TPTP Problem File: SEV606+1.p
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%------------------------------------------------------------------------------
% File : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - ArithCompl Zle square simpl
% 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.Zle.square.simpl.p [Kal26]
% Status : Theorem
% Rating : 0.30 v9.3.0
% Syntax : Number of formulae : 1728 ( 464 unt; 0 def)
% Number of atoms : 6903 (1645 equ)
% Maximal formula atoms : 76 ( 3 avg)
% Number of connectives : 5273 ( 98 ~; 286 |; 876 &)
% ( 431 <=>;3582 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 6 avg)
% Maximal term depth : 13 ( 1 avg)
% Number of predicates : 179 ( 178 usr; 0 prp; 1-5 aty)
% Number of functors : 601 ( 601 usr; 367 con; 0-12 aty)
% Number of variables : 3814 (3522 !; 292 ?)
% 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.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$16639',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__16644] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__16644)
& ? [Vvar__3___24Anonymous__16645] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__16645)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__16644,Vvar__3___24Anonymous__16645)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416639___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__0,Vvar__2___24Anonymous__16644),Vvar__3___24Anonymous__16645)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3___24Anonymous__16645))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3___24Anonymous__16645,Vv__CANONICAL__0)) ) ) ) ) ) ) ).
fof('$_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$964',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ? [Vvar__2___24Anonymous__969] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__969)
& ? [Vvar__3___24Anonymous__970] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__970)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__969,Vvar__3___24Anonymous__970)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_24964___24a1(Vv__CANONICAL__0)
<=> ( Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2___24Anonymous__969,Vvar__2___24Anonymous__969),Vvar__3___24Anonymous__970)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3___24Anonymous__970))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__3___24Anonymous__970,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vvar__2___24Anonymous__969))) ) ) ) ) ) ).
fof('$_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_$_let_11_subst_l_14524',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__14524___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_1_s_19231',axiom,
! [V0__p] : c_24__let__1__s__19231___24a1(V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V0__p) ).
fof('$_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_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.nat_rec',axiom,
! [V0__P] : cCoq_2eInit_2eDatatypes_2enat__rec___24a1(V0__P) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V0__P) ).
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('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__59289] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59289)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59289)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__59290] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59290)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59290)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__59293] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59293)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59293)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__59290,Vvar__0___24Anonymous__59293) ) ) ) ) ) ) ) ).
fof('$_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.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('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Init.Wf.well_founded_induction_type',axiom,
! [V0__A,V1__R,V3__P,V4__X,V5__a] : cCoq_2eInit_2eWf_2ewell__founded__induction__type___24a5(V0__A,V1__R,V3__P,V4__X,V5__a) = cCoq_2eInit_2eWf_2eAcc__rect___24a5(V0__A,V1__R,V3__P,c_24__lam__59478___24a4(V0__A,V1__R,V3__P,V4__X),V5__a) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__19085] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19085)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19085)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__19088] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19088)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19088)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19085,Vvar__0___24Anonymous__19088)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__60494] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60494)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60494)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__60495] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60495)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60495)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__60498] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60498)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__60498)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__60495,Vvar__0___24Anonymous__60498) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__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.sub',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__65606] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65606)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65606)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__65611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65611)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65606)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65611)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65611)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__65606,Vvar__0___24Anonymous__65611) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__65614] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65614)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__65606,Vvar__0___24Anonymous__65611) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__65614)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65614) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__65606,Vvar__0___24Anonymous__65611) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__65604] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65604)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65604)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__65604)) ) ) ) ).
fof('$_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.sqrt',axiom,
! [V0__p] : cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,cCoq_2ePArith_2eBinPosDef_2ePos_2esqrtrem___24a1(V0__p)) ).
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.Qle',axiom,
! [V0__x,V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQle___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ) ).
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.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('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.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('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__399___24a1(V0__A) ).
fof('$_def_Coq.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('$_def_Coq.ZArith.BinInt.Z.b2z',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_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('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.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.lnot',axiom,
! [V0__a] : cCoq_2eZArith_2eBinInt_2eZ_2elnot___24a1(V0__a) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a)) ).
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('$_def_Coq.ZArith.BinInt.Z.ones',axiom,
! [V0__n] : cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n)) ).
fof('$_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.eqb',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__64761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64761)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64761)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64762)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64762)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__64763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64763)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64763)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64767)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64767)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__64763,Vvar__0___24Anonymous__64767) )
| ? [Vvar__0___24Anonymous__64768] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64768)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64768)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__64769] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64769)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64769)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64773] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64773)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__64773)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__64774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__64774)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__64774)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__64769,Vvar__0___24Anonymous__64774) ) ) ) ) ) ) ) ).
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.pos_sub',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__19280] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19280)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19280)
& ( ? [Vvar__0___24Anonymous__19284] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19284)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19284)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__19280,Vvar__0___24Anonymous__19284)) )
| ? [Vvar__0___24Anonymous__19285] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19285)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19285)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__19280,Vvar__0___24Anonymous__19285)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19280)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19286] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19286)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19286)
& ( ? [Vvar__0___24Anonymous__19290] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19290)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19290)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__19286,Vvar__0___24Anonymous__19290)) )
| ? [Vvar__0___24Anonymous__19291] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19291)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19291)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__19286,Vvar__0___24Anonymous__19291)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__19286)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__19292] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19292)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19292)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19292)) )
| ? [Vvar__0___24Anonymous__19293] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19293)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19293)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__19293)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ) ).
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.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.sqrtrem',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__496)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__496)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__496)
& ? [Vvar__2___24Anonymous__506] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__506)
& ? [Vvar__3___24Anonymous__507] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__3___24Anonymous__507)
& ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__3___24Anonymous__507)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2esqrtrem___24a1(Vvar__0___24Anonymous__496) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__2___24Anonymous__506,Vvar__3___24Anonymous__507)
& ( ( Vvar__3___24Anonymous__507 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__506),cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__513] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__513)
& Vvar__3___24Anonymous__507 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__513)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__506),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__513)) )
| ( Vvar__3___24Anonymous__507 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__506),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__514)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__514)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
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.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.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__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)
& ( 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)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__16724 = cCoq_2eNumbers_2eBinNums_2exH
& ( 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)
& ( 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)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__16730 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.Zpower.Zdiv_rest_proofs_rect',axiom,
! [V0__x,V1__p,V2__P,V3__f,V4__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( c_24__type__18888___24t(V0__x,V1__p,V2__P,V2__P)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V0__x,V1__p,V4__z)
=> ? [Vvar__2__q__18878] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__18878)
& ? [Vvar__3__r__18879] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__18879)
& V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__18878,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V1__p)),Vvar__3__r__18879)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__18879))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__18879,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V1__p)))
& V4__z = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V0__x,V1__p,Vvar__2__q__18878,Vvar__3__r__18879)
& cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs__rect___24a5(V0__x,V1__p,V2__P,V3__f,V4__z) = happ(happ(V3__f,Vvar__2__q__18878),Vvar__3__r__18879) ) ) ) ) ) ) ).
fof('$_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.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.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('$_discrim_Coq.Init.Datatypes.Eq$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('$_discrim_Coq.Init.Datatypes.nil$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('$_discrim_Coq.Init.Specif.left$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('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$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.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('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__13329,Vvar__0__A__13330,Vvar__1___24Anonymous__13331,Vvar__1___24Anonymous__13332,Vvar__2___24Anonymous__13333,Vvar__2___24Anonymous__13334] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13329,Vvar__1___24Anonymous__13331,Vvar__2___24Anonymous__13333) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13330,Vvar__1___24Anonymous__13332,Vvar__2___24Anonymous__13334)
=> ( Vvar__2___24Anonymous__13333 = Vvar__2___24Anonymous__13334
& Vvar__1___24Anonymous__13331 = Vvar__1___24Anonymous__13332
& Vvar__0__A__13329 = Vvar__0__A__13330 ) ) ).
fof('$_inj_Coq.Init.Datatypes.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.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('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__125,Vvar__0__A__126,Vvar__1__B__127,Vvar__1__B__128,Vvar__2___24Anonymous__129,Vvar__2___24Anonymous__130] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__125,Vvar__1__B__127) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__126,Vvar__1__B__128)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__127 = Vvar__1__B__128
& Vvar__0__A__125 = Vvar__0__A__126 ) ) ).
