__n)),V2__n) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_rem_idemp_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( V2__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V2__n),V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_rem_idemp_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( V2__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V1__b,V2__n)),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_shuffle1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V3__q)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_shuffle3',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_simpl_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V1__m) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.add_square_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b)))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_sub_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_sub_swap',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('Coq.ZArith.BinInt.Z.b2z_inj',axiom,
! [V0__a0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a0)
=> ! [V1__b0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__a0) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V1__b0)
=> V0__a0 = V1__b0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.ZArith.BinInt.Z.bits_inj\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n) ) )
=> V0__a = V1__b ) ) ) ).
fof('Coq.ZArith.BinInt.Z.crossmul_le_addsquare',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_1_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__a ) ).
fof('Coq.ZArith.BinInt.Z.div_exact',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_le_lower_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__q,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,V2__c))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_le_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_lt_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_mod_unique',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ! [V1__q1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q1)
=> ! [V2__q2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q2)
=> ! [V3__r1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r1)
=> ! [V4__r2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r2)
=> ( ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r1,V0__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__b,V3__r1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__r1,cCoq_2eNumbers_2eBinNums_2eZ0)) ) )
=> ( ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V4__r2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__r2,V0__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__b,V4__r2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V4__r2,cCoq_2eNumbers_2eBinNums_2eZ0)) ) )
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V1__q1),V3__r1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V2__q2),V4__r2)
=> ( V1__q1 = V2__q2
& V3__r1 = V4__r2 ) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = V0__a ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_mul_cancel_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_mul_cancel_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_unique_exact',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_unique_neg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__r,cCoq_2eNumbers_2eBinNums_2eZ0)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_unique_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('Coq.ZArith.BinInt.Z.divide_add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_add_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_antisym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__m,V0__n)
=> ( V0__n = V1__m
| V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_factor_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_factor_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n)) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_mul_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_mul_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_mul_split',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))
=> ? [V5__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__q)
& ? [V6__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__r)
& V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V5__q,V6__r)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__q,V1__m)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__r,V2__p) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.divide_sub_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__74,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__19713___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
| V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
| V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_1_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
& V1__m = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_1_nonneg\'',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
& V1__m = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m
<=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_square_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_sym',axiom,
cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.even_add',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eBool_2eBool_2eeqb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.even_mul',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.even_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.even_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.gauss',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_add_mult_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n))) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_bezout',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = V2__p
=> cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V0__n,V1__m,V2__p) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_div_swap',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b)),V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b))) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_divide_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b),V0__a) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_divide_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b),V1__b) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_eq_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
& V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_mul_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_mul_mono_r_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m),V2__p) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b))) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ))),cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('Coq.ZArith.BinInt.Z.ge_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ge_le_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ggcd_correct_divisors',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419795___24a2(V0__a,V1__b) ) ) ).
fof('Coq.ZArith.BinInt.Z.gt_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gt_lt_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ))),cCoq_2eZArith_2eBinInt_2eZ_2elcm) ).
fof('Coq.ZArith.BinInt.Z.le_0_1',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.le_0_mul',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_exists_sub',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ? [V3__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__p)
& V1__m = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__p,V0__n)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__p)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ind',axiom,
! [V0__A] :
( c_24__type__74___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__74,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(happ(V0__A,V2__n))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,V4__m))
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,V5__m))
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_le_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_add_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__q,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,V3__q)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lteq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ngt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
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.BinInt.Z.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.le_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n))) ) ).
fof('Coq.ZArith.BinInt.Z.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__74,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.log2_lt_cancel',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V1__b)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a))) ) ).
fof('Coq.ZArith.BinInt.Z.log2_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_lt_cancel',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a),cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V1__b)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a))) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),cCoq_2eZArith_2eBinInt_2eZ_2elog2__up) ).
fof('Coq.ZArith.BinInt.Z.log2_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_0_mul',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.ZArith.BinInt.Z.lt_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_1_mul_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
| cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_1_mul_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_asymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_m1_0',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0)) ).
fof('Coq.ZArith.BinInt.Z.lt_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0))
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_mul_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_mul_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_mul_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> V0__n != V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_nge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_sub_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n))) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_pred',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__z,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V1__n)) = V1__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__61,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__74,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,cCoq_2eZArith_2eBinInt_2eZ_2eeq,c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('Coq.ZArith.BinInt.Z.max_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V2__c) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_bound_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b),V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_neg_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_pos_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b),V1__b)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = V0__a ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_unique_neg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__r,cCoq_2eNumbers_2eBinNums_2eZ0)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_unique_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_add_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_add_distr_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_div_ge',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_div_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),V0__a)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_divide_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_divide_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_divide_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_divide_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_eq_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
| V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_eq_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_eq_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_eq_1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
| V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_id_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = V1__m
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_neg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_neg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V3__q))) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_nonneg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_nonneg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__q,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V3__q),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p))) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_nonpos_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_nonpos_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_pos_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_pos_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_neg_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__p,V2__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__p,V1__n))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_neg_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__m,V0__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__n,V0__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V3__q))) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__q,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V3__q),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p))) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_pos_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__p,V1__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__p,V2__m))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_pos_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__n,V0__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__m,V0__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( V2__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V2__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V1__b,V2__n)),V2__n) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_neg_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_neg_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonneg_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonneg_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonneg_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonneg_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonpos_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonpos_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_opp',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V3__q)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V3__q)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V3__q)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V3__q),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle3',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_sub_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_sub_distr_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('Coq.ZArith.BinInt.Z.negb_even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.negb_odd',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.neq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
& V1__m != cCoq_2eNumbers_2eBinNums_2eZ0 )
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.nlt_square_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ).
fof('Coq.ZArith.BinInt.Z.odd_add',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eDatatypes_2exorb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.odd_mul',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.odd_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.odd_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue
<=> cCoq_2eZArith_2eBinInt_2eZ_2eOdd___24a1(V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.odd_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.ZArith.BinInt.Z.opp_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.opp_add_distr',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_eq_mul_m1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.ZArith.BinInt.Z.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_inj_wd',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_involutive',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.opp_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_neg_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),cCoq_2eNumbers_2eBinNums_2eZ0))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_nonneg_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('Coq.ZArith.BinInt.Z.pow_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('Coq.ZArith.BinInt.Z.pow_1_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__a ) ).
fof('Coq.ZArith.BinInt.Z.pow_2_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a) ) ).
fof('Coq.ZArith.BinInt.Z.pow_add_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V2__c)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_mul_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V1__b,V2__c)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_mul_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b),V2__c) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_neg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_pos_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.quot_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V0__a)))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V2__c),V1__b) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_add_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__c),V2__c)))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__c),V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V2__c,V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_le_lower_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__q,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V1__b,V2__c))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_le_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_lt_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = V0__a ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_mul_cancel_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_mul_cancel_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_rem',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_rem_unique',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ! [V1__q1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q1)
=> ! [V2__q2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q2)
=> ! [V3__r1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r1)
=> ! [V4__r2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r2)
=> ( ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r1,V0__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__b,V3__r1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__r1,cCoq_2eNumbers_2eBinNums_2eZ0)) ) )
=> ( ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V4__r2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__r2,V0__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__b,V4__r2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V4__r2,cCoq_2eNumbers_2eBinNums_2eZ0)) ) )
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V1__q1),V3__r1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V2__q2),V4__r2)
=> ( V1__q1 = V2__q2
& V3__r1 = V4__r2 ) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_unique_exact',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quotrem_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419767___24a2(V0__a,V1__b) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V0__a)))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V2__c) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_opp_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a),V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_opp_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_sign_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b),V0__a))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('Coq.ZArith.BinInt.Z.sgn_abs',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_mul',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_null',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_null_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_sgn',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__x)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V1__b))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_le_square',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b),V0__a))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_lt_cancel',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V1__b)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_lt_square',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a),V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_mul_below',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)))) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a))) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(c_24__let__2__s__19729___24a1(V0__n),c_24__let__2__s__19729___24a1(V0__n)),V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(c_24__let__2__s__19729___24a1(V0__n)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(c_24__let__2__s__19729___24a1(V0__n))))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_spec_nonneg',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V0__b),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__b),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__b))))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__b)) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_square',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a)) = V0__a ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b),V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__b)))) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a) = V1__b ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_unique\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__c,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b))) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b),V2__c)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a) = V1__b ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_eqn',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__a))) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_eqn0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_le_mono',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a),cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V1__b))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_le_square',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a),V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_lt_cancel',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a),cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V1__b)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a))) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_square',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a)) = V0__a ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V1__b)),V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b))) )
=> cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a) = V1__b ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up) ).
