TPTP Problem File: SEV605+1.p
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%------------------------------------------------------------------------------
% File : SEV605+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - ArithCompl frac rat
% 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_frac_rat.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2576 ( 999 unt; 0 def)
% Number of atoms : 8264 (2544 equ)
% Maximal formula atoms : 76 ( 3 avg)
% Number of connectives : 5936 ( 248 ~; 426 |;1279 &)
% ( 757 <=>;3226 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 5 avg)
% Maximal term depth : 19 ( 2 avg)
% Number of predicates : 335 ( 334 usr; 0 prp; 1-15 aty)
% Number of functors : 1365 (1365 usr; 815 con; 0-16 aty)
% Number of variables : 6186 (5714 !; 472 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.bool$19369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__19331__19341__19343__19365___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419369___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),c_24__let__var__var__var__6__r_27__19331__19341__19343__19365___24a1(Vv__CANONICAL__2)) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__19331__19341__19343__19365___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419369___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(c_24__let__var__var__var__6__r_27__19331__19341__19343__19365___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$19375',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__19349__19359__19361__19371___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419375___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),c_24__let__var__var__var__6__r_27__19349__19359__19361__19371___24a1(Vv__CANONICAL__2)) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__19349__19359__19361__19371___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419375___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(c_24__let__var__var__var__6__r_27__19349__19359__19361__19371___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.comparison$19712',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eEq
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2419712___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eLt
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2419712___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eGt
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2419712___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_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$19737',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__19742] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19742)
& ? [Vvar__3___24Anonymous__19743] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19743)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19742,Vvar__3___24Anonymous__19743)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419737___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2___24Anonymous__19742,Vv__CANONICAL__1),Vvar__3___24Anonymous__19743) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$19752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__19757] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19757)
& ? [Vvar__3___24Anonymous__19758] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19758)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19757,Vvar__3___24Anonymous__19758)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419752___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__1,Vvar__2___24Anonymous__19757),Vvar__3___24Anonymous__19758) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$32085',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__32086] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32086)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32086)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32086) )
| ? [Vvar__0___24Anonymous__32087] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32087)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32087)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32087) ) ) ) ).
fof('$_def_$_cast_16432',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& c_24__cast__16432___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__16433,c_24__prop__16434) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& c_24__cast__16432___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__16436,c_24__prop__16437,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ecomparison,cCoq_2eInit_2eDatatypes_2eLt)) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& c_24__cast__16432___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__16438,c_24__prop__16439) ) ) ) ) ).
fof('$_def_$_cast_59730',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& c_24__cast__59730___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__59731,c_24__prop__59732) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& c_24__cast__59730___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__59734,c_24__prop__59735) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& c_24__cast__59730___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__59737,c_24__prop__59738) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_14524',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__14524___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_32944',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__32947] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32947)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32947)
& c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__32948] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32948)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32948)
& c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_32945',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__32945___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_32946',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__32946___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__32944___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_2_s_19729',axiom,
! [V0__n] : c_24__let__2__s__19729___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) ).
fof('$_def_$_let_6_lmp_13887',axiom,
! [V2__lpe] : c_24__let__6__lmp__13887___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_6_lmp_16424',axiom,
! [V2__lpe] : c_24__let__6__lmp__16424___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_6_lmp_32026',axiom,
! [V2__lpe] : c_24__let__6__lmp__32026___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_var_11_x_35460_35510',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35459] : c_24__let__var__11__x__35460__35510___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35459) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35459) ).
fof('$_def_$_let_var_11_x_35463_35511',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35462] : c_24__let__var__11__x__35463__35511___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35462) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35462) ).
fof('$_def_$_let_var_4_a0_17034_17122',axiom,
! [V0__a] : c_24__let__var__4__a0__17034__17122___24a1(V0__a) = V0__a ).
fof('$_def_$_let_var_6_a0_17037_17124',axiom,
! [V1__b] : c_24__let__var__6__a0__17037__17124___24a1(V1__b) = V1__b ).
fof('$_def_$_let_var_6_p_14926_14929',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925] : c_24__let__var__6__p__14926__14929___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925) ).
fof('$_def_$_let_var_6_p_14928_14930',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927] : c_24__let__var__6__p__14928__14930___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927) ).
fof('$_def_$_let_var_var_12_x_35418_35421_35491',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415] : c_24__let__var__var__12__x__35418__35421__35491___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415) ).
fof('$_def_$_let_var_var_12_x_35431_35434_35497',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428] : c_24__let__var__var__12__x__35431__35434__35497___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428) ).
fof('$_def_$_let_var_var_12_x_35444_35448_35506',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441] : c_24__let__var__var__12__x__35444__35448__35506___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441) ).