fof('$_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.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('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__16818,Vvar__0__a__16819,Vvar__1__b__16820,Vvar__1__b__16821,Vvar__2__u__16822,Vvar__2__u__16823,Vvar__3__v__16824,Vvar__3__v__16825,Vvar__4__d__16826,Vvar__4__d__16827,Vvar__5___24Anonymous__16828,Vvar__5___24Anonymous__16829,Vvar__6___24Anonymous__16830,Vvar__6___24Anonymous__16831] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16818,Vvar__1__b__16820,Vvar__2__u__16822,Vvar__3__v__16824,Vvar__4__d__16826) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__16819,Vvar__1__b__16821,Vvar__2__u__16823,Vvar__3__v__16825,Vvar__4__d__16827)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__16826 = Vvar__4__d__16827
& Vvar__3__v__16824 = Vvar__3__v__16825
& Vvar__2__u__16822 = Vvar__2__u__16823
& Vvar__1__b__16820 = Vvar__1__b__16821
& Vvar__0__a__16818 = Vvar__0__a__16819 ) ) ).
fof('$_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('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__14464,Vvar__0__C__14465] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14464) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14465)
=> Vvar__0__C__14464 = Vvar__0__C__14465 ) ).
fof('$_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('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__368,Vvar__1__B__369,VX370] :
( cType___24t(Vvar__0__A__368)
=> ( cType___24t(Vvar__1__B__369)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__368,Vvar__1__B__369,VX370)
=> ? [Vvar__2___24Anonymous__373] :
( t(Vvar__2___24Anonymous__373,Vvar__0__A__368)
& ? [Vvar__3___24Anonymous__374] :
( t(Vvar__3___24Anonymous__374,Vvar__1__B__369)
& VX370 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__368,Vvar__1__B__369,Vvar__2___24Anonymous__373,Vvar__3___24Anonymous__374) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX27] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX27)
=> VX27 = cCoq_2eInit_2eDatatypes_2ett ) ).
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.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.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('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX58788] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX58788)
=> ( VX58788 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX58788 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX58788 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_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('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX14259] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX14259)
=> ( VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__14260] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14260)
& ? [Vvar__1___24Anonymous__14261] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__14261)
& VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14260,Vvar__1___24Anonymous__14261) ) )
| ? [Vvar__0___24Anonymous__14262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14262)
& ? [Vvar__1___24Anonymous__14263] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__14263)
& VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__14262,Vvar__1___24Anonymous__14263) ) ) ) ) ).
fof('$_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('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__14078,VX14079] :
( cType___24t(Vvar__0__C__14078)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,VX14079)
=> ( ? [Vvar__1___24Anonymous__14081] :
( t(Vvar__1___24Anonymous__14081,Vvar__0__C__14078)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14078,Vvar__1___24Anonymous__14081) )
| ? [Vvar__1___24Anonymous__14083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14083)
& ? [Vvar__2___24Anonymous__14084] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__2___24Anonymous__14084)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14078,Vvar__1___24Anonymous__14083,Vvar__2___24Anonymous__14084) ) )
| ? [Vvar__1___24Anonymous__14086] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__1___24Anonymous__14086)
& ? [Vvar__2___24Anonymous__14087] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14087)
& ? [Vvar__3___24Anonymous__14088] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__3___24Anonymous__14088)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__14078,Vvar__1___24Anonymous__14086,Vvar__2___24Anonymous__14087,Vvar__3___24Anonymous__14088) ) ) ) ) ) ) ).
fof('$_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('$_lam_259',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__264] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__264)
& ? [Vvar__3___24Anonymous__265] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__265)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__264,Vvar__3___24Anonymous__265)
& ( c_24__lam__259___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( Vv__CANONICAL__1 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__0,Vvar__2___24Anonymous__264),Vvar__3___24Anonymous__265)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3___24Anonymous__265))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3___24Anonymous__265,Vv__CANONICAL__0)) ) ) ) ) ) ).
fof('$_lam_300',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__305] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__305)
& ? [Vvar__3___24Anonymous__306] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__306)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__305,Vvar__3___24Anonymous__306)
& ( c_24__lam__300___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( Vv__CANONICAL__1 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__0,Vvar__2___24Anonymous__305),Vvar__3___24Anonymous__306)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3___24Anonymous__306))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3___24Anonymous__306,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(Vv__CANONICAL__0))) ) ) ) ) ) ).
fof('$_lam_59478',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6] : c_24__lam__59478___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__6) ).
fof('$_lam_68508',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__68508___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vv__CANONICAL__1) ) ).
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('$_prop_35229',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__35229___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_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_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_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('$_type_13636',axiom,
! [Vv__CANONICAL__0,Vvar__13637] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vvar__13637)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13637,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_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('$_type_13849',axiom,
! [Vvar__13850] :
( c_24__type__13849___24t(Vvar__13850)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__13850,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_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_14048',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14049] :
( c_24__type__14048___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14049)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__14049,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
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_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('$_type_16386',axiom,
! [Vvar__16387] :
( c_24__type__16386___24t(Vvar__16387)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__16387,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_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_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_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('$_type_18888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18889] :
( c_24__type__18888___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18889)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cType___24t(happ(Vvar__18889,Vv__CANONICAL__3)) ) ) ).
fof('$_type_18949',axiom,
! [Vvar__18950] :
( c_24__type__18949___24t(Vvar__18950)
<=> ! [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] :
( c_24__type__18953___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__18982___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__18950,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_18953',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18954] :
( c_24__type__18953___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18954)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__18954,Vv__CANONICAL__2)) ) ) ).
fof('$_type_18982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18983] :
( c_24__type__18982___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18983)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ( Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__3,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vv__CANONICAL__1)),Vv__CANONICAL__4)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__4))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__4,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vv__CANONICAL__1)))
=> t(happ(happ(Vvar__18983,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ) ) ).
fof('$_type_18997',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18998] :
( c_24__type__18997___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18998)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__18998,Vv__CANONICAL__2)) ) ) ).
fof('$_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('$_type_19295',axiom,
! [Vvar__19296] :
( c_24__type__19295___24t(Vvar__19296)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__19296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_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('$_type_21994',axiom,
! [Vvar__21995] :
( c_24__type__21994___24t(Vvar__21995)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21995,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_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('$_type_245',axiom,
! [Vvar__246] :
( c_24__type__245___24t(Vvar__246)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),c_24__lam__259___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(happ(Vvar__246,Vv__CANONICAL__0),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_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('$_type_286',axiom,
! [Vvar__287] :
( c_24__type__286___24t(Vvar__287)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( Vv__CANONICAL__0 != cCoq_2eNumbers_2eBinNums_2eZ0
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),c_24__lam__300___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(happ(Vvar__287,Vv__CANONICAL__0),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_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('$_type_31256',axiom,
! [Vvar__31257] :
( c_24__type__31256___24t(Vvar__31257)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__31257,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_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_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('$_type_34421',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34422] :
( c_24__type__34421___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34422)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__2))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) )
=> t(happ(Vvar__34422,Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ).
fof('$_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('$_type_35232',axiom,
! [Vvar__35233] :
( c_24__type__35232___24t(Vvar__35233)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__956___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__956___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35233,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_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_515',axiom,
! [Vvar__516] :
( c_24__type__515___24t(Vvar__516)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__516,Vv__CANONICAL__0)) ) ) ).