fof('Coq.ZArith.BinInt.Z.sqrt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt) ).
fof('Coq.ZArith.BinInt.Z.square_le_mono_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_le_mono_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_le_simpl_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_le_simpl_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_lt_mono_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_lt_mono_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_lt_simpl_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_lt_simpl_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a))) ) ).
fof('Coq.ZArith.BinInt.Z.square_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.sub_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.sub_move_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) = V2__p
<=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n2)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_inj_wd',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n2)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n2)
<=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('Coq.ZArith.BinInt.Z.testbit_neg_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.ZArith.BinInt.Z.two_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.ZArith.BinInt.Z.zero_pos_neg',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__74,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e),V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__n))
=> ( p(happ(V0__P,V3__n))
& p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V3__n))) ) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__n)
=> p(happ(V0__P,V4__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z_eq_mult',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Zeq_minus',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Zmult_0_r_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eNumbers_2eBinNums_2eZ0 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.ZArith.BinInt.Zmult_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Zmult_integral',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
| V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Zmult_integral_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Zmult_minus_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Zmult_succ_l_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Zmult_succ_r_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Zopp_mult_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Zopp_mult_distr_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Zplus_diag_eq_mult_2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.Zcompare.Zcompare_mult_compat',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p),V1__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p),V2__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V1__n,V2__m) ) ) ) ).
fof('Coq.ZArith.Zcomplements.sqr_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.ZArith.Zdiv.Z_div_exact_1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_div_exact_full_1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_div_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416654___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_div_mod_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_div_mult',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = V0__a ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_div_mult_full',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = V0__a ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_mod_lt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b),V1__b)) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_mod_mult',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.Zdiv.Z_mod_plus_full',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V2__c) ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_mult_div_ge',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),V0__a)) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.Zdiv.Zdiv_Zdiv',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_le_lower_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__q,V1__b),V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__q,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_le_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__q,V1__b)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_lt_upper_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__q,V1__b)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__q)) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_mod_unique',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ! [V1__q1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q1)
=> ! [V2__q2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q2)
=> ! [V3__r1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r1)
=> ! [V4__r2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r2)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r1,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__b))) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V4__r2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__r2,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__b))) )
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V1__q1),V3__r1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V2__q2),V4__r2)
=> ( V1__q1 = V2__q2
& V3__r1 = V4__r2 ) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_mod_unique_2',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ! [V1__q1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q1)
=> ! [V2__q2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q2)
=> ! [V3__r1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r1)
=> ! [V4__r2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r2)
=> ( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V3__r1,V0__b)
=> ( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V4__r2,V0__b)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V1__q1),V3__r1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V2__q2),V4__r2)
=> ( V1__q1 = V2__q2
& V3__r1 = V4__r2 ) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_mult_cancel_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_mult_cancel_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_unique_full',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V3__r,V1__b)
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V2__q = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmod_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.Zdiv.Zmod_0_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.Zdiv.Zmod_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__n),V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__n) ) ) ).
fof('Coq.ZArith.Zdiv.Zmod_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__r,V1__b)) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmod_unique_full',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V3__r,V1__b)
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__q),V3__r)
=> V3__r = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmult_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V2__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V1__b,V2__n)),V2__n) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmult_mod_distr_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmult_mod_distr_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b),V2__c) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmult_mod_idemp_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V2__n),V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__n) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmult_mod_idemp_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V2__n)),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V0__a),V2__n) ) ) ) ).
fof('Coq.ZArith.Zeven.Zdiv2_odd_eqn',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V0__n)),c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n)) ) ).
fof('Coq.ZArith.Zeven.Zeven_2p',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__p))) ) ).
fof('Coq.ZArith.Zeven.Zeven_Sn',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n))) ) ) ).
fof('Coq.ZArith.Zeven.Zeven_bool_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue
<=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) ) ) ).
fof('Coq.ZArith.Zeven.Zeven_ex',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))
=> ? [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
& V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V2__m) ) ) ) ).
fof('Coq.ZArith.Zeven.Zeven_mult_Zeven_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__a))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b))) ) ) ) ).
fof('Coq.ZArith.Zeven.Zeven_mult_Zeven_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V1__b))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b))) ) ) ) ).
fof('Coq.ZArith.Zeven.Zeven_not_Zodd',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))
=> ~ p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) ) ) ).
fof('Coq.ZArith.Zeven.Zeven_plus_Zodd',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__a))
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__b))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.Zeven.Zeven_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n))) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_2p_plus_1',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ).
fof('Coq.ZArith.Zeven.Zodd_Sn',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n))) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_bool_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue
<=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V0__n)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_equiv',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eOdd___24a1(V0__z) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_ex',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> ? [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
& V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V2__m),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_ex_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
<=> ? [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
& V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__m),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_mult_Zodd',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a))
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__b))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_not_Zeven',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> ~ p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_plus_Zeven',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a))
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V1__b))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_plus_Zodd',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a))
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__b))
=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n))) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_quot2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__n)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.ZArith.Zeven.Zodd_quot2_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))
=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__n)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.ZArith.Zeven.Zquot2_odd_eqn',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V0__n)),c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466341___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.Nat2Z.is_nonneg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n))) ) ).