fof('$_def_$_let_var_var_12_x_35468_35472_35518',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465] : c_24__let__var__var__12__x__35468__35472__35518___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465) ).
fof('$_def_$_let_var_var_12_x_35485_35487_35522',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35483] : c_24__let__var__var__12__x__35485__35487__35522___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35483) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35483) ).
fof('$_def_$_let_var_var_13_y_35419_35422_35492',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35416] : c_24__let__var__var__13__y__35419__35422__35492___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35416) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35416) ).
fof('$_def_$_let_var_var_13_y_35432_35435_35498',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35429] : c_24__let__var__var__13__y__35432__35435__35498___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35429) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35429) ).
fof('$_def_$_let_var_var_13_y_35445_35449_35507',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35442] : c_24__let__var__var__13__y__35445__35449__35507___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35442) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35442) ).
fof('$_def_$_let_var_var_13_y_35469_35473_35519',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35466] : c_24__let__var__var__13__y__35469__35473__35519___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35466) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35466) ).
fof('$_def_$_let_var_var_14_s1_35446_35450_35508',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442] : c_24__let__var__var__14__s1__35446__35450__35508___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__35444__35448__35506___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__35445__35449__35507___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35442))) ).
fof('$_def_$_let_var_var_14_s1_35470_35474_35520',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466] : c_24__let__var__var__14__s1__35470__35474__35520___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__35468__35472__35518___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__35469__35473__35519___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35466))) ).
fof('$_def_$_let_var_var_14_s_35420_35423_35493',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416] : c_24__let__var__var__14__s__35420__35423__35493___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__35418__35421__35491___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__35419__35422__35492___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35416))) ).
fof('$_def_$_let_var_var_14_s_35433_35436_35499',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429] : c_24__let__var__var__14__s__35433__35436__35499___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__35431__35434__35497___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__35432__35435__35498___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35429))) ).
fof('$_def_$_let_var_var_15_s2_35447_35451_35509',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442] : c_24__let__var__var__15__s2__35447__35451__35509___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__35445__35449__35507___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35442)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__35444__35448__35506___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441))) ).
fof('$_def_$_let_var_var_15_s2_35471_35475_35521',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466] : c_24__let__var__var__15__s2__35471__35475__35521___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__35468__35472__35518___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__35469__35473__35519___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35466))) ).
fof('$_def_$_let_var_var_var_6_r\'_19331_19341_19343_19365',axiom,
! [Vvar__3___24Anonymous__19339] : c_24__let__var__var__var__6__r_27__19331__19341__19343__19365___24a1(Vvar__3___24Anonymous__19339) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vvar__3___24Anonymous__19339),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_$_let_var_var_var_6_r\'_19349_19359_19361_19371',axiom,
! [Vvar__3___24Anonymous__19357] : c_24__let__var__var__var__6__r_27__19349__19359__19361__19371___24a1(Vvar__3___24Anonymous__19357) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vvar__3___24Anonymous__19357) ).
fof('$_def_ArithCompl.R_p4',axiom,
! [V0__x,V1__y] :
( cArithCompl_2eR__p4___24a2(V0__x,V1__y)
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))
& ? [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__d,V2__d),V0__x)
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V2__d)) ) ) ) ).
fof('$_def_ArithCompl.distinct_parity',axiom,
! [V0__a,V1__b] :
( cArithCompl_2edistinct__parity___24a2(V0__a,V1__b)
<=> ( ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__a)
& cCoq_2eZArith_2eZeven_2eZodd___24a1(V1__b) )
| ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__a)
& cCoq_2eZArith_2eZeven_2eZeven___24a1(V1__b) ) ) ) ).
fof('$_def_ArithCompl.frac',axiom,
! [V0__a,V1__b] : cArithCompl_2efrac___24a2(V0__a,V1__b) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__a),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__b)) ).
fof('$_def_Coq.Arith.Factorial.fact',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__19991] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19991)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19991)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19991),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__19991)) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
! [V0__r] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
=> ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__35244] :
( t(Vvar__1___24Anonymous__35244,V0__A)
& ? [Vvar__2___24Anonymous__35245] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35245)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35244,Vvar__2___24Anonymous__35245)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35244,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__35245,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__64813] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__64813)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__64813)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__64813 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__20897] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20897)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20897)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__20900] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20900)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20900)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__20897,Vvar__0___24Anonymous__20900) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__66267___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__66261] :
( t(Vvar__2__x__66261,V0__A)
& p(happ(V1__P,Vvar__2__x__66261))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__66261)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__66261 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.sig_rec',axiom,
! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esig__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V0__A,V1__P,V2__P) ).
fof('$_def_Coq.Init.Specif.sumbool_rec',axiom,
! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V0__A,V1__B,V2__P) ).