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_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('$_type_59295',axiom,
! [Vvar__59296] :
( c_24__type__59295___24t(Vvar__59296)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__59296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_59418',axiom,
! [Vvar__59419] :
( c_24__type__59418___24t(Vvar__59419)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__59419,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_59522',axiom,
! [Vvar__59523] :
( c_24__type__59522___24t(Vvar__59523)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eWf_2ewell__founded___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( c_24__type__59528___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__59550___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__59523,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_59528',axiom,
! [Vv__CANONICAL__0,Vvar__59529] :
( c_24__type__59528___24t(Vv__CANONICAL__0,Vvar__59529)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__59529,Vv__CANONICAL__1)) ) ) ).
fof('$_type_59550',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__59551] :
( c_24__type__59550___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__59551)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( c_24__type__59565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__59551,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_59565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__59566] :
( c_24__type__59565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__59566)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> t(happ(Vvar__59566,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_59575',axiom,
! [Vvar__59576] :
( c_24__type__59575___24t(Vvar__59576)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__16414___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__59578___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__2))
=> t(happ(happ(happ(Vvar__59576,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_59578',axiom,
! [Vv__CANONICAL__0,Vvar__59579] :
( c_24__type__59578___24t(Vv__CANONICAL__0,Vvar__59579)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__59579,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_59635',axiom,
! [Vvar__59636] :
( c_24__type__59635___24t(Vvar__59636)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__16414___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__59653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__59636,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_59653',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__59654] :
( c_24__type__59653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__59654)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__59662___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> t(happ(happ(Vvar__59654,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_59662',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__59663] :
( c_24__type__59662___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__59663)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> t(happ(Vvar__59663,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_60221',axiom,
! [Vvar__60222] :
( c_24__type__60221___24t(Vvar__60222)
<=> ! [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_2eZArith_2eBinIntDef_2eZ_2emin___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__60222,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_60500',axiom,
! [Vvar__60501] :
( c_24__type__60500___24t(Vvar__60501)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__60501,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60503',axiom,
! [Vvar__60504] :
( c_24__type__60503___24t(Vvar__60504)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__60504,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60511',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__60512] :
( c_24__type__60511___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__60512)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__60512,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_60515',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__60516] :
( c_24__type__60515___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__60516)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__60516,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
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_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('$_type_68505',axiom,
! [Vvar__68506] :
( c_24__type__68505___24t(Vvar__68506)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__0))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__68508___24a1(Vv__CANONICAL__0),happ(Vvar__68506,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_68531',axiom,
! [Vvar__68532] :
( c_24__type__68531___24t(Vvar__68532)
<=> ! [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__68539___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__68532,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_68539',axiom,
! [Vv__CANONICAL__0,Vvar__68540] :
( c_24__type__68539___24t(Vv__CANONICAL__0,Vvar__68540)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(Vv__CANONICAL__1)))
=> t(happ(happ(Vvar__68540,Vv__CANONICAL__1),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_68555',axiom,
! [Vvar__68556] :
( c_24__type__68555___24t(Vvar__68556)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__16414___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__68565___24t(Vv__CANONICAL__0,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))
=> t(happ(happ(happ(Vvar__68556,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_68565',axiom,
! [Vv__CANONICAL__0,Vvar__68566] :
( c_24__type__68565___24t(Vv__CANONICAL__0,Vvar__68566)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__34421___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__68566,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_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('$_type_90',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__91] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__91)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__91,Vv__CANONICAL__2)) ) ) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__13342___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__13209___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__13189___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_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.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_rec',axiom,
c_24__type__13227___24t(cCoq_2eInit_2eDatatypes_2enat__rec) ).
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.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.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.Nat.add',axiom,
c_24__type__13849___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__59295___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_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.sub',axiom,
c_24__type__13849___24t(cCoq_2eInit_2eNat_2esub) ).
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.sumbool',axiom,
c_24__type__117___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__59418___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Init.Wf.well_founded_induction_type',axiom,
c_24__type__59522___24t(cCoq_2eInit_2eWf_2ewell__founded__induction__type) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__13361___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__60503___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__60503___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__19090___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__60500___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__19090___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
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('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__19090___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__57851___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
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('$_typeof_Coq.PArith.BinPosDef.Pos.sqrt',axiom,
c_24__type__12___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt) ).
fof('$_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.Qle',axiom,
c_24__type__22011___24t(cCoq_2eQArith_2eQArith__base_2eQle) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__22003___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_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.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('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__16816___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.IZN_var',axiom,
c_24__type__68505___24t(cCoq_2eReals_2eRiemannInt__SF_2eIZN__var) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__31256___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__401___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Odd',axiom,
c_24__type__74___24t(cCoq_2eZArith_2eBinInt_2eZ_2eOdd) ).
fof('$_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.eqf',axiom,
c_24__type__35232___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
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('$_typeof_Coq.ZArith.BinInt.Z.lnot',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinInt_2eZ_2elnot) ).
fof('$_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.ones',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinInt_2eZ_2eones) ).
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.eqb',axiom,
c_24__type__525___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb) ).
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('$_typeof_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
c_24__type__19295___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub) ).
fof('$_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.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.sqrtrem',axiom,
c_24__type__515___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem) ).
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('$_typeof_Coq.ZArith.Wf_Z.Z_lt_rec',axiom,
c_24__type__68555___24t(cCoq_2eZArith_2eWf__Z_2eZ__lt__rec) ).
fof('$_typeof_Coq.ZArith.Wf_Z.Z_of_nat_complete_inf',axiom,
c_24__type__68505___24t(cCoq_2eZArith_2eWf__Z_2eZ__of__nat__complete__inf) ).
fof('$_typeof_Coq.ZArith.Wf_Z.Z_of_nat_set',axiom,
c_24__type__59575___24t(cCoq_2eZArith_2eWf__Z_2eZ__of__nat__set) ).
fof('$_typeof_Coq.ZArith.Wf_Z.Zlt_lower_bound_rec',axiom,
c_24__type__59635___24t(cCoq_2eZArith_2eWf__Z_2eZlt__lower__bound__rec) ).
fof('$_typeof_Coq.ZArith.Wf_Z.natlike_rec',axiom,
c_24__type__16412___24t(cCoq_2eZArith_2eWf__Z_2enatlike__rec) ).
fof('$_typeof_Coq.ZArith.Wf_Z.natlike_rec2',axiom,
c_24__type__16412___24t(cCoq_2eZArith_2eWf__Z_2enatlike__rec2) ).
fof('$_typeof_Coq.ZArith.Wf_Z.natlike_rec3',axiom,
c_24__type__68531___24t(cCoq_2eZArith_2eWf__Z_2enatlike__rec3) ).
fof('$_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.Zdiv.Remainder',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Zdiv.Zdiv_eucl_exist',axiom,
c_24__type__245___24t(cCoq_2eZArith_2eZdiv_2eZdiv__eucl__exist) ).
fof('$_typeof_Coq.ZArith.Zdiv.Zdiv_eucl_extended',axiom,
c_24__type__286___24t(cCoq_2eZArith_2eZdiv_2eZdiv__eucl__extended) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__74___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zmin.Zmin_le_prime_inf',axiom,
c_24__type__60221___24t(cCoq_2eZArith_2eZmin_2eZmin__le__prime__inf) ).
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('$_typeof_Coq.ZArith.Znumtheory.euclid_rec',axiom,
c_24__type__31442___24t(cCoq_2eZArith_2eZnumtheory_2eeuclid__rec) ).
fof('$_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('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs_rect',axiom,
c_24__type__18949___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs__rect) ).
fof('$_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('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_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('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__14511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_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.Peq',axiom,
c_24__type__14254___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
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.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('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_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_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_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_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_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_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.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.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.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.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.iter_swap_gen',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__60511___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__60515___24t(V0__A,V1__B,V3__g)
=> ! [V4__h] :
( c_24__type__14048___24t(V0__A,V1__B,V4__h)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.sqrt_spec',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(c_24__let__1__s__19231___24a1(V0__p),c_24__let__1__s__19231___24a1(V0__p)),V0__p)
& cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(c_24__let__1__s__19231___24a1(V0__p)),cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(c_24__let__1__s__19231___24a1(V0__p)))) ) ) ).
fof('Coq.PArith.BinPos.Pos.sqrtrem_spec',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrtrem___24a1(V0__p),V0__p) ) ).
fof('Coq.Reals.RIneq.IZN',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ? [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
& V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V2__m) ) ) ) ).
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.le_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ).
fof('Coq.Reals.RIneq.le_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(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.Raxioms.Rmult_1_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__r) = V0__r ) ).
fof('Coq.Reals.Rfunctions.Zpower_NR0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eZpower_2eZpower__nat___24a2(V0__x,V1__n))) ) ) ) ).