fof('Coq.ZArith.Znumtheory.Bezout_ind',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ! [V4__u] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__u)
=> ! [V5__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__v)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__u,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V5__v,V1__b)) = V2__d
=> p(V3__P) ) ) )
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V0__a,V1__b,V2__d)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Bezout_intro',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
=> ! [V3__u] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__u)
=> ! [V4__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__v)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__u,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__v,V1__b)) = V2__d
=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V0__a,V1__b,V2__d) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Bezout_sind',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ! [V4__u] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__u)
=> ! [V5__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__v)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__u,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V5__v,V1__b)) = V2__d
=> p(V3__P) ) ) )
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V0__a,V1__b,V2__d)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Euclid_ind',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__P] :
( c_24__type__16945___24t(V0__a,V1__b,V2__P)
=> ( ! [V3__u] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__u)
=> ! [V4__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__v)
=> ! [V5__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__d)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__u,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__v,V1__b)) = V5__d
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V5__d)
=> p(happ(V2__P,cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V0__a,V1__b,V3__u,V4__v,V5__d))) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V0__a,V1__b,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Euclid_sind',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__P] :
( c_24__type__16945___24t(V0__a,V1__b,V2__P)
=> ( ! [V3__u] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__u)
=> ! [V4__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__v)
=> ! [V5__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__d)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__u,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__v,V1__b)) = V5__d
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V5__d)
=> p(happ(V2__P,cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V0__a,V1__b,V3__u,V4__v,V5__d))) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V0__a,V1__b,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Gauss',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c))
=> ( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,V2__c) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zdivide_Zdiv_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,V1__b)
=> V1__b = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,V0__a)) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zdivide_intro',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ( V1__b = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__q,V0__a)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,V1__b) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zdivide_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__b,V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zdivide_opp_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a),V1__b) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zdivide_opp_l_rev',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a),V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zgcd_is_gcd',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b)) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_bezout',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__d)
=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V0__a,V1__b,V2__d) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_for_euclid',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__q,V1__b)),V2__d)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__d) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_for_euclid2',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ! [V1__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__d)
=> ! [V2__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__q)
=> ! [V3__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__r)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V3__r,V0__b,V1__d)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__b,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__b,V2__q),V3__r),V1__d) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_ind',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__g] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__g)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V1__b)
=> ( ! [V6__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__x,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__x,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__x,V2__g) ) ) )
=> p(V3__P) ) ) )
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__g)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_intro',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__g] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__g)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V1__b)
=> ( ! [V5__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V2__g) ) ) )
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__g) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_mult',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ! [V3__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__d)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V3__d)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V3__d)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_sym',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__d)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V1__b,V0__a,V2__d) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zmult_one',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_aux_subproof',axiom,
! [V0__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__m)) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_aux_subproof0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__x))
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V2__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__x)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_aux_subproof1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__x))
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V2__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_mult',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V0__p)
=> ! [V2__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__p,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__a,V3__b))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__p,V2__a)
| cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__p,V3__b) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_rel_prime',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V0__p)
=> ! [V2__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__a)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__p,V2__a)
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__p,V2__a) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.rel_prime_bezout',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V0__a,V1__b,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.ZArith.Znumtheory.rel_prime_cross_prod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ! [V3__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__d)
=> ( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
=> ( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V2__c,V3__d)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__d,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V3__d) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)
=> ( V0__a = V2__c
& V1__b = V3__d ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.rel_prime_mult',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
=> ( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V2__c)
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.square_not_prime',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ~ cCoq_2eZArith_2eZnumtheory_2eprime___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a)) ) ).
fof('Coq.ZArith.Zorder.Zgt_square_simpl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zle_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zlt_square_simpl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_ge_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V1__m,V3__q)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V3__q,cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V3__q)) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_ge_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_ge_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_ge_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_le_0_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n))) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_le_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_lt_0_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_lt_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_lt_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_lt_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_reg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_le_0_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_le_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V3__q))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V3__q))) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_le_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_le_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_le_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_0_le_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_0_le_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_0_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V3__q)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_compat2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V3__q)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_lt_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_gt_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_lt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.Zplus_le_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zplus_lt_compat_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zplus_lt_compat_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.Zorder.dec_Zgt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.Zorder.not_Zeq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zmult_le_approx',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n),V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORrt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.ropp_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___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__13657___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rplus_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___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__13636___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__13657___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rtimes_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___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__13636___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__13657___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.sor_setoid_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.ropp_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___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__13657___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req),V6__ropp) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rplus_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___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__13636___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__13657___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V3__rplus) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.rtimes_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__13636___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__13636___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__13636___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__399___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__399___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__13636___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__13657___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V7__req,V7__req)),V4__rtimes) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.narrow_interval_lower_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V2__x),V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V2__x,cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V1__b,V0__a)) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA11',axiom,
! [V0__v1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v1)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k1)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,V1__c1),V2__l1),V4__k1),V3__l2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V4__k1)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l1,V4__k1),V3__l2)) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA16',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
=> ! [V2__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l)
=> ! [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k)) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA17',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_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA18',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__k)
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__k)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA19',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA20',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_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA3',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__k)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__k,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__k)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__y = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA4',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__y,V0__x))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V1__y),V0__x) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA5',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)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA7',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.Zred_factor0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.omega.OmegaLemmas.Zred_factor1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.omega.OmegaLemmas.Zred_factor2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__m)) ) ) ).
fof('Coq.omega.OmegaLemmas.Zred_factor3',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__m)) ) ) ).
fof('Coq.omega.OmegaLemmas.Zred_factor4',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.Zred_factor5',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0),V1__m) = V1__m ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> ! [V7__P] :
( c_24__type__74___24t(V7__P)
=> ( p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2)))))
=> p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA11',axiom,
! [V0__v1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v1)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k1)
=> ! [V5__P] :
( c_24__type__74___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V4__k1)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l1,V4__k1),V3__l2))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,V1__c1),V2__l1),V4__k1),V3__l2))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> ! [V5__P] :
( c_24__type__74___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__74___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__74___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__74___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA16',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
=> ! [V2__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l)
=> ! [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
=> ! [V4__P] :
( c_24__type__74___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k))))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zmult_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__74___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zmult_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__74___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zmult_plus_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__74___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__74___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_mult_distr_r',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__74___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__74___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__74___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p)))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__74___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__74___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_permute',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__74___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__74___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__74___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__74___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor3',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__74___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),V0__x))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor4',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__P] :
( c_24__type__74___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V2__z))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__74___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__74___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.Field_theory.F_R',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__13636___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__13657___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__399___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Ztriv_div_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__399___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> ! [V3__zphi] :
( c_24__type__32002___24t(V0__R,V3__zphi)
=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V1__req,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V3__zphi,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.rmul_ext3_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__13636___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__13636___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__13657___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__399___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__13636___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__13657___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.ropp_ext3_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__13636___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__13636___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__13657___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__399___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__13657___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
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__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___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__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___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.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__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___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_mul_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__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___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)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V11__x),V12__y))),happ(happ(V4__rmul,V11__x),happ(V6__ropp,V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__13636___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__13636___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__13657___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.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.Ropp_opp',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___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)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(V6__ropp,V11__x))),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___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__13636___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__13636___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__13657___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__399___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13636___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__13657___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__13636___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__13657___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__13657___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.ZArithRing.Zr_ring_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__pe1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__pe1)
=> ! [V4__pe2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__pe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V1__l,V2__lpe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__16424___24a1(V2__lpe),V3__pe1),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__16424___24a1(V2__lpe),V4__pe2)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V1__l,V3__pe1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V1__l,V4__pe2) ) ) ) ) ) ) ) ).
fof('$adef_Coq.Reals.Raxioms.bound_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRaxioms_2ebound,V_24X1))
<=> cCoq_2eReals_2eRaxioms_2ebound___24a1(V_24X1) ) ).
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('$adef_Coq.ZArith.BinInt.Z.Even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eBinInt_2eZ_2eEven,V_24X1))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eEven___24a1(V_24X1) ) ).
fof('$adef_$_lam_36855_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__36855,V_24X1),V_24X2),V_24X3) = c_24__lam__36855___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$19767_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419767,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419767___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rlimit.Build_Metric_Space_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space,V_24X1),V_24X2) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$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('$adef_Coq.Reals.Rfunctions.R_dist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eR__dist,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eR__dist___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('$adef_ArithCompl.is_sqr_$a1',axiom,
! [V_24X1] :
( p(happ(cArithCompl_2eis__sqr,V_24X1))
<=> cArithCompl_2eis__sqr___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Init.Specif.sig_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_6_p_14928_14930_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__14928__14930,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__14928__14930___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$66341_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466341,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466341___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('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.eval_pol_$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('$adef_Coq.micromega.RingMicromega.psubC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2epsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$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('$adef_Coq.micromega.ZCoeff.gen_order_phi_Z_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).