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.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_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.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__34690] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34690)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34690)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__34693] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34693)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34693)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__34690,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__31340] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31340)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31340)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__31341] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31341)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31341)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31344] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31344)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31344)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31341,Vvar__0___24Anonymous__31344) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__19092] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19092)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19092)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__19095] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19095)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__19095)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__19092,Vvar__0___24Anonymous__19095)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__31346] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31346)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31346)
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__31346)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.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] :
( p(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('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__66277] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66277)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66277)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__66277)) ) ) ) ).
fof('$_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.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__22005] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__22005)
& ? [Vvar__1__Qden__22006] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__22006)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__22005,Vvar__1__Qden__22006)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__22006 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq',axiom,
! [V0__p,V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__p,V1__q)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qinv',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ( ( cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__32014] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32014)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32014)
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)),Vvar__0___24Anonymous__32014) )
| ? [Vvar__0___24Anonymous__32015] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32015)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32015)
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)),Vvar__0___24Anonymous__32015) ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qmult',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y)),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__22000] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__22000)
& ? [Vvar__1__Qden__22001] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__22001)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__22000,Vvar__1__Qden__22001)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__22000 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qpower',axiom,
! [V0__q,V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ( V1__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__32021] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32021)
& V1__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32021)
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V0__q,Vvar__0___24Anonymous__32021) )
| ? [Vvar__0___24Anonymous__32022] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32022)
& V1__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32022)
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQinv___24a1(cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V0__q,Vvar__0___24Anonymous__32022)) ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qpower_positive',axiom,
cCoq_2eQArith_2eQArith__base_2eQpower__positive = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_def_Coq.Reals.AltSeries.tg_alt',axiom,
! [V0__Un,V1__i] : cCoq_2eReals_2eAltSeries_2etg__alt___24a2(V0__Un,V1__i) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__i),happ(V0__Un,V1__i)) ).
fof('$_def_Coq.Reals.PSeries_reg.Boule',axiom,
! [V0__x,V1__r,V2__y] :
( cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V0__x,V1__r,V2__y)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__y,V0__x)),cCoq_2eReals_2eRIneq_2epos___24a1(V1__r))) ) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.RIneq.pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> ? [Vvar__0__pos__64828] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__64828)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__64828))
& V0__p = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__64828)
& cCoq_2eReals_2eRIneq_2epos___24a1(V0__p) = Vvar__0__pos__64828 ) ) ).
fof('$_def_Coq.Reals.R_Ifp.Int_part',axiom,
! [V0__r] : cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V0__r) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.Reals.R_Ifp.frac_part',axiom,
! [V0__r] : cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V0__r))) ).
fof('$_def_Coq.Reals.R_sqrt.sqrt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = cCoq_2eReals_2eRsqrt__def_2eRsqrt___24a1(cCoq_2eReals_2eRIneq_2emknonnegreal___24a2(V0__x,cCoq_2eReals_2eRIneq_2eRge__le___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.comp',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f1,V1__f2,V2__x) = happ(V0__f1,happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.continuity',axiom,
! [V0__f] :
( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f)
<=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V1__x) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.continuity_pt',axiom,
! [V0__f,V1__x0] :
( cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V1__x0)
<=> cCoq_2eReals_2eRderiv_2econtinue__in___24a3(V0__f,cCoq_2eReals_2eRanalysis1_2eno__cond,V1__x0) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt',axiom,
! [V0__f,V1__x] : cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V0__f,V1__x) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__22033___24a2(V0__f,V1__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt_abs',axiom,
! [V0__f,V1__x,V2__l] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(V0__f,V1__x,V2__l)
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt_lim',axiom,
! [V0__f,V1__x,V2__l] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l)
<=> ! [V3__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V3__eps))
=> ? [V5__delta] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V5__delta)
& ! [V6__h] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__h)
=> ( V6__h != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V6__h),cCoq_2eReals_2eRIneq_2epos___24a1(V5__delta)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__x,V6__h)),happ(V0__f,V1__x)),V6__h),V2__l)),V3__eps)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derive_pt',axiom,
! [V0__f,V1__x,V2__pr] : cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__22033___24a2(V0__f,V1__x),V2__pr) ).
fof('$_def_Coq.Reals.Ranalysis1.div_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2ediv__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.fct_cte',axiom,
! [V0__a,V1__x] : cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V0__a,V1__x) = V0__a ).
fof('$_def_Coq.Reals.Ranalysis1.id',axiom,
! [V0__x] : cCoq_2eReals_2eRanalysis1_2eid___24a1(V0__x) = V0__x ).
fof('$_def_Coq.Reals.Ranalysis1.minus_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2eminus__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.mult_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.no_cond',axiom,
! [V0__x] :
( cCoq_2eReals_2eRanalysis1_2eno__cond___24a1(V0__x)
<=> p(c_24True) ) ).