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.A\'A_left',axiom,
! [V0__A] :
( c_24__type__74___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ! [Vvar__4__m__61068] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__m__61068)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__4__m__61068,V1__z))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,Vvar__4__m__61068))
=> p(happ(V0__A,Vvar__4__m__61068)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__n,V1__z))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.A\'A_right',axiom,
! [V0__A] :
( c_24__type__74___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ! [Vvar__4__m__60991] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__m__60991)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__z,Vvar__4__m__60991))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__4__m__60991,V2__n))
=> p(happ(V0__A,Vvar__4__m__60991)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__z,V3__n))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.add_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)
=> ( 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(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.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.add_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)
=> ( 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(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.Private_Div.NZQuot.div_1_r',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_2equot___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__a ) ) ).
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_div',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_2equot___24a2(V0__a,V1__b),V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_exact',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))
=> ( V0__a = 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) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_le_compat_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__q))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__q,V2__r)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__p,V2__r),cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__p,V1__q))) ) ) ) ) ) ).
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_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_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.Private_Div.NZQuot.div_mul_le',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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,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_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_2equot___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_small_iff',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(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_str_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V0__a)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.div_str_pos_iff',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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V0__a)) ) ) ) ) ) ).
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_1_r',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_2erem___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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_divides',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_2erem___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ? [V4__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__c)
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V4__c) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mod_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_2erem___24a2(V0__a,V1__b),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mod_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( 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__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__n),V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__n) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mod_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_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mod_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,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_2erem___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b),V2__c))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.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_2erem___24a2(V0__a,V1__b) = V0__a ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mod_small_iff',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_2erem___24a2(V0__a,V1__b) = V0__a
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ) ) ).
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.NZQuot.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)
=> ( 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_2emul___24a2(V0__a,V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___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.Private_Div.NZQuot.mul_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)
=> ( 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_2erem___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_2erem___24a2(V0__a,V1__b)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mul_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)
=> ( 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_2erem___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_2erem___24a2(V0__a,V1__b),V2__c) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mul_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_2emul___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_2emul___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mul_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)
=> ( 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_2emul___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_2emul___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.NZQuot.mul_succ_div_gt',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_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))))) ) ) ) ) ).
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_Div.Quot2Div.mod_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_2erem) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.add_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)
=> ( 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_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___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.Private_NZDiv.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_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___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_2eadd___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.add_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)
=> ( 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_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V1__b,V2__n)),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_1_r',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_2ediv___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__a ) ) ).
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_div',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_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.BinInt.Z.Private_NZDiv.div_exact',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))
=> ( 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.Private_NZDiv.div_le_compat_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__q))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__q,V2__r)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__p,V2__r),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__p,V1__q))) ) ) ) ) ) ).
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_mul_le',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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,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_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.Private_NZDiv.div_small_iff',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(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_str_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V0__a)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_str_pos_iff',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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V0__a)) ) ) ) ) ) ).
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_1_r',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_2emodulo___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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_divides',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_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ? [V4__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__c)
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V4__c) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.mod_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_2emodulo___24a2(V0__a,V1__b),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.mod_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( 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__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.BinInt.Z.Private_NZDiv.mod_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_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.mod_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,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_2emodulo___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V2__c))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.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.Private_NZDiv.mod_small_iff',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_2emodulo___24a2(V0__a,V1__b) = V0__a
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b)) ) ) ) ) ) ).
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_NZDiv.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)
=> ( 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_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.Private_NZDiv.mul_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)
=> ( 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_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.BinInt.Z.Private_NZDiv.mul_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)
=> ( 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_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.BinInt.Z.Private_NZDiv.mul_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_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.BinInt.Z.Private_NZDiv.mul_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)
=> ( 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_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V1__b,V2__n)),V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V2__n) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.mul_succ_div_gt',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_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))))) ) ) ) ) ).
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.le_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_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.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_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_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_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_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_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_Tac.le_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_2ele___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_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_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.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_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_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_spec',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 )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___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.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_le_cases',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_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V3__q)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V3__q)) ) ) ) ) ) ) ).
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_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_neg_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_2elt___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_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_nonneg_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(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___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)) ) ) ) ) ).
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_nonneg_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_2ele___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_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_nonpos_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(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,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(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_nonpos_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_2ele___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_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_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_pos_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_2elt___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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_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_2eadd___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_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_sqrt_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_2esqrt___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b))))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_sqrt_up_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_2eBinInt_2eZ_2esqrt__up___24a1(V0__a),cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b)))))) ) ) ) ) ).
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.bit0_odd',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__a) ) ).
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_above_log2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__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.bits_inj_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a1(V1__b))
<=> V0__a = V1__b ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_inj_iff\'',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.bits_m1',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_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_opp',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a),V1__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__a),V1__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_antisym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V1__m,V0__n) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(c_24__prop__35229___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_sub',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
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.div2_bits',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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_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_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.div_div',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_2elt___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.BinInt.Z.div_le_compat_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__q))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__q,V2__r)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__p,V2__r),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__p,V1__q))) ) ) ) ) ) ).
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_le',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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),V1__b))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_opp_opp',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_2eopp___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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.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_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.divide_1_r_nonneg',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_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_antisym_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))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_gcd_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_lcm_eq_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_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2elcm___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_lcm_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
<=> cCoq_2eZArith_2eBinInt_2eZ_2elcm___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
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_pos_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ) ).
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_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_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_sym',axiom,
cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.gcd_0_l_nonneg',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_2egcd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_0_r_nonneg',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_2egcd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_diag_nonneg',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_2egcd___24a2(V0__n,V0__n) = V0__n ) ) ).
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_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_l_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(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m)) ) ) ) ) ).
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_unique',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_2eBinInt_2eZ_2edivide___24a2(V2__p,V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__p,V1__m)
=> ( ! [V6__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__q)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__q,V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__q,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__q,V2__p) ) ) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = V2__p ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_unique_alt',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))
=> ( ! [V4__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__q)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V4__q,V2__p)
<=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V4__q,V0__n)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V4__q,V1__m) ) ) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = V2__p ) ) ) ) ) ).
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.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.land_comm',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V1__b,V0__a) ) ) ).
fof('Coq.ZArith.BinInt.Z.land_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_2eland___24a2(V0__a,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)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lbase',axiom,
! [V0__A] :
( c_24__type__74___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ! [Vvar__3__m__61065] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__m__61065)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__3__m__61065,V1__z))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__z),Vvar__3__m__61065))
=> p(happ(V0__A,Vvar__3__m__61065)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_1_l_nonneg',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_2eBinInt_2eZ_2elcm___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_1_r_nonneg',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_2eBinInt_2eZ_2elcm___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_diag_nonneg',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_2eBinInt_2eZ_2elcm___24a2(V0__n,V0__n) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_mul_mono_l_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_2eBinInt_2eZ_2elcm___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,cCoq_2eZArith_2eBinInt_2eZ_2elcm___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_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_2eBinInt_2eZ_2elcm___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_2eBinInt_2eZ_2elcm___24a2(V0__n,V1__m),V2__p) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_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_2eBinInt_2eZ_2elcm___24a2(V0__a,V1__b))) ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_unique',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_2eBinInt_2eZ_2edivide___24a2(V0__n,V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__m,V2__p)
=> ( ! [V6__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__q)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V6__q)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__m,V6__q)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__p,V6__q) ) ) )
=> cCoq_2eZArith_2eBinInt_2eZ_2elcm___24a2(V0__n,V1__m) = V2__p ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lcm_unique_alt',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))
=> ( ! [V4__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__q)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__p,V4__q)
<=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V4__q)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__m,V4__q) ) ) )
=> cCoq_2eZArith_2eBinInt_2eZ_2elcm___24a2(V0__n,V1__m) = V2__p ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ldiff_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,V1__b))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eldiff___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ldiff_neg',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_2eldiff___24a2(V0__a,V1__b),cCoq_2eNumbers_2eBinNums_2eZ0))
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ldiff_spec',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_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eldiff___24a2(V0__a,V1__b),V2__n) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n),cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ldiff_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_2eldiff) ).
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_0_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(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_add_le_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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_antisymm',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))
=> V0__n = V1__m ) ) ) ) ).