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('$adef_Coq.Reals.Ranalysis1.derivable_pt_lim_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$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__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Init.Decimal.Pos_$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('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_$_lam_78226_$a1',axiom,
! [V_24X1] : happ(c_24__lam__78226,V_24X1) = c_24__lam__78226___24a1(V_24X1) ).
fof('$adef_$_lam_78226_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__78226,V_24X1),V_24X2))
<=> c_24__lam__78226___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.setoid_ring.Field_theory.FEdiv_$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('$adef_Coq.micromega.ZMicromega.ceiling_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eceiling,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V_24X1,V_24X2) ).
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('$adef_$_prop_34425_$a1',axiom,
! [V_24X1] : happ(c_24__prop__34425,V_24X1) = c_24__prop__34425___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.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_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ1_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_59316_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__59316,V_24X1),V_24X2),V_24X3) = c_24__lam__59316___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V_24X1) ).
fof('$adef_$_lam_14596_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__14596,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__14596___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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.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.Reals.Ranalysis1.derive_pt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederive__pt,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.fct_cte_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2efct__cte,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PsubC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Env.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_6_lmp_16424_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__16424,V_24X1) = c_24__let__6__lmp__16424___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Raxioms.INR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRaxioms_2eINR,V_24X1) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V_24X1) ).
fof('$adef_$_lam_18639_$a1',axiom,
! [V_24X1] : happ(c_24__lam__18639,V_24X1) = c_24__lam__18639___24a1(V_24X1) ).
fof('$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.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.ZArith.Zpower.Zpower_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2eZpower__nat,V_24X1) = cCoq_2eZArith_2eZpower_2eZpower__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.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.Reals.Rfunctions.sum_f_R0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2esum__f__R0,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V_24X1,V_24X2) ).
fof('$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_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quot2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot2___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.log2_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons2_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zpower.shift_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eshift__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eshift__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.PEsimp_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePEsimp,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons1_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.micromega.Env.jump_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnv_2ejump___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_14596_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__14596,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__14596___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1) = cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_32944_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__32944,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__32944___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.mul_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a1(V_24X1) ).
fof('$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.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_$_lam_59332_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__59332,V_24X1),V_24X2) = c_24__lam__59332___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('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$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('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$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('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.div2_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$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('$adef_$_case_Coq.Init.Datatypes.nat$32090_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(V_24X1) ).
fof('$adef_$_let_17_mkopp_pow_32945_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__32945,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__32945___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$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.Reals.NewtonInt.Newton_integrable_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eNewtonInt_2eNewton__integrable,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eNewtonInt_2eNewton__integrable___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.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.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$66339_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V_24X1) ).
fof('$adef_$_fix_413_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__413__1__add__carry,V_24X1),V_24X2) = c_24__fix__413__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_odd_dec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZeven_2eZeven__odd__dec,V_24X1) = cCoq_2eZArith_2eZeven_2eZeven__odd__dec___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.ZArith_dec.Z_zerop_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZArith__dec_2eZ__zerop,V_24X1) = cCoq_2eZArith_2eZArith__dec_2eZ__zerop___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Sumbool.bool_of_sumbool_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eSumbool_2ebool__of__sumbool,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eSumbool_2ebool__of__sumbool___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_17_mkopp_pow_32945_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__32945,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__32945___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_avoid_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Env.tail_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnv_2etail,V_24X1),V_24X2) = cCoq_2emicromega_2eEnv_2etail___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_59322_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__59322,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__59322___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rseries.Un_growing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRseries_2eUn__growing,V_24X1))
<=> cCoq_2eReals_2eRseries_2eUn__growing___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zdiv.Remainder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZdiv_2eRemainder,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.square_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.Pphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_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.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Raxioms.is_upper_bound_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRaxioms_2eis__upper__bound,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V_24X1,V_24X2) ) ).
fof('$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.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.Reals.Ranalysis1.plus_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eplus__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.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.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.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$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.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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.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.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.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmult,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$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_ArithCompl.distinct_parity_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cArithCompl_2edistinct__parity,V_24X1),V_24X2))
<=> cArithCompl_2edistinct__parity___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_cast_16752_$a1',axiom,
! [V_24X1] : happ(c_24__cast__16752,V_24X1) = c_24__cast__16752___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zpower.two_p_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__p,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__p___24a1(V_24X1) ).
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('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_18639_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__18639,V_24X1),V_24X2) = c_24__lam__18639___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_19713_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__19713,V_24X1),V_24X2) = c_24__prop__19713___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.ZArith.Zdiv.eqm_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZdiv_2eeqm,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZdiv_2eeqm___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.ZArith.BinIntDef.Z.shiftr_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.mult_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2emult__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_let_11_subst_l_14524_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__14524,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__14524___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a1(V_24X1) ).
fof('$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.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_18_mkmult_pow_32946_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__32946,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__32946___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).
fof('$adef_$_cast_16753_$a1',axiom,
! [V_24X1] : happ(c_24__cast__16753,V_24X1) = c_24__cast__16753___24a1(V_24X1) ).
fof('$adef_$_lam_59316_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__59316,V_24X1),V_24X2) = c_24__lam__59316___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_$_let_var_6_p_14926_14929_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__14926__14929,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__14926__14929___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_35312_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35312,V_24X1),V_24X2) = c_24__prop__35312___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$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('$adef_Coq.QArith.QArith_base.inject_Z_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2einject__Z,V_24X1) = cCoq_2eQArith_2eQArith__base_2einject__Z___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$adef_$_lam_59322_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__59322,V_24X1),V_24X2) = c_24__lam__59322___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1) = cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2edouble,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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.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_$_prop_13363_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__13363,V_24X1),V_24X2) = c_24__prop__13363___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('$adef_Coq.Reals.Ranalysis1.derivable_pt_abs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_22033_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__22033,V_24X1),V_24X2) = c_24__lam__22033___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Reals.Ranalysis1.antiderivative_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eantiderivative,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.map_option2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.prod$16654_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416654,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416654___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_22033_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__22033,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__22033___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_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_$_let_2_s_19729_$a1',axiom,
! [V_24X1] : happ(c_24__let__2__s__19729,V_24X1) = c_24__let__2__s__19729___24a1(V_24X1) ).
fof('$adef_$_cast_16750_$a1',axiom,
! [V_24X1] : happ(c_24__cast__16750,V_24X1) = c_24__cast__16750___24a1(V_24X1) ).
fof('$adef_$_cast_16749_$a1',axiom,
! [V_24X1] : happ(c_24__cast__16749,V_24X1) = c_24__cast__16749___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.get_signZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$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('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.ZMicromega.Zdivide_pol_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eZdivide__pol,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Specif.sumor_$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('$adef_Coq.ZArith.BinIntDef.Z.rem_$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('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.ggcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$32085_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___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('$adef_$_prop_34426_$a1',axiom,
! [V_24X1] : happ(c_24__prop__34426,V_24X1) = c_24__prop__34426___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.sqrt_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V_24X1) ).
fof('$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.Reals.Rseries.EUn_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRseries_2eEUn,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRseries_2eEUn___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_18637_$a1',axiom,
! [V_24X1] : happ(c_24__lam__18637,V_24X1) = c_24__lam__18637___24a1(V_24X1) ).