fof('$_def_Coq.Reals.Ratan.Datan_seq',axiom,
! [V0__x,V1__n] : cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V0__x,V1__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n)) ).
fof('$_def_Coq.Reals.Ratan.Ratan_seq',axiom,
! [V0__x,V1__n] : cCoq_2eReals_2eRatan_2eRatan__seq___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ).
fof('$_def_Coq.Reals.Ratan.atan',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__65918] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__65918)
& c_24__lam__65922___24a2(V0__x,Vvar__2__x__65918)
& cCoq_2eReals_2eRatan_2epre__atan___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__65922___24a1(V0__x),Vvar__2__x__65918)
& cCoq_2eReals_2eRatan_2eatan___24a1(V0__x) = Vvar__2__x__65918 ) ) ).
fof('$_def_Coq.Reals.Ratan.ps_atan_exists_01',axiom,
! [V0__x] : cCoq_2eReals_2eRatan_2eps__atan__exists__01___24a1(V0__x) = cCoq_2eReals_2eAltSeries_2ealternated__series___24a3(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V0__x),cCoq_2eReals_2eRatan_2eRatan__seq__decreasing___24a1(V0__x),cCoq_2eReals_2eRatan_2eRatan__seq__converging___24a1(V0__x)) ).
fof('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__13864] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13864)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13864)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13864)
& ( ( Vvar__0___24Anonymous__13864 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__13867] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13867)
& Vvar__0___24Anonymous__13864 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13867)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__13864),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Raxioms.bound',axiom,
! [V0__E] :
( cCoq_2eReals_2eRaxioms_2ebound___24a1(V0__E)
<=> ? [V1__m] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__m)
& cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m) ) ) ).
fof('$_def_Coq.Reals.Raxioms.is_lub',axiom,
! [V0__E,V1__m] :
( cCoq_2eReals_2eRaxioms_2eis__lub___24a2(V0__E,V1__m)
<=> ( cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m)
& ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V2__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__m,V2__b)) ) ) ) ) ).
fof('$_def_Coq.Reals.Raxioms.is_upper_bound',axiom,
! [V0__E,V1__m] :
( cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V0__E,V1__m)
<=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(happ(V0__E,V2__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__x,V1__m)) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rabs',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) )
| ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmax',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__77795___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V1__y )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__77796___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V0__x ) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmin',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__65001___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V0__x )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__65002___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V1__y ) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IPR',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__13881] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13881)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__13881)
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__13881)) )
| ? [Vvar__0___24Anonymous__13882] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13882)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__13882)
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__13882) )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eR1 ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IPR_2',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__13877] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13877)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__13877)
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__13877))) )
| ? [Vvar__0___24Anonymous__13878] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13878)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__13878)
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1),cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__13878)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__13883] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13883)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13883)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__13883) )
| ? [Vvar__0___24Anonymous__13884] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13884)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13884)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__13884)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rderiv.D_x',axiom,
! [V0__D,V1__y,V2__x] :
( cCoq_2eReals_2eRderiv_2eD__x___24a3(V0__D,V1__y,V2__x)
<=> ( p(happ(V0__D,V2__x))
& V1__y != V2__x ) ) ).
fof('$_def_Coq.Reals.Rfunctions.R_dist',axiom,
! [V0__x,V1__y] : cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__x,V1__y)) ).
fof('$_def_Coq.Reals.Rfunctions.powerRZ',axiom,
! [V0__x,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__57111] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__57111)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__57111)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__57111)) )
| ? [Vvar__0___24Anonymous__57112] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__57112)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__57112)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__57112))) ) ) ) ).
fof('$_def_Coq.Reals.Rfunctions.sum_f_R0',axiom,
! [V1__f,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__13890] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13890)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13890)
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,Vvar__0___24Anonymous__13890),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13890))) ) ) ) ).