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_add_le',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(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_2ele___24a2(V2__p,V3__q)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_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_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_le_sub_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_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V3__q,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q)) ) ) ) ) ) ) ).
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_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(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(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_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,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_pred_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n),V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.le_pred_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_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
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_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_2ele___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_stepr',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.le_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_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_sub_le_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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V2__p),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_sub_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_2esub___24a2(V0__n,V1__m),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.leb_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.leb_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lnot_shiftr',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinInt_2eZ_2elnot___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elnot___24a1(V0__a),V1__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lnot_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elnot___24a1(V0__a),V1__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_land',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_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V1__b)))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_le_lin',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),V0__a)) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_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_2elog2___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V1__b))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_log2_up_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a)),V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a)))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_lor',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V1__b)) ) ) ) ) ).
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_lt_lin',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),V0__a)) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_lt_pow2',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(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),V1__b)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_lxor',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_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V1__b)))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_mul_above',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_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V1__b)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_mul_pow2',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b))) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a)) ) ) ) ) ).
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_pow2',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_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__a)) = V0__a ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__n)),V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__n))))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_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_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b),V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__b)))) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a) = V1__b ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_1',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.log2_up_eqn',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a))
=> 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))) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_eqn0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))
=> cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_le_lin',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a),V0__a)) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_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_2elog2__up___24a1(V0__a),cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V1__b))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_le_pow2',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(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a),V1__b)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_lt_lin',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a),V0__a)) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_mul_above',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_2eBinInt_2eZ_2elog2__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a),cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V1__b)))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_mul_pow2',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))
=> cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b))) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__b,cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a)) ) ) ) ) ).
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_nonpos',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_2elog2__up___24a1(V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( 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_2eZ0,cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a))) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_pow2',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_2elog2__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__a)) = V0__a ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( 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_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(V0__a))),V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),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.lor_spec',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_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b),V2__n) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n),cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n)) ) ) ) ).
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_0_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
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_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_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_exists_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))
=> ? [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
& V1__n = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V3__k)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__z,V3__k)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_exists_pred_strong',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ! [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__z,V2__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__m,V1__n))
=> ? [V5__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k)
& V2__m = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V5__k)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__z,V5__k)) ) ) ) ) ) ) ).
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_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,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V2__n)))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___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_2elt___24a2(V2__n,V5__m))
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
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_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_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_pred_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n),V0__n)) ) ).
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_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_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_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( 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.ltb_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lxor_comm',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V1__b,V0__a) ) ) ).
fof('Coq.ZArith.BinInt.Z.lxor_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_2elxor___24a2(V0__a,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)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lxor_spec',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_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b),V2__n) = cCoq_2eInit_2eDatatypes_2exorb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n),cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n)) ) ) ) ).
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_le',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_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V0__n))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_lub',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,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m),V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_lub_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_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m),V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_lub_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_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m),V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p)) ) ) ) ) ).
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.max_spec',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_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = 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.min_glb',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,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_glb_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_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_glb_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_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,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_le',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_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m),V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p)) ) ) ) ) ) ).
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.min_spec',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_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( 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_bound_or',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_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)) )
| ( 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_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_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_2emodulo___24a2(V0__a,V1__b),V0__a)) ) ) ) ) ).
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_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_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_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_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_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_max_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_max_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___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_2emax___24a2(V0__n,V1__m),V2__p) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_max_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_max_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___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_2emin___24a2(V0__n,V1__m),V2__p) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_min_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_min_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___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_2emin___24a2(V0__n,V1__m),V2__p) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_min_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_min_distr_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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___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_2emax___24a2(V0__n,V1__m),V2__p) ) ) ) ) ).
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_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_pow2_bits',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__m,V1__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pow2_bits_add',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__n,V2__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pred_quot_gt',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(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pred_quot_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_2ele___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( 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(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_quot_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_2ele___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( 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_2equot___24a2(V0__a,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)),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_quot_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))
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,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.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_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_quot_gt',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_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_succ_quot_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_2ele___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b))),V0__a)) ) ) ) ) ).
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.neg_nonneg_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,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.nle_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_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.nonpos_nonneg_cases',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_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ).
fof('Coq.ZArith.BinInt.Z.nonpos_pos_cases',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_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,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.ones_spec_high',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)) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ones_spec_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ones_spec_low',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(V1__m,V0__n)) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
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_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_nonpos_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),cCoq_2eNumbers_2eBinNums_2eZ0))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ).
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.order_induction_0',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)
=> ( p(happ(V0__A,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__n))
=> ( p(happ(V0__A,V3__n))
=> p(happ(V0__A,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V3__n))) ) ) )
=> ( ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(happ(V0__A,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V4__n)))
=> p(happ(V0__A,V4__n)) ) ) )
=> ! [V5__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__n)
=> p(happ(V0__A,V5__n)) ) ) ) ) ) ) ).
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_l',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_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a) = 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_add_lower',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,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V1__b,V2__c)),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__c))) ) ) ) ) ) ) ).
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_add_upper',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,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V2__c)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___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_eq_0',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))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_gt_lin_r',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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_inj_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V2__c) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V1__b,V2__c)
=> V0__a = V1__b ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_inj_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a))
=> ( 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,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V2__c)
=> V1__b = V2__c ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_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)
=> ! [V3__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__d)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,V2__c)) )
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V3__d))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V2__c,V3__d))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_le_mono_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_2ele___24a2(V0__a,V1__b)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___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_le_mono_l_iff',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,V1__b))
=> ( 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_2epow___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V1__b,V2__c))) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_le_mono_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___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_le_mono_r_iff',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_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__b,V2__c))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___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_lt_mono_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_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_2elt___24a2(V0__a,V1__b)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___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_lt_mono_l_iff',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,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__b))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___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_lt_mono_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___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_lt_mono_r_iff',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_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V2__c))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___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_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_odd_sgn',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))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2eOdd___24a1(V1__b)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__a) ) ) ) ) ).
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.pow_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_2epow) ).
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.pred_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_2epred) ).
fof('Coq.ZArith.BinInt.Z.quadmul_le_squareadd',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(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V0__a),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.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_div_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_le_compat_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__q))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__q,V2__r)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__p,V2__r),cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__p,V1__q))) ) ) ) ) ) ).
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_le',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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),V1__b))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_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_2equot___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a),V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_opp_opp',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_2eopp___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_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_2equot___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.quot_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.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_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_2equot___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
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.quot_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_2equot) ).
fof('Coq.ZArith.BinInt.Z.rbase',axiom,
! [V0__A] :
( c_24__type__74___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ! [Vvar__3__m__60988] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__m__60988)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__z,Vvar__3__m__60988))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__m__60988,V1__z))
=> p(happ(V0__A,Vvar__3__m__60988)) ) ) ) ) ) ).
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_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.rem_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_2erem___24a2(V0__a,V1__b),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_mod_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_nonneg',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,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_nonpos',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(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,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_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_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.setbit_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esetbit___24a2(V0__a,V1__n),V1__n) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.ZArith.BinInt.Z.setbit_neq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> ( V1__n != V2__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esetbit___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__m) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.sgn_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_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ).
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_spec',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) )
| ( cCoq_2eNumbers_2eBinNums_2eZ0 = V0__n
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftl_eq_0_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__a = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftl_mul_pow2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftl_shiftl',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__n,V2__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftl_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__m,V1__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftl_spec_alt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__m,V1__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftl_spec_high',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__n,V2__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__m,V1__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_div_pow2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_eq_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_mul_pow2',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_shiftl_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__m,V1__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_shiftr',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__n,V2__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__m,V1__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_spec_aux',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n),V2__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__m,V1__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.shiftr_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_2eshiftr) ).
fof('Coq.ZArith.BinInt.Z.sqrt_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.sqrt_1',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ).
fof('Coq.ZArith.BinInt.Z.sqrt_eq_succ_iff_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_2esucc___24a1(V0__a)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a))
<=> ? [V2__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__b))
& cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__a) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__b,V2__b) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_le_lin',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a),V0__a)) ) ) ).
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_above',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(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(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_pred_square',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_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a))) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___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_alt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__r)
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a)),V2__r)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__r,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a)))) ) ) ) ).