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('$adef_$_let_16_mkpow_32944_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__32944,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__32944___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_18_mkmult_pow_32946_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__32946,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__32946___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.gcd_$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('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$19795_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419795,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419795___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_36855_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__36855,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__36855___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.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.Reals.Rbasic_fun.Rabs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRabs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Zbool.Zeven_odd_bool_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZbool_2eZeven__odd__bool,V_24X1) = cCoq_2eZArith_2eZbool_2eZeven__odd__bool___24a1(V_24X1) ).
fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_ArithCompl.both_odd_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cArithCompl_2eboth__odd,V_24X1),V_24X2))
<=> cArithCompl_2eboth__odd___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.left_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$32068_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.fct_cte_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2efct__cte,V_24X1) = cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(V_24X1) ).
fof('$adef_$_lam_59347_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__59347,V_24X1),V_24X2) = c_24__lam__59347___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V_24X1,V_24X2) ).
fof('$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.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.Arith.Factorial.fact_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2eFactorial_2efact,V_24X1) = cCoq_2eArith_2eFactorial_2efact___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.map_option_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$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.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinInt.Z.Odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eBinInt_2eZ_2eOdd,V_24X1))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eOdd___24a1(V_24X1) ) ).
fof('$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.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.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.Init.Specif.right_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eright___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.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.ZArith.BinInt.Z.lcm_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elcm,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elcm___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.no_cond_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2eno__cond,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2eno__cond___24a1(V_24X1) ) ).
fof('$tdef_$_type_19197',axiom,
! [V_24Y] :
( c_24__type__19197___24t(V_24Y)
<=> t(V_24Y,c_24__type__19197) ) ).
fof('$tdef_$_type_65103',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__65103___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__65103___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19160',axiom,
! [V_24Y] :
( c_24__type__19160___24t(V_24Y)
<=> t(V_24Y,c_24__type__19160) ) ).
fof('$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_13192',axiom,
! [V_24Y] :
( c_24__type__13192___24t(V_24Y)
<=> t(V_24Y,c_24__type__13192) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22040',axiom,
! [V_24Y] :
( c_24__type__22040___24t(V_24Y)
<=> t(V_24Y,c_24__type__22040) ) ).
fof('$tdef_$_type_13361',axiom,
! [V_24Y] :
( c_24__type__13361___24t(V_24Y)
<=> t(V_24Y,c_24__type__13361) ) ).
fof('$tdef_Coq.Reals.Rlimit.Metric_Space',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRlimit_2eMetric__Space) ) ).
fof('$tdef_$_type_19325',axiom,
! [V_24Y] :
( c_24__type__19325___24t(V_24Y)
<=> t(V_24Y,c_24__type__19325) ) ).
fof('$tdef_$_type_21998',axiom,
! [V_24Y] :
( c_24__type__21998___24t(V_24Y)
<=> t(V_24Y,c_24__type__21998) ) ).
fof('$tdef_$_type_32002',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32002___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32002___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35350',axiom,
! [V_24Y] :
( c_24__type__35350___24t(V_24Y)
<=> t(V_24Y,c_24__type__35350) ) ).
fof('$tdef_$_type_30593',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__30593___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__30593___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_31442',axiom,
! [V_24Y] :
( c_24__type__31442___24t(V_24Y)
<=> t(V_24Y,c_24__type__31442) ) ).
fof('$tdef_$_type_410',axiom,
! [V_24Y] :
( c_24__type__410___24t(V_24Y)
<=> t(V_24Y,c_24__type__410) ) ).
fof('$tdef_$_type_12',axiom,
! [V_24Y] :
( c_24__type__12___24t(V_24Y)
<=> t(V_24Y,c_24__type__12) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22038',axiom,
! [V_24Y] :
( c_24__type__22038___24t(V_24Y)
<=> t(V_24Y,c_24__type__22038) ) ).
fof('$tdef_$_type_16378',axiom,
! [V_24Y] :
( c_24__type__16378___24t(V_24Y)
<=> t(V_24Y,c_24__type__16378) ) ).
fof('$tdef_$_type_30398',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__30398___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__30398___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_21935',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__21935___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__21935___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_16945',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16945___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16945___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30806',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__30806___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__30806___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_28925',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__28925___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__28925___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_15458',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15458___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__15458___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_29138',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__29138___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__29138___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16391',axiom,
! [V_24Y] :
( c_24__type__16391___24t(V_24Y)
<=> t(V_24Y,c_24__type__16391) ) ).
fof('$tdef_$_type_13631',axiom,
! [V_24Y] :
( c_24__type__13631___24t(V_24Y)
<=> t(V_24Y,c_24__type__13631) ) ).
fof('$tdef_Coq.Init.Decimal.decimal',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2edecimal) ) ).
fof('$tdef_$_type_20866',axiom,
! [V_24Y] :
( c_24__type__20866___24t(V_24Y)
<=> t(V_24Y,c_24__type__20866) ) ).
fof('$tdef_$_type_16412',axiom,
! [V_24Y] :
( c_24__type__16412___24t(V_24Y)
<=> t(V_24Y,c_24__type__16412) ) ).
fof('$tdef_$_type_956',axiom,
! [V_24Y] :
( c_24__type__956___24t(V_24Y)
<=> t(V_24Y,c_24__type__956) ) ).
fof('$tdef_$_type_19822',axiom,
! [V_24Y] :
( c_24__type__19822___24t(V_24Y)
<=> t(V_24Y,c_24__type__19822) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_27524',axiom,
! [V_24Y] :
( c_24__type__27524___24t(V_24Y)
<=> t(V_24Y,c_24__type__27524) ) ).
fof('$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_$_type_15858',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15858___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__15858___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_13592',axiom,
! [V_24Y] :
( c_24__type__13592___24t(V_24Y)
<=> t(V_24Y,c_24__type__13592) ) ).
fof('$tdef_$_type_13999',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13999___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13999___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_14746',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14746___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14746___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13990',axiom,
! [V_24Y] :
( c_24__type__13990___24t(V_24Y)
<=> t(V_24Y,c_24__type__13990) ) ).
fof('$tdef_$_type_16130',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16130___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16130___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_13871',axiom,
! [V_24Y] :
( c_24__type__13871___24t(V_24Y)
<=> t(V_24Y,c_24__type__13871) ) ).
fof('$tdef_$_type_16295',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16295___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16295___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_13928',axiom,
! [V_24Y] :
( c_24__type__13928___24t(V_24Y)
<=> t(V_24Y,c_24__type__13928) ) ).
fof('$tdef_$_type_16869',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__16869___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__16869___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_19321',axiom,
! [V_24Y] :
( c_24__type__19321___24t(V_24Y)
<=> t(V_24Y,c_24__type__19321) ) ).
fof('$tdef_$_type_14961',axiom,
! [V_24Y] :
( c_24__type__14961___24t(V_24Y)
<=> t(V_24Y,c_24__type__14961) ) ).
fof('$tdef_$_type_13702',axiom,
! [V_24Y] :
( c_24__type__13702___24t(V_24Y)
<=> t(V_24Y,c_24__type__13702) ) ).
fof('$tdef_$_type_13303',axiom,
! [V_24Y] :
( c_24__type__13303___24t(V_24Y)
<=> t(V_24Y,c_24__type__13303) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).
fof('$tdef_$_type_32497',axiom,
! [V_24Y] :
( c_24__type__32497___24t(V_24Y)
<=> t(V_24Y,c_24__type__32497) ) ).
fof('$tdef_$_type_20576',axiom,
! [V_24Y] :
( c_24__type__20576___24t(V_24Y)
<=> t(V_24Y,c_24__type__20576) ) ).
fof('$tdef_$_type_13849',axiom,
! [V_24Y] :
( c_24__type__13849___24t(V_24Y)
<=> t(V_24Y,c_24__type__13849) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_15975',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15975___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__15975___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_19459',axiom,
! [V_24Y] :
( c_24__type__19459___24t(V_24Y)
<=> t(V_24Y,c_24__type__19459) ) ).