fof('$_def_Coq.Reals.Rlimit.Base',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ? [Vvar__0__Base__66153] :
( cType___24t(Vvar__0__Base__66153)
& ? [Vvar__1__dist__66154] :
( c_24__type__65044___24t(Vvar__0__Base__66153,Vvar__1__dist__66154)
& ! [Vvar__var__2__x__66160__66162] :
( t(Vvar__var__2__x__66160__66162,Vvar__0__Base__66153)
=> ! [Vvar__var__3__y__66161__66163] :
( t(Vvar__var__3__y__66161__66163,Vvar__0__Base__66153)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__66154,Vvar__var__2__x__66160__66162),Vvar__var__3__y__66161__66163),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__66165__66167] :
( t(Vvar__var__3__x__66165__66167,Vvar__0__Base__66153)
=> ! [Vvar__var__4__y__66166__66168] :
( t(Vvar__var__4__y__66166__66168,Vvar__0__Base__66153)
=> happ(happ(Vvar__1__dist__66154,Vvar__var__3__x__66165__66167),Vvar__var__4__y__66166__66168) = happ(happ(Vvar__1__dist__66154,Vvar__var__4__y__66166__66168),Vvar__var__3__x__66165__66167) ) )
& ! [Vvar__var__4__x__66170__66172] :
( t(Vvar__var__4__x__66170__66172,Vvar__0__Base__66153)
=> ! [Vvar__var__5__y__66171__66173] :
( t(Vvar__var__5__y__66171__66173,Vvar__0__Base__66153)
=> ( happ(happ(Vvar__1__dist__66154,Vvar__var__4__x__66170__66172),Vvar__var__5__y__66171__66173) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__66170__66172 = Vvar__var__5__y__66171__66173 ) ) )
& ! [Vvar__var__5__x__66175__66178] :
( t(Vvar__var__5__x__66175__66178,Vvar__0__Base__66153)
=> ! [Vvar__var__6__y__66176__66179] :
( t(Vvar__var__6__y__66176__66179,Vvar__0__Base__66153)
=> ! [Vvar__var__7__z__66177__66180] :
( t(Vvar__var__7__z__66177__66180,Vvar__0__Base__66153)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__66154,Vvar__var__5__x__66175__66178),Vvar__var__6__y__66176__66179),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__66154,Vvar__var__5__x__66175__66178),Vvar__var__7__z__66177__66180),happ(happ(Vvar__1__dist__66154,Vvar__var__7__z__66177__66180),Vvar__var__6__y__66176__66179)))) ) ) )
& V0__m = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__66153,Vvar__1__dist__66154)
& cCoq_2eReals_2eRlimit_2eBase___24a1(V0__m) = Vvar__0__Base__66153 ) ) ) ).
fof('$_def_Coq.Reals.Rlimit.R_met',axiom,
cCoq_2eReals_2eRlimit_2eR__met = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRfunctions_2eR__dist,cCoq_2eReals_2eRfunctions_2eR__dist__pos,cCoq_2eReals_2eRfunctions_2eR__dist__sym,cCoq_2eReals_2eRfunctions_2eR__dist__refl,cCoq_2eReals_2eRfunctions_2eR__dist__tri) ).
fof('$_def_Coq.Reals.Rlimit.dist',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ? [Vvar__0__Base__68669] :
( cType___24t(Vvar__0__Base__68669)
& ? [Vvar__1__dist__68670] :
( c_24__type__65044___24t(Vvar__0__Base__68669,Vvar__1__dist__68670)
& ! [Vvar__var__2__x__68676__68678] :
( t(Vvar__var__2__x__68676__68678,Vvar__0__Base__68669)
=> ! [Vvar__var__3__y__68677__68679] :
( t(Vvar__var__3__y__68677__68679,Vvar__0__Base__68669)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__68670,Vvar__var__2__x__68676__68678),Vvar__var__3__y__68677__68679),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__68681__68683] :
( t(Vvar__var__3__x__68681__68683,Vvar__0__Base__68669)
=> ! [Vvar__var__4__y__68682__68684] :
( t(Vvar__var__4__y__68682__68684,Vvar__0__Base__68669)
=> happ(happ(Vvar__1__dist__68670,Vvar__var__3__x__68681__68683),Vvar__var__4__y__68682__68684) = happ(happ(Vvar__1__dist__68670,Vvar__var__4__y__68682__68684),Vvar__var__3__x__68681__68683) ) )
& ! [Vvar__var__4__x__68686__68688] :
( t(Vvar__var__4__x__68686__68688,Vvar__0__Base__68669)
=> ! [Vvar__var__5__y__68687__68689] :
( t(Vvar__var__5__y__68687__68689,Vvar__0__Base__68669)
=> ( happ(happ(Vvar__1__dist__68670,Vvar__var__4__x__68686__68688),Vvar__var__5__y__68687__68689) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__68686__68688 = Vvar__var__5__y__68687__68689 ) ) )
& ! [Vvar__var__5__x__68691__68694] :
( t(Vvar__var__5__x__68691__68694,Vvar__0__Base__68669)
=> ! [Vvar__var__6__y__68692__68695] :
( t(Vvar__var__6__y__68692__68695,Vvar__0__Base__68669)
=> ! [Vvar__var__7__z__68693__68696] :
( t(Vvar__var__7__z__68693__68696,Vvar__0__Base__68669)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__68670,Vvar__var__5__x__68691__68694),Vvar__var__6__y__68692__68695),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__68670,Vvar__var__5__x__68691__68694),Vvar__var__7__z__68693__68696),happ(happ(Vvar__1__dist__68670,Vvar__var__7__z__68693__68696),Vvar__var__6__y__68692__68695)))) ) ) )
& V0__m = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__68669,Vvar__1__dist__68670)
& cCoq_2eReals_2eRlimit_2edist___24a1(V0__m) = Vvar__1__dist__68670 ) ) ) ).