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_sqrt_up_exact',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(V0__a) = cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a)
<=> ? [V2__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__b))
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__b,V2__b) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_sqrt_up_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( 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(V0__a)),V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a),cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a)))) ) ) ) ).
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_succ_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__a)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a)))) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_succ_or',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_2esucc___24a1(V0__a)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a))
| cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__a)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(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_0',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_eq_succ_iff_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_2esucc___24a1(V0__a)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a))
<=> ? [V2__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__b))
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__b,V2__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_lin',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a),V0__a)) ) ) ).
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_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(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b),V0__a))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_mul_above',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_2eBinInt_2eZ_2esqrt__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___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_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_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a)),cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a))),V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a),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_succ_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__a)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a)))) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_succ_or',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_2esucc___24a1(V0__a)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a))
| cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__a)) = cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V0__a) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_up_succ_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_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a))) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(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.sqrtrem_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_24964___24a1(V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.square_add_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_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),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.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.strong_right_induction',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__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__z,V3__n))
=> ( ! [Vvar__6__m__60998] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__6__m__60998)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__z,Vvar__6__m__60998))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__6__m__60998,V3__n))
=> p(happ(V0__A,Vvar__6__m__60998)) ) ) )
=> p(happ(V0__A,V3__n)) ) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__z,V4__n))
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.sub_add',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_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ).
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_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_2esub___24a2(V2__p,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__p,V0__n))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_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_2esub___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_nonneg_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(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___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(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_nonpos_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(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,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.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.sub_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_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),V1__m) = V0__n ) ) ).
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_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_even_succ',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) ) ) ) ).
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.testbit_odd_succ',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(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__a),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_of_N\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__a),V1__n) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_ones_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__i)
=> ( 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__i))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V0__n),V1__i) = cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V1__i,V0__n) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_spec',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> ? [V3__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l)
& ? [V4__h] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__h)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__l))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__l,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)))
& V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V4__h)),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_spec\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_succ_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___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(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__a),cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V2__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_unique',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__a0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__a0)
=> ! [V3__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l)
=> ! [V4__h] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__h)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__l))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__l,cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n))) )
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V2__a0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V4__h)),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__n)))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = V2__a0 ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.testbit_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__525,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__956,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eZArith_2eBinInt_2eZ_2eeq,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool))),cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit) ).
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.Z2Pos.to_pos_nonpos',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
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.Wf_Z.Z_lt_induction',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( ! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
=> ( ! [V2__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__y))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__y,V1__x)) )
=> p(happ(V0__P,V2__y)) ) )
=> p(happ(V0__P,V1__x)) ) )
=> ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__x))
=> p(happ(V0__P,V2__x)) ) ) ) ) ).
fof('Coq.ZArith.Wf_Z.Z_of_nat_complete',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ? [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
& V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V2__n) ) ) ) ).
fof('Coq.ZArith.Wf_Z.Z_of_nat_prop',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__n))) )
=> ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__x))
=> p(happ(V0__P,V2__x)) ) ) ) ) ).
fof('Coq.ZArith.Wf_Z.Zlt_0_ind',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( ! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
=> ( ! [V2__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__y))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__y,V1__x)) )
=> p(happ(V0__P,V2__y)) ) )
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__x))
=> p(happ(V0__P,V1__x)) ) ) )
=> ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__x))
=> p(happ(V0__P,V2__x)) ) ) ) ) ).
fof('Coq.ZArith.Wf_Z.Zlt_lower_bound_ind',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__x)
=> ( ! [V3__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__y)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__z,V3__y))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__y,V2__x)) )
=> p(happ(V0__P,V3__y)) ) )
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__z,V2__x))
=> p(happ(V0__P,V2__x)) ) ) )
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__z,V3__x))
=> p(happ(V0__P,V3__x)) ) ) ) ) ) ).
fof('Coq.ZArith.Wf_Z.natlike_ind',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__x))
=> ( p(happ(V0__P,V2__x))
=> p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V2__x))) ) ) )
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__x))
=> p(happ(V0__P,V3__x)) ) ) ) ) ) ).
fof('Coq.ZArith.Zabs.Zabs_nat_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) )
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Zabs.Zabs_nat_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) )
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Zbool.Zle_bool_imp_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__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_le',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_2egt___24a2(V2__c,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_2ediv___24a2(V0__a,V2__c),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,V2__c))) ) ) ) ) ) ).
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_POS',axiom,
! [V0__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ! [V2__a] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__a)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416639___24a2(V0__b,V2__a) ) ) ) ).
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_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_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( 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_2ediv___24a2(V0__a,V1__b))) ) ) ) ) ).
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_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_compat_l',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__q))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__q,V2__r)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__p,V2__r),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__p,V1__q))) ) ) ) ) ) ).
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_mult_le',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,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__c))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),V1__b))) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zdiv_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.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_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_2eNumbers_2eBinNums_2eZ0,V0__a))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Zmod_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,V1__n)) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__n) = V0__a ) ) ) ).
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.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___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.Znat.Z2N.id',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_2eof__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj',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))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_add',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_compare',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))
=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_div',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_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_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,V1__m))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_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_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_2elt___24a2(V0__n,V1__m))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_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,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_pow',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_quot',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_rem',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_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(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Z2N.inj_succ',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_2eto__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n)) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.id',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_2eof__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj',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))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_add',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_compare',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))
=> cCoq_2eInit_2eNat_2ecompare___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_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_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,V1__m))
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_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_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_2elt___24a2(V0__n,V1__m))
<=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_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,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_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(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Z2Nat.inj_succ',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_2eto__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n)) ) ) ).
fof('Coq.ZArith.Znat.Z_N_nat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n) ) ).
fof('Coq.ZArith.Znat.Zabs2N.abs_N_nonneg',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__N___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__n) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_add',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_compare',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))
=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_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_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,V1__m))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_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_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_2elt___24a2(V0__n,V1__m))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_max',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_min',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_pow',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_2eabs__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_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(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2N.inj_succ',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__N___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__n)) ) ) ).
fof('Coq.ZArith.Znat.Zabs2Nat.abs_nat_nonneg',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__nat___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__n) ) ) ).
fof('Coq.ZArith.Znat.Zabs2Nat.inj_add',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))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2Nat.inj_compare',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))
=> cCoq_2eInit_2eNat_2ecompare___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2Nat.inj_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_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,V1__m))
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2Nat.inj_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_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_2elt___24a2(V0__n,V1__m))
<=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m)) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2Nat.inj_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(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) )
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Zabs2Nat.inj_succ',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__nat___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__n)) ) ) ).
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.Z_0_1_more',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
| V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__x)) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zdivide_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))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,V1__b)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___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_mod_minus',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_2elt___24a2(V2__c,V1__b)) )
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__a,V2__c))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = V2__c ) ) ) ) ) ).
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_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_gcd',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))
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__c)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = V2__c ) ) ) ) ) ).
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.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_ind',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__P] :
( cProp___24t(V1__P)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__p))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V3__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V3__n,V0__p)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V3__n,V0__p) ) )
=> p(V1__P) ) )
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V0__p)
=> p(V1__P) ) ) ) ) ).
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.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_0_minus_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_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
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.Zle_minus_le_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(V1__m,V0__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m))) ) ) ) ).
fof('Coq.ZArith.Zorder.Zle_succ_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_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(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_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_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_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_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_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_le_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)
=> ( 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)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zplus_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_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ) ).