fof('$tdef_$_type_13858',axiom,
! [V_24Y] :
( c_24__type__13858___24t(V_24Y)
<=> t(V_24Y,c_24__type__13858) ) ).
fof('$tdef_$_type_13597',axiom,
! [V_24Y] :
( c_24__type__13597___24t(V_24Y)
<=> t(V_24Y,c_24__type__13597) ) ).
fof('$tdef_$_type_13189',axiom,
! [V_24Y] :
( c_24__type__13189___24t(V_24Y)
<=> t(V_24Y,c_24__type__13189) ) ).
fof('$tdef_$_type_68',axiom,
! [V_24Y] :
( c_24__type__68___24t(V_24Y)
<=> t(V_24Y,c_24__type__68) ) ).
fof('$tdef_$_type_13370',axiom,
! [V_24Y] :
( c_24__type__13370___24t(V_24Y)
<=> t(V_24Y,c_24__type__13370) ) ).
fof('$tdef_$_type_29351',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__29351___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__29351___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_31256',axiom,
! [V_24Y] :
( c_24__type__31256___24t(V_24Y)
<=> t(V_24Y,c_24__type__31256) ) ).
fof('$tdef_$_type_23282',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__23282___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__23282___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_65004',axiom,
! [V_24Y] :
( c_24__type__65004___24t(V_24Y)
<=> t(V_24Y,c_24__type__65004) ) ).
fof('$tdef_$_type_35307',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__35307___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__35307___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15215',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15215___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__15215___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_22590',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__22590___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__22590___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Specif.sumbool',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13657',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13657___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13657___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16941',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__16941___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__16941___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22936',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__22936___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__22936___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_19967',axiom,
! [V_24Y] :
( c_24__type__19967___24t(V_24Y)
<=> t(V_24Y,c_24__type__19967) ) ).
fof('$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_399',axiom,
! [V_24X1,V_24Y] :
( c_24__type__399___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__399___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13892',axiom,
! [V_24Y] :
( c_24__type__13892___24t(V_24Y)
<=> t(V_24Y,c_24__type__13892) ) ).
fof('$tdef_$_type_117',axiom,
! [V_24Y] :
( c_24__type__117___24t(V_24Y)
<=> t(V_24Y,c_24__type__117) ) ).
fof('$tdef_$_type_65044',axiom,
! [V_24X1,V_24Y] :
( c_24__type__65044___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__65044___24a1(V_24X1)) ) ).
fof('$tdef_$_type_65878',axiom,
! [V_24Y] :
( c_24__type__65878___24t(V_24Y)
<=> t(V_24Y,c_24__type__65878) ) ).
fof('$tdef_$_type_13229',axiom,
! [V_24Y] :
( c_24__type__13229___24t(V_24Y)
<=> t(V_24Y,c_24__type__13229) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_57851',axiom,
! [V_24Y] :
( c_24__type__57851___24t(V_24Y)
<=> t(V_24Y,c_24__type__57851) ) ).
fof('$tdef_$_type_19311',axiom,
! [V_24Y] :
( c_24__type__19311___24t(V_24Y)
<=> t(V_24Y,c_24__type__19311) ) ).
fof('$tdef_$_type_31259',axiom,
! [V_24Y] :
( c_24__type__31259___24t(V_24Y)
<=> t(V_24Y,c_24__type__31259) ) ).
fof('$tdef_$_type_45',axiom,
! [V_24Y] :
( c_24__type__45___24t(V_24Y)
<=> t(V_24Y,c_24__type__45) ) ).
fof('$tdef_$_type_471',axiom,
! [V_24Y] :
( c_24__type__471___24t(V_24Y)
<=> t(V_24Y,c_24__type__471) ) ).
fof('$tdef_$_type_36732',axiom,
! [V_24Y] :
( c_24__type__36732___24t(V_24Y)
<=> t(V_24Y,c_24__type__36732) ) ).
fof('$tdef_$_type_13605',axiom,
! [V_24Y] :
( c_24__type__13605___24t(V_24Y)
<=> t(V_24Y,c_24__type__13605) ) ).
fof('$tdef_$_type_16184',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16184___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16184___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22035',axiom,
! [V_24Y] :
( c_24__type__22035___24t(V_24Y)
<=> t(V_24Y,c_24__type__22035) ) ).
fof('$tdef_$_type_20627',axiom,
! [V_24Y] :
( c_24__type__20627___24t(V_24Y)
<=> t(V_24Y,c_24__type__20627) ) ).
fof('$tdef_$_type_16100',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16100___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16100___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_58008',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__58008___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__58008___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_323',axiom,
! [V_24Y] :
( c_24__type__323___24t(V_24Y)
<=> t(V_24Y,c_24__type__323) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20647',axiom,
! [V_24Y] :
( c_24__type__20647___24t(V_24Y)
<=> t(V_24Y,c_24__type__20647) ) ).
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_$_type_14906',axiom,
! [V_24Y] :
( c_24__type__14906___24t(V_24Y)
<=> t(V_24Y,c_24__type__14906) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_61',axiom,
! [V_24Y] :
( c_24__type__61___24t(V_24Y)
<=> t(V_24Y,c_24__type__61) ) ).
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_$_type_28159',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__28159___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__28159___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_21632',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__21632___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__21632___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.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_24643',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__24643___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__24643___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_13227',axiom,
! [V_24Y] :
( c_24__type__13227___24t(V_24Y)
<=> t(V_24Y,c_24__type__13227) ) ).
fof('$tdef_$_type_13209',axiom,
! [V_24Y] :
( c_24__type__13209___24t(V_24Y)
<=> t(V_24Y,c_24__type__13209) ) ).
fof('$tdef_$_type_14067',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14067___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14067___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31001',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__31001___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__31001___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('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16422',axiom,
! [V_24X1,V_24Y] :
( c_24__type__16422___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__16422___24a1(V_24X1)) ) ).
fof('$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_22029',axiom,
! [V_24Y] :
( c_24__type__22029___24t(V_24Y)
<=> t(V_24Y,c_24__type__22029) ) ).
fof('$tdef_$_type_19318',axiom,
! [V_24Y] :
( c_24__type__19318___24t(V_24Y)
<=> t(V_24Y,c_24__type__19318) ) ).
fof('$tdef_$_type_16816',axiom,
! [V_24Y] :
( c_24__type__16816___24t(V_24Y)
<=> t(V_24Y,c_24__type__16816) ) ).
fof('$tdef_$_type_19818',axiom,
! [V_24Y] :
( c_24__type__19818___24t(V_24Y)
<=> t(V_24Y,c_24__type__19818) ) ).
fof('$tdef_$_type_30',axiom,
! [V_24Y] :
( c_24__type__30___24t(V_24Y)
<=> t(V_24Y,c_24__type__30) ) ).
fof('$tdef_$_type_13754',axiom,
! [V_24Y] :
( c_24__type__13754___24t(V_24Y)
<=> t(V_24Y,c_24__type__13754) ) ).
fof('$tdef_$_type_401',axiom,
! [V_24Y] :
( c_24__type__401___24t(V_24Y)
<=> t(V_24Y,c_24__type__401) ) ).
fof('$tdef_$_type_21834',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__21834___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__21834___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14940',axiom,
! [V_24Y] :
( c_24__type__14940___24t(V_24Y)
<=> t(V_24Y,c_24__type__14940) ) ).
fof('$tdef_$_type_13956',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13956___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13956___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_13378',axiom,
! [V_24Y] :
( c_24__type__13378___24t(V_24Y)
<=> t(V_24Y,c_24__type__13378) ) ).