fof('$_def_Coq.Reals.Rlimit.limit1_in',axiom,
! [V0__f,V1__D,V2__l,V3__x0] :
( cCoq_2eReals_2eRlimit_2elimit1__in___24a4(V0__f,V1__D,V2__l,V3__x0)
<=> cCoq_2eReals_2eRlimit_2elimit__in___24a6(cCoq_2eReals_2eRlimit_2eR__met,cCoq_2eReals_2eRlimit_2eR__met,V0__f,V1__D,V3__x0,V2__l) ) ).
fof('$_def_Coq.Reals.Rlimit.limit_in',axiom,
! [V0__X,V1__X_27,V2__f,V3__D,V4__x0,V5__l] :
( cCoq_2eReals_2eRlimit_2elimit__in___24a6(V0__X,V1__X_27,V2__f,V3__D,V4__x0,V5__l)
<=> ! [V6__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V6__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V6__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V8__alp] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__alp)
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V8__alp,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& ! [V9__x] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__X,V9__x)
=> ( ( p(happ(V3__D,V9__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRlimit_2edist___24a3(V0__X,V9__x,V4__x0),V8__alp)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRlimit_2edist___24a3(V1__X_27,happ(V2__f,V9__x),V5__l),V6__eps)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__31254] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31254)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31254)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__31254)) ) ) ) ).
fof('$_def_Coq.Reals.Rpower.Rpower',axiom,
! [V0__x,V1__y] : cCoq_2eReals_2eRpower_2eRpower___24a2(V0__x,V1__y) = cCoq_2eReals_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__y,cCoq_2eReals_2eRpower_2eln___24a1(V0__x))) ).
fof('$_def_Coq.Reals.Rpower.ln',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& cCoq_2eReals_2eRIneq_2eRlt__dec___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x),c_24__prop__75281___24a1(V0__x))
& cCoq_2eReals_2eRpower_2eln___24a1(V0__x) = cCoq_2eReals_2eRpower_2eRln___24a1(cCoq_2eReals_2eRIneq_2emkposreal___24a1(V0__x)) )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& cCoq_2eReals_2eRIneq_2eRlt__dec___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x),c_24__prop__75282___24a1(V0__x))
& cCoq_2eReals_2eRpower_2eln___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.EUn',axiom,
! [V0__Un,V1__r] :
( cCoq_2eReals_2eRseries_2eEUn___24a2(V0__Un,V1__r)
<=> ? [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
& V1__r = happ(V0__Un,V2__i) ) ) ).
fof('$_def_Coq.Reals.Rseries.Un_cv',axiom,
! [V0__Un,V1__l] :
( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
<=> ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V4__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__N)
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(happ(V0__Un,V5__n),V1__l),V2__eps)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.Un_growing',axiom,
! [V0__Un] :
( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V1__n),happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)))) ) ) ).
fof('$_def_Coq.Reals.Rtrigo1.PI',axiom,
cCoq_2eReals_2eRtrigo1_2ePI = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo1_2ePI2) ).
fof('$_def_Coq.Reals.Rtrigo1.tan',axiom,
! [V0__x] : cCoq_2eReals_2eRtrigo1_2etan___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x)) ).
fof('$_def_Coq.Reals.Rtrigo_def.cos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__66000] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__66000)
& c_24__lam__66004___24a2(V0__x,Vvar__2__x__66000)
& cCoq_2eReals_2eRtrigo__def_2eexist__cos___24a1(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__66004___24a1(V0__x),Vvar__2__x__66000)
& cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) = Vvar__2__x__66000 ) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.exp',axiom,
! [V0__x] : cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__78308___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2eexist__exp___24a1(V0__x)) ).
fof('$_def_Coq.Reals.Rtrigo_def.sin',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__66015] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__66015)
& c_24__lam__66019___24a2(V0__x,Vvar__2__x__66015)
& cCoq_2eReals_2eRtrigo__def_2eexist__sin___24a1(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__66019___24a1(V0__x),Vvar__2__x__66015)
& cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,Vvar__2__x__66015) ) ) ).
fof('$_def_Coq.Reals.SeqProp.Un_decreasing',axiom,
! [V0__Un] :
( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)),happ(V0__Un,V1__n))) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__399___24a1(V0__A) ).