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.Zpower.Zdiv_rest_proofs_ind',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ! [V2__P] :
( c_24__type__18997___24t(V0__x,V1__p,V2__P)
=> ( ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ! [V4__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r)
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__q,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V1__p)),V4__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V4__r))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__r,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V1__p)))
=> p(happ(V2__P,cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V0__x,V1__p,V3__q,V4__r))) ) ) ) ) )
=> ! [V4__z] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V0__x,V1__p,V4__z)
=> p(happ(V2__P,V4__z)) ) ) ) ) ) ).
fof('Coq.ZArith.Zpower.Zdiv_rest_proofs_sind',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ! [V2__P] :
( c_24__type__18997___24t(V0__x,V1__p,V2__P)
=> ( ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ! [V4__r] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__r)
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__q,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V1__p)),V4__r)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V4__r))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V4__r,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V1__p)))
=> p(happ(V2__P,cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V0__x,V1__p,V3__q,V4__r))) ) ) ) ) )
=> ! [V4__z] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V0__x,V1__p,V4__z)
=> p(happ(V2__P,V4__z)) ) ) ) ) ) ).
fof('Coq.ZArith.Zpower.Zpower_nat_Zpower',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__z,V1__n) = cCoq_2eZArith_2eZpower_2eZpower__nat___24a2(V0__z,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__n)) ) ) ) ).
fof('Coq.ZArith.Zpower.two_p_S',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> cCoq_2eZArith_2eZpower_2etwo__p___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x)) ) ) ).
fof('Coq.ZArith.Zpower.two_p_gt_ZERO',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.ZArith.Zpower.two_p_is_exp',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))
=> cCoq_2eZArith_2eZpower_2etwo__p___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x),cCoq_2eZArith_2eZpower_2etwo__p___24a1(V1__y)) ) ) ) ) ).
fof('Coq.ZArith.Zpower.two_p_pred',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eZpower_2etwo__p___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x)),cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x))) ) ) ).
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.Zle_left_rev',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_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_mult_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(V2__p,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_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n),V2__p))) ) ) ) ) ) ) ).
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.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.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.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.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.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.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_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_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.omega.PreOmega.Z.rem_bound_neg_neg',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,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ).
fof('Coq.omega.PreOmega.Z.rem_bound_neg_pos',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,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,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.omega.PreOmega.Z.rem_bound_pos_neg',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(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y),cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ).
fof('Coq.omega.PreOmega.Z.rem_bound_pos_pos',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(cCoq_2eNumbers_2eBinNums_2eZ0,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,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y),V1__y)) ) ) ) ) ) ).
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('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$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('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$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('$adef_Coq.ZArith.BinIntDef.Z.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elxor,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEc_$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('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$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('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$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('$adef_Coq.setoid_ring.Ring_polynom.Pol_$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('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_34425_$a1',axiom,
! [V_24X1] : happ(c_24__prop__34425,V_24X1) = c_24__prop__34425___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.ZArith.BinIntDef.Z.testbit_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_lam_68508_$a1',axiom,
! [V_24X1] : happ(c_24__lam__68508,V_24X1) = c_24__lam__68508___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.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.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_$_lam_18639_$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('$adef_$_lam_300_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__300,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__300___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.ZArith.BinIntDef.Z.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2esub,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_59478_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__59478,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__59478___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$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('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
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('$adef_Coq.ZArith.BinIntDef.Z.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_259_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__259,V_24X1),V_24X2) = c_24__lam__259___24a2(V_24X1,V_24X2) ).
fof('$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_$_let_1_s_19231_$a1',axiom,
! [V_24X1] : happ(c_24__let__1__s__19231,V_24X1) = c_24__let__1__s__19231___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.QArith.QArith_base.Qle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQle,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$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('$adef_Coq.Init.Datatypes.nil_$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('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$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('$adef_Coq.ZArith.Znumtheory.Bezout_$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('$adef_Coq.Numbers.BinNums.xI_$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.BinIntDef.Z.sqrtrem_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrtrem___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_Coq.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.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.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.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_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_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.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_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.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.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.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.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_$_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('$adef_Coq.ZArith.BinIntDef.Z.add_$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('$adef_$_case_Coq.Init.Datatypes.prod$16639_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416639,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416639___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sqrtrem_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrtrem,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrtrem___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.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.ZArith.Zpower.Zpower_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZpower__nat,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZpower__nat___24a2(V_24X1,V_24X2) ).
fof('$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.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_$_prop_35229_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35229,V_24X1),V_24X2) = c_24__prop__35229___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_68508_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__68508,V_24X1),V_24X2))
<=> c_24__lam__68508___24a2(V_24X1,V_24X2) ) ).
fof('$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.Init.Wf.Acc_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2eAcc__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_$_lam_300_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__300,V_24X1),V_24X2) = c_24__lam__300___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_259_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__259,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__259___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.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.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.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.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.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.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.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_$_lam_18639_$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('$adef_$_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.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.BinIntDef.Z.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eland,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.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.Init.Wf.well_founded_induction_type_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2ewell__founded__induction__type,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2ewell__founded__induction__type___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_let_11_subst_l_14524_$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('$adef_Coq.ZArith.BinIntDef.Z.testbit_$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('$adef_$_lam_59478_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__59478,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__59478___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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.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.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.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_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.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.NArith.BinNatDef.N.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epow,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.nat_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rec___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.ones_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eones,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eones___24a1(V_24X1) ).
fof('$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('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$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('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$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('$adef_$_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('$adef_Coq.Classes.Morphisms.respectful_$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('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.setbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2esetbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2esetbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___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_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.ZArith.BinIntDef.Z.rem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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.BinIntDef.Z.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eldiff,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eldiff___24a2(V_24X1,V_24X2) ).
fof('$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('$adef_Coq.ZArith.BinIntDef.Z.quot_$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('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div2_$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('$adef_Coq.ZArith.BinIntDef.Z.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double___24a1(V_24X1) ).
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.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_18637_$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('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lnot_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2elnot,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2elnot___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('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$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('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$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('$adef_$_case_Coq.Init.Datatypes.prod$964_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_24964,V_24X1))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_24964___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('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$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('$adef_Coq.ZArith.BinIntDef.Z.min_$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('$adef_Coq.ZArith.BinInt.Zne_$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('$adef_$_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('$adef_Coq.Init.Specif.left_$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('$adef_Coq.ZArith.BinIntDef.Z.pow_$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('$adef_Coq.ZArith.BinInt.Z.Odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eBinInt_2eZ_2eOdd,V_24X1))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eOdd___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.PreOrder_$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('$adef_Coq.ZArith.BinIntDef.Z.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elor,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2elor___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('$adef_Coq.PArith.BinPosDef.Pos.add_$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('$tdef_$_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('$tdef_$_type_13192',axiom,
! [V_24Y] :
( c_24__type__13192___24t(V_24Y)
<=> t(V_24Y,c_24__type__13192) ) ).
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_$_type_13361',axiom,
! [V_24Y] :
( c_24__type__13361___24t(V_24Y)
<=> t(V_24Y,c_24__type__13361) ) ).
fof('$tdef_$_type_19325',axiom,
! [V_24Y] :
( c_24__type__19325___24t(V_24Y)
<=> t(V_24Y,c_24__type__19325) ) ).
fof('$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_$_type_59418',axiom,
! [V_24Y] :
( c_24__type__59418___24t(V_24Y)
<=> t(V_24Y,c_24__type__59418) ) ).
fof('$tdef_$_type_19295',axiom,
! [V_24Y] :
( c_24__type__19295___24t(V_24Y)
<=> t(V_24Y,c_24__type__19295) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_18949',axiom,
! [V_24Y] :
( c_24__type__18949___24t(V_24Y)
<=> t(V_24Y,c_24__type__18949) ) ).
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_$_type_16412',axiom,
! [V_24Y] :
( c_24__type__16412___24t(V_24Y)
<=> t(V_24Y,c_24__type__16412) ) ).
fof('$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_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_13871',axiom,
! [V_24Y] :
( c_24__type__13871___24t(V_24Y)
<=> t(V_24Y,c_24__type__13871) ) ).
fof('$tdef_$_type_60503',axiom,
! [V_24Y] :
( c_24__type__60503___24t(V_24Y)
<=> t(V_24Y,c_24__type__60503) ) ).
fof('$tdef_$_type_19321',axiom,
! [V_24Y] :
( c_24__type__19321___24t(V_24Y)
<=> t(V_24Y,c_24__type__19321) ) ).
fof('$tdef_$_type_60221',axiom,
! [V_24Y] :
( c_24__type__60221___24t(V_24Y)
<=> t(V_24Y,c_24__type__60221) ) ).