fof('$tdef_$_type_13286',axiom,
! [V_24Y] :
( c_24__type__13286___24t(V_24Y)
<=> t(V_24Y,c_24__type__13286) ) ).
fof('$tdef_$_type_35250',axiom,
! [V_24Y] :
( c_24__type__35250___24t(V_24Y)
<=> t(V_24Y,c_24__type__35250) ) ).
fof('$tdef_$_type_22042',axiom,
! [V_24Y] :
( c_24__type__22042___24t(V_24Y)
<=> t(V_24Y,c_24__type__22042) ) ).
fof('$tdef_$_type_22019',axiom,
! [V_24Y] :
( c_24__type__22019___24t(V_24Y)
<=> t(V_24Y,c_24__type__22019) ) ).
fof('$tdef_$_type_16322',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16322___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16322___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_14055',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14055___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14055___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23951',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__23951___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__23951___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_27516',axiom,
! [V_24Y] :
( c_24__type__27516___24t(V_24Y)
<=> t(V_24Y,c_24__type__27516) ) ).
fof('$tdef_$_type_31271',axiom,
! [V_24Y] :
( c_24__type__31271___24t(V_24Y)
<=> t(V_24Y,c_24__type__31271) ) ).
fof('$tdef_$_type_26350',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__26350___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__26350___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).
fof('$tdef_$_type_58002',axiom,
! [V_24Y] :
( c_24__type__58002___24t(V_24Y)
<=> t(V_24Y,c_24__type__58002) ) ).
fof('$tdef_$_type_26996',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26996___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26996___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_90',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__90___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__90___24a2(V_24X1,V_24X2)) ) ).
fof('$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_$_type_36859',axiom,
! [V_24Y] :
( c_24__type__36859___24t(V_24Y)
<=> t(V_24Y,c_24__type__36859) ) ).
fof('$tdef_$_type_15395',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15395___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__15395___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_36610',axiom,
! [V_24X1,V_24Y] :
( c_24__type__36610___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__36610___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29759',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__29759___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__29759___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_22011',axiom,
! [V_24Y] :
( c_24__type__22011___24t(V_24Y)
<=> t(V_24Y,c_24__type__22011) ) ).
fof('$tdef_$_type_21994',axiom,
! [V_24Y] :
( c_24__type__21994___24t(V_24Y)
<=> t(V_24Y,c_24__type__21994) ) ).
fof('$tdef_$_type_65161',axiom,
! [V_24Y] :
( c_24__type__65161___24t(V_24Y)
<=> t(V_24Y,c_24__type__65161) ) ).
fof('$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_31996',axiom,
! [V_24Y] :
( c_24__type__31996___24t(V_24Y)
<=> t(V_24Y,c_24__type__31996) ) ).
fof('$tdef_$_type_443',axiom,
! [V_24Y] :
( c_24__type__443___24t(V_24Y)
<=> t(V_24Y,c_24__type__443) ) ).
fof('$tdef_$_type_13186',axiom,
! [V_24Y] :
( c_24__type__13186___24t(V_24Y)
<=> t(V_24Y,c_24__type__13186) ) ).
fof('$tdef_$_type_13214',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13214___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13214___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13175',axiom,
! [V_24Y] :
( c_24__type__13175___24t(V_24Y)
<=> t(V_24Y,c_24__type__13175) ) ).
fof('$tdef_$_type_12714',axiom,
! [V_24Y] :
( c_24__type__12714___24t(V_24Y)
<=> t(V_24Y,c_24__type__12714) ) ).
fof('$tdef_$_type_24297',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__24297___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__24297___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_22008',axiom,
! [V_24Y] :
( c_24__type__22008___24t(V_24Y)
<=> t(V_24Y,c_24__type__22008) ) ).
fof('$tdef_$_type_31118',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31118___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31118___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_392',axiom,
! [V_24Y] :
( c_24__type__392___24t(V_24Y)
<=> t(V_24Y,c_24__type__392) ) ).
fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14076___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14076___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_28284',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__28284___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__28284___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_36605',axiom,
! [V_24Y] :
( c_24__type__36605___24t(V_24Y)
<=> t(V_24Y,c_24__type__36605) ) ).
fof('$tdef_$_type_22003',axiom,
! [V_24Y] :
( c_24__type__22003___24t(V_24Y)
<=> t(V_24Y,c_24__type__22003) ) ).
fof('$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_33224',axiom,
! [V_24Y] :
( c_24__type__33224___24t(V_24Y)
<=> t(V_24Y,c_24__type__33224) ) ).
fof('$tdef_$_type_18641',axiom,
! [V_24Y] :
( c_24__type__18641___24t(V_24Y)
<=> t(V_24Y,c_24__type__18641) ) ).
fof('$tdef_$_type_27511',axiom,
! [V_24Y] :
( c_24__type__27511___24t(V_24Y)
<=> t(V_24Y,c_24__type__27511) ) ).
fof('$tdef_$_type_19222',axiom,
! [V_24Y] :
( c_24__type__19222___24t(V_24Y)
<=> t(V_24Y,c_24__type__19222) ) ).
fof('$tdef_$_type_15795',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15795___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__15795___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_28520',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__28520___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__28520___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_13869',axiom,
! [V_24Y] :
( c_24__type__13869___24t(V_24Y)
<=> t(V_24Y,c_24__type__13869) ) ).
fof('$tdef_$_type_13340',axiom,
! [V_24Y] :
( c_24__type__13340___24t(V_24Y)
<=> t(V_24Y,c_24__type__13340) ) ).
fof('$tdef_$_type_21340',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__21340___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__21340___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28034',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__28034___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__28034___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_16414',axiom,
! [V_24Y] :
( c_24__type__16414___24t(V_24Y)
<=> t(V_24Y,c_24__type__16414) ) ).
fof('$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_27342',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__27342___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__27342___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_31162',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31162___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31162___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_14506',axiom,
! [V_24Y] :
( c_24__type__14506___24t(V_24Y)
<=> t(V_24Y,c_24__type__14506) ) ).
fof('$tdef_$_type_30185',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__30185___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__30185___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_13636',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13636___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13636___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13938',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13938___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13938___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15912',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15912___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__15912___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_13952',axiom,
! [V_24Y] :
( c_24__type__13952___24t(V_24Y)
<=> t(V_24Y,c_24__type__13952) ) ).
fof('$tdef_$_type_29546',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__29546___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__29546___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_19307',axiom,
! [V_24Y] :
( c_24__type__19307___24t(V_24Y)
<=> t(V_24Y,c_24__type__19307) ) ).