fof('$_def_Coq.ZArith.BinInt.Z.b2z',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eq_dec',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ__rec___24a6(c_24__lam__529,c_24__lam__578,c_24__lam__699,c_24__lam__872,V0__x,V1__y) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( p(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.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.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.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.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___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__19379] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19379)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19379)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___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__19389] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19389)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19389)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19379,V1__b) )
| ? [Vvar__0___24Anonymous__19390] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19390)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19379)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19390)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19390)
& ? [Vvar__2___24Anonymous__19401] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19401)
& ? [Vvar__3___24Anonymous__19402] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19402)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19402)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19379,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19390)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19401,Vvar__3___24Anonymous__19402)
& ( ( Vvar__3___24Anonymous__19402 = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(Vvar__2___24Anonymous__19401),cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__19410] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19410)
& Vvar__3___24Anonymous__19402 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19410)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___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_2eadd___24a2(Vvar__2___24Anonymous__19401,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__b,Vvar__3___24Anonymous__19402)) )
| ? [Vvar__0___24Anonymous__19411] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19411)
& Vvar__3___24Anonymous__19402 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19411)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___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_2eadd___24a2(Vvar__2___24Anonymous__19401,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__b,Vvar__3___24Anonymous__19402)) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19412] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19412)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19412)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___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__19425] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19425)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19412)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19425)
& ? [Vvar__2___24Anonymous__19436] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19436)
& ? [Vvar__3___24Anonymous__19437] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19437)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19437)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19412,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19436,Vvar__3___24Anonymous__19437)
& ( ( Vvar__3___24Anonymous__19437 = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(Vvar__2___24Anonymous__19436),cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__19445] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19445)
& Vvar__3___24Anonymous__19437 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19445)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___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_2eadd___24a2(Vvar__2___24Anonymous__19436,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__b,Vvar__3___24Anonymous__19437)) )
| ? [Vvar__0___24Anonymous__19446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19446)
& Vvar__3___24Anonymous__19437 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19446)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___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_2eadd___24a2(Vvar__2___24Anonymous__19436,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__b,Vvar__3___24Anonymous__19437)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19447] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19447)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19412)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19447)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19447)
& ? [Vvar__2___24Anonymous__19455] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19455)
& ? [Vvar__3___24Anonymous__19456] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19456)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19412,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19447)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19455,Vvar__3___24Anonymous__19456)
& 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__19455,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(Vvar__3___24Anonymous__19456)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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.land',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35190] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35190)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35190)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35194] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35194)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35194)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(Vvar__0___24Anonymous__35190,Vvar__0___24Anonymous__35194)) )
| ? [Vvar__0___24Anonymous__35195] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35195)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35195)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35190),cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35195))) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35196] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35196)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35196)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35200] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35200)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35200)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35200),cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35196))) )
| ? [Vvar__0___24Anonymous__35201] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35201)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35201)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eland___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35196),cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35201)))) ) ) ) ) ) ) ) ).
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.lor',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = V1__b )
| ? [Vvar__0___24Anonymous__35177] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35177)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35177)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__35181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35181)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35181)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(Vvar__0___24Anonymous__35177,Vvar__0___24Anonymous__35181)) )
| ? [Vvar__0___24Anonymous__35182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35182)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35182)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35182),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35177)))) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35183] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35183)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35183)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__35187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35187)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35187)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35183),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35187)))) )
| ? [Vvar__0___24Anonymous__35188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35188)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35188)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elor___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35183),cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35188)))) ) ) ) ) ) ) ) ).
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.lxor',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = V1__b )
| ? [Vvar__0___24Anonymous__35216] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35216)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35216)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__35220] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35220)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35220)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__35216,Vvar__0___24Anonymous__35220)) )
| ? [Vvar__0___24Anonymous__35221] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35221)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35221)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35216),cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35221)))) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35222] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35222)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35222)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__35226] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35226)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35226)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35222),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35226)))) )
| ? [Vvar__0___24Anonymous__35227] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35227)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35227)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elxor___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35222),cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__35227))) ) ) ) ) ) ) ) ).