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_59295',axiom,
! [V_24Y] :
( c_24__type__59295___24t(V_24Y)
<=> t(V_24Y,c_24__type__59295) ) ).
fof('$tdef_$_type_19459',axiom,
! [V_24Y] :
( c_24__type__19459___24t(V_24Y)
<=> t(V_24Y,c_24__type__19459) ) ).
fof('$tdef_$_type_13189',axiom,
! [V_24Y] :
( c_24__type__13189___24t(V_24Y)
<=> t(V_24Y,c_24__type__13189) ) ).
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_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('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$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_$_type_117',axiom,
! [V_24Y] :
( c_24__type__117___24t(V_24Y)
<=> t(V_24Y,c_24__type__117) ) ).
fof('$tdef_$_type_68505',axiom,
! [V_24Y] :
( c_24__type__68505___24t(V_24Y)
<=> t(V_24Y,c_24__type__68505) ) ).
fof('$tdef_$_type_13229',axiom,
! [V_24Y] :
( c_24__type__13229___24t(V_24Y)
<=> t(V_24Y,c_24__type__13229) ) ).
fof('$tdef_$_type_68565',axiom,
! [V_24X1,V_24Y] :
( c_24__type__68565___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__68565___24a1(V_24X1)) ) ).
fof('$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_$_type_45',axiom,
! [V_24Y] :
( c_24__type__45___24t(V_24Y)
<=> t(V_24Y,c_24__type__45) ) ).
fof('$tdef_$_type_68539',axiom,
! [V_24X1,V_24Y] :
( c_24__type__68539___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__68539___24a1(V_24X1)) ) ).
fof('$tdef_$_type_471',axiom,
! [V_24Y] :
( c_24__type__471___24t(V_24Y)
<=> t(V_24Y,c_24__type__471) ) ).
fof('$tdef_$_type_323',axiom,
! [V_24Y] :
( c_24__type__323___24t(V_24Y)
<=> t(V_24Y,c_24__type__323) ) ).
fof('$tdef_$_type_14906',axiom,
! [V_24Y] :
( c_24__type__14906___24t(V_24Y)
<=> t(V_24Y,c_24__type__14906) ) ).
fof('$tdef_$_type_61',axiom,
! [V_24Y] :
( c_24__type__61___24t(V_24Y)
<=> t(V_24Y,c_24__type__61) ) ).
fof('$tdef_$_type_59662',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__59662___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__59662___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_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('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$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_$_type_19318',axiom,
! [V_24Y] :
( c_24__type__19318___24t(V_24Y)
<=> t(V_24Y,c_24__type__19318) ) ).
fof('$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_$_type_401',axiom,
! [V_24Y] :
( c_24__type__401___24t(V_24Y)
<=> t(V_24Y,c_24__type__401) ) ).
fof('$tdef_$_type_18953',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18953___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18953___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_90',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__90___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__90___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
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_286',axiom,
! [V_24Y] :
( c_24__type__286___24t(V_24Y)
<=> t(V_24Y,c_24__type__286) ) ).
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_22008',axiom,
! [V_24Y] :
( c_24__type__22008___24t(V_24Y)
<=> t(V_24Y,c_24__type__22008) ) ).
fof('$tdef_$_type_14048',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14048___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14048___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_392',axiom,
! [V_24Y] :
( c_24__type__392___24t(V_24Y)
<=> t(V_24Y,c_24__type__392) ) ).
fof('$tdef_$_type_59635',axiom,
! [V_24Y] :
( c_24__type__59635___24t(V_24Y)
<=> t(V_24Y,c_24__type__59635) ) ).
fof('$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_59653',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__59653___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__59653___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35232',axiom,
! [V_24Y] :
( c_24__type__35232___24t(V_24Y)
<=> t(V_24Y,c_24__type__35232) ) ).
fof('$tdef_$_type_18888',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18888___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18888___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_18982',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18982___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18982___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_34421',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34421___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34421___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22003',axiom,
! [V_24Y] :
( c_24__type__22003___24t(V_24Y)
<=> t(V_24Y,c_24__type__22003) ) ).
fof('$tdef_$_type_18641',axiom,
! [V_24Y] :
( c_24__type__18641___24t(V_24Y)
<=> t(V_24Y,c_24__type__18641) ) ).
fof('$tdef_$_type_59565',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__59565___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__59565___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_19222',axiom,
! [V_24Y] :
( c_24__type__19222___24t(V_24Y)
<=> t(V_24Y,c_24__type__19222) ) ).
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_16414',axiom,
! [V_24Y] :
( c_24__type__16414___24t(V_24Y)
<=> t(V_24Y,c_24__type__16414) ) ).
fof('$tdef_$_type_14506',axiom,
! [V_24Y] :
( c_24__type__14506___24t(V_24Y)
<=> t(V_24Y,c_24__type__14506) ) ).
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_59522',axiom,
! [V_24Y] :
( c_24__type__59522___24t(V_24Y)
<=> t(V_24Y,c_24__type__59522) ) ).
fof('$tdef_$_type_515',axiom,
! [V_24Y] :
( c_24__type__515___24t(V_24Y)
<=> t(V_24Y,c_24__type__515) ) ).
fof('$tdef_$_type_60511',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__60511___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__60511___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19307',axiom,
! [V_24Y] :
( c_24__type__19307___24t(V_24Y)
<=> t(V_24Y,c_24__type__19307) ) ).
fof('$tdef_$_type_19298',axiom,
! [V_24Y] :
( c_24__type__19298___24t(V_24Y)
<=> t(V_24Y,c_24__type__19298) ) ).
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_59578',axiom,
! [V_24X1,V_24Y] :
( c_24__type__59578___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__59578___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13342',axiom,
! [V_24Y] :
( c_24__type__13342___24t(V_24Y)
<=> t(V_24Y,c_24__type__13342) ) ).
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_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_$_type_19220',axiom,
! [V_24Y] :
( c_24__type__19220___24t(V_24Y)
<=> t(V_24Y,c_24__type__19220) ) ).
fof('$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_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('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_59575',axiom,
! [V_24Y] :
( c_24__type__59575___24t(V_24Y)
<=> t(V_24Y,c_24__type__59575) ) ).
fof('$tdef_$_type_14511',axiom,
! [V_24Y] :
( c_24__type__14511___24t(V_24Y)
<=> t(V_24Y,c_24__type__14511) ) ).
fof('$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_$_type_68531',axiom,
! [V_24Y] :
( c_24__type__68531___24t(V_24Y)
<=> t(V_24Y,c_24__type__68531) ) ).
fof('$tdef_$_type_19090',axiom,
! [V_24Y] :
( c_24__type__19090___24t(V_24Y)
<=> t(V_24Y,c_24__type__19090) ) ).
fof('$tdef_$_type_59550',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__59550___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__59550___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_59528',axiom,
! [V_24X1,V_24Y] :
( c_24__type__59528___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__59528___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18835',axiom,
! [V_24Y] :
( c_24__type__18835___24t(V_24Y)
<=> t(V_24Y,c_24__type__18835) ) ).
fof('$tdef_$_type_68555',axiom,
! [V_24Y] :
( c_24__type__68555___24t(V_24Y)
<=> t(V_24Y,c_24__type__68555) ) ).
fof('$tdef_$_type_19157',axiom,
! [V_24Y] :
( c_24__type__19157___24t(V_24Y)
<=> t(V_24Y,c_24__type__19157) ) ).
fof('$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('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_14503',axiom,
! [V_24Y] :
( c_24__type__14503___24t(V_24Y)
<=> t(V_24Y,c_24__type__14503) ) ).
fof('$tdef_$_type_60515',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__60515___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__60515___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_60500',axiom,
! [V_24Y] :
( c_24__type__60500___24t(V_24Y)
<=> t(V_24Y,c_24__type__60500) ) ).
fof('$tdef_$_type_16386',axiom,
! [V_24Y] :
( c_24__type__16386___24t(V_24Y)
<=> t(V_24Y,c_24__type__16386) ) ).
fof('$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_$_type_245',axiom,
! [V_24Y] :
( c_24__type__245___24t(V_24Y)
<=> t(V_24Y,c_24__type__245) ) ).
fof('$tdef_$_type_18997',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18997___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18997___24a2(V_24X1,V_24X2)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [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)) ) ) ) ) ) ).
%------------------------------------------------------------------------------