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_$_type_19298',axiom,
! [V_24Y] :
( c_24__type__19298___24t(V_24Y)
<=> t(V_24Y,c_24__type__19298) ) ).
fof('$tdef_$_type_16912',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16912___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16912___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_58020',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__58020___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__58020___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_13291',axiom,
! [V_24Y] :
( c_24__type__13291___24t(V_24Y)
<=> t(V_24Y,c_24__type__13291) ) ).
fof('$tdef_$_type_15732',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15732___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__15732___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_16755',axiom,
! [V_24Y] :
( c_24__type__16755___24t(V_24Y)
<=> t(V_24Y,c_24__type__16755) ) ).
fof('$tdef_$_type_13253',axiom,
! [V_24Y] :
( c_24__type__13253___24t(V_24Y)
<=> t(V_24Y,c_24__type__13253) ) ).
fof('$tdef_$_type_31347',axiom,
! [V_24Y] :
( c_24__type__31347___24t(V_24Y)
<=> t(V_24Y,c_24__type__31347) ) ).
fof('$tdef_$_type_16853',axiom,
! [V_24Y] :
( c_24__type__16853___24t(V_24Y)
<=> t(V_24Y,c_24__type__16853) ) ).
fof('$tdef_$_type_33256',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33256___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33256___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_13342',axiom,
! [V_24Y] :
( c_24__type__13342___24t(V_24Y)
<=> t(V_24Y,c_24__type__13342) ) ).
fof('$tdef_$_type_35298',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__35298___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__35298___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_94',axiom,
! [V_24Y] :
( c_24__type__94___24t(V_24Y)
<=> t(V_24Y,c_24__type__94) ) ).
fof('$tdef_$_type_376',axiom,
! [V_24Y] :
( c_24__type__376___24t(V_24Y)
<=> t(V_24Y,c_24__type__376) ) ).
fof('$tdef_$_type_31014',axiom,
! [V_24Y] :
( c_24__type__31014___24t(V_24Y)
<=> t(V_24Y,c_24__type__31014) ) ).
fof('$tdef_$_type_14728',axiom,
! [V_24Y] :
( c_24__type__14728___24t(V_24Y)
<=> t(V_24Y,c_24__type__14728) ) ).
fof('$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_27784',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__27784___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__27784___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_27529',axiom,
! [V_24Y] :
( c_24__type__27529___24t(V_24Y)
<=> t(V_24Y,c_24__type__27529) ) ).
fof('$tdef_$_type_19220',axiom,
! [V_24Y] :
( c_24__type__19220___24t(V_24Y)
<=> t(V_24Y,c_24__type__19220) ) ).
fof('$tdef_$_type_21733',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__21733___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__21733___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_16381',axiom,
! [V_24Y] :
( c_24__type__16381___24t(V_24Y)
<=> t(V_24Y,c_24__type__16381) ) ).
fof('$tdef_$_type_13885',axiom,
! [V_24Y] :
( c_24__type__13885___24t(V_24Y)
<=> t(V_24Y,c_24__type__13885) ) ).
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_$_type_13874',axiom,
! [V_24Y] :
( c_24__type__13874___24t(V_24Y)
<=> t(V_24Y,c_24__type__13874) ) ).
fof('$tdef_$_type_18872',axiom,
! [V_24Y] :
( c_24__type__18872___24t(V_24Y)
<=> t(V_24Y,c_24__type__18872) ) ).
fof('$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_15341',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15341___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__15341___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_19204',axiom,
! [V_24Y] :
( c_24__type__19204___24t(V_24Y)
<=> t(V_24Y,c_24__type__19204) ) ).
fof('$tdef_$_type_15278',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__15278___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__15278___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_25335',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__25335___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__25335___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_14520',axiom,
! [V_24Y] :
( c_24__type__14520___24t(V_24Y)
<=> t(V_24Y,c_24__type__14520) ) ).
fof('$tdef_$_type_14511',axiom,
! [V_24Y] :
( c_24__type__14511___24t(V_24Y)
<=> t(V_24Y,c_24__type__14511) ) ).
fof('$tdef_$_type_24989',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__24989___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__24989___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_13234',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13234___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13234___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19090',axiom,
! [V_24Y] :
( c_24__type__19090___24t(V_24Y)
<=> t(V_24Y,c_24__type__19090) ) ).
fof('$tdef_$_type_16908',axiom,
! [V_24Y] :
( c_24__type__16908___24t(V_24Y)
<=> t(V_24Y,c_24__type__16908) ) ).
fof('$tdef_$_type_26673',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__26673___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__26673___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_57068',axiom,
! [V_24Y] :
( c_24__type__57068___24t(V_24Y)
<=> t(V_24Y,c_24__type__57068) ) ).
fof('$tdef_$_type_31198',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31198___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31198___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_59363',axiom,
! [V_24Y] :
( c_24__type__59363___24t(V_24Y)
<=> t(V_24Y,c_24__type__59363) ) ).
fof('$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_31242',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31242___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31242___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21441',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__21441___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__21441___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.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_23605',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__23605___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__23605___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_18835',axiom,
! [V_24Y] :
( c_24__type__18835___24t(V_24Y)
<=> t(V_24Y,c_24__type__18835) ) ).
fof('$tdef_$_type_25658',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__25658___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__25658___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_78221',axiom,
! [V_24Y] :
( c_24__type__78221___24t(V_24Y)
<=> t(V_24Y,c_24__type__78221) ) ).
fof('$tdef_$_type_16238',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16238___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16238___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_19157',axiom,
! [V_24Y] :
( c_24__type__19157___24t(V_24Y)
<=> t(V_24Y,c_24__type__19157) ) ).
fof('$tdef_$_type_16271',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16271___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16271___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_16214',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16214___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16214___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_13861',axiom,
! [V_24Y] :
( c_24__type__13861___24t(V_24Y)
<=> t(V_24Y,c_24__type__13861) ) ).
fof('$tdef_$_type_97',axiom,
! [V_24X1,V_24Y] :
( c_24__type__97___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__97___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13315',axiom,
! [V_24Y] :
( c_24__type__13315___24t(V_24Y)
<=> t(V_24Y,c_24__type__13315) ) ).
fof('$tdef_$_type_14243',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14243___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14243___24a1(V_24X1)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_29972',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__29972___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__29972___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_Coq.Reals.Ranalysis1.derivable_pt',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14503',axiom,
! [V_24Y] :
( c_24__type__14503___24t(V_24Y)
<=> t(V_24Y,c_24__type__14503) ) ).
fof('$tdef_$_type_16154',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__16154___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__16154___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_21542',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__21542___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__21542___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_13251',axiom,
! [V_24Y] :
( c_24__type__13251___24t(V_24Y)
<=> t(V_24Y,c_24__type__13251) ) ).
fof('$tdef_$_type_16386',axiom,
! [V_24Y] :
( c_24__type__16386___24t(V_24Y)
<=> t(V_24Y,c_24__type__16386) ) ).
fof('$tdef_$_type_57106',axiom,
! [V_24Y] :
( c_24__type__57106___24t(V_24Y)
<=> t(V_24Y,c_24__type__57106) ) ).
fof('$tdef_$_type_13335',axiom,
! [V_24Y] :
( c_24__type__13335___24t(V_24Y)
<=> t(V_24Y,c_24__type__13335) ) ).
fof('$tdef_$_type_525',axiom,
! [V_24Y] :
( c_24__type__525___24t(V_24Y)
<=> t(V_24Y,c_24__type__525) ) ).
fof('$tdef_$_type_25',axiom,
! [V_24Y] :
( c_24__type__25___24t(V_24Y)
<=> t(V_24Y,c_24__type__25) ) ).
fof('$tdef_$_type_14254',axiom,
! [V_24Y] :
( c_24__type__14254___24t(V_24Y)
<=> t(V_24Y,c_24__type__14254) ) ).
fof('$tdef_$_type_34423',axiom,
! [V_24Y] :
( c_24__type__34423___24t(V_24Y)
<=> t(V_24Y,c_24__type__34423) ) ).
fof('$tdef_$_type_27909',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__27909___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__27909___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_26004',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26004___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26004___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_57077',axiom,
! [V_24Y] :
( c_24__type__57077___24t(V_24Y)
<=> t(V_24Y,c_24__type__57077) ) ).
fof('$tdef_$_type_28409',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__28409___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__28409___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('_HAMMER_GOAL',conjecture,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n)))
=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) ) ) ).
%------------------------------------------------------------------------------