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_div_eucl',axiom,
! [V1__a,V2__b] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__a)
=> ( ? [Vvar__0___24Anonymous__19328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19328)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19328)
=> ( V1__a = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19328)
& ? [Vvar__2___24Anonymous__19338] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19338)
& ? [Vvar__3___24Anonymous__19339] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19339)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19328,V2__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19338,Vvar__3___24Anonymous__19339)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V1__a,V2__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419369___24a3(V2__b,Vvar__2___24Anonymous__19338,Vvar__3___24Anonymous__19339) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19346] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19346)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19346)
=> ( V1__a = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19346)
& ? [Vvar__2___24Anonymous__19356] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__19356)
& ? [Vvar__3___24Anonymous__19357] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__19357)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__19346,V2__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__19356,Vvar__3___24Anonymous__19357)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V1__a,V2__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419375___24a3(V2__b,Vvar__2___24Anonymous__19356,Vvar__3___24Anonymous__19357) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
=> ( V1__a = cCoq_2eNumbers_2eBinNums_2exH
& ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V2__b) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V1__a,V2__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V2__b) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V1__a,V2__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_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_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('$_def_Coq.ZArith.ZArith_dec.Z_le_dec',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eZArith__dec_2eZ__le__dec___24a2(V0__x,V1__y) = c_24__cast__59730___24a2(V0__x,V1__y) ).
fof('$_def_Coq.ZArith.ZArith_dec.Z_le_gt_dec',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eZArith__dec_2eZ__le__gt__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y),c_24__prop__137___24a2(V0__x,V1__y),c_24__lam__140___24a2(V0__x,V1__y),c_24__lam__143___24a2(V0__x,V1__y),c_24__lam__217___24a2(V0__x,V1__y),cCoq_2eZArith_2eZArith__dec_2eZ__le__dec___24a2(V0__x,V1__y)) ).
fof('$_def_Coq.ZArith.ZArith_dec.Z_lt_dec',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eZArith__dec_2eZ__lt__dec___24a2(V0__x,V1__y) = c_24__cast__16432___24a2(V0__x,V1__y) ).
fof('$_def_Coq.ZArith.ZArith_dec.Z_lt_ge_dec',axiom,
! [V0__x,V1__y] : cCoq_2eZArith_2eZArith__dec_2eZ__lt__ge__dec___24a2(V0__x,V1__y) = cCoq_2eZArith_2eZArith__dec_2eZ__lt__dec___24a2(V0__x,V1__y) ).
fof('$_def_Coq.ZArith.ZArith_dec.not_Zeq_inf',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
& cCoq_2eZArith_2eZArith__dec_2eZ__lt__ge__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
& cCoq_2eZArith_2eZArith__dec_2enot__Zeq__inf___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
=> ( cCoq_2eZArith_2eZArith__dec_2eZ__lt__ge__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
& ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
& cCoq_2eZArith_2eZArith__dec_2eZ__le__lt__eq__dec___24a3(V1__y,V0__x,cCoq_2eZArith_2eBinInt_2eZ_2ege__le___24a2(V0__x,V1__y)) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x),c_24__prop__60006___24a2(V0__x,V1__y))
& cCoq_2eZArith_2eZArith__dec_2enot__Zeq__inf___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)) )
| ( V1__y = V0__x
& cCoq_2eZArith_2eZArith__dec_2eZ__le__lt__eq__dec___24a3(V1__y,V0__x,cCoq_2eZArith_2eBinInt_2eZ_2ege__le___24a2(V0__x,V1__y)) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x),c_24__prop__60007___24a2(V0__x,V1__y))
& cCoq_2eZArith_2eZArith__dec_2enot__Zeq__inf___24a2(V0__x,V1__y) = cCoq_2eInit_2eLogic_2eFalse__rec___24a1(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.Znumtheory.rel_prime',axiom,
! [V0__a,V1__b] :
( p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('$_def_Coq.ZArith.Znumtheory.rel_prime_dec',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
& cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__17066___24a2(V0__a,V1__b),c_24__prop__17067___24a2(V0__a,V1__b))
& cCoq_2eZArith_2eZnumtheory_2erel__prime__dec___24a2(V0__a,V1__b) = cCoq_2eInit_2eSpecif_2eleft___24a3(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b),c_24__prop__17068___24a2(V0__a,V1__b),c_24__generic__case__17142) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
& cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__17143___24a2(V0__a,V1__b),c_24__prop__17144___24a2(V0__a,V1__b))
& cCoq_2eZArith_2eZnumtheory_2erel__prime__dec___24a2(V0__a,V1__b) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b),c_24__prop__17145___24a2(V0__a,V1__b)) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zpower.two_p',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__31337] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31337)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31337)
& cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__0___24Anonymous__31337) )
| ? [Vvar__0___24Anonymous__31338] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31338)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31338)
& cCoq_2eZArith_2eZpower_2etwo__p___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.Zpower.two_power_pos',axiom,
! [V0__x] : cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eZArith_2eZpower_2eshift__pos___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
! [Vvar__65869] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__65869)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__65869) ) ).
fof('$_def_Coq.micromega.Tauto.BFormula',axiom,
! [V0__A] : cCoq_2emicromega_2eTauto_2eBFormula___24a1(V0__A) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_def_Coq.micromega.VarMap.find',axiom,
! [V0__A,V1__default,V3__vm,V4__p] :
( cType___24t(V0__A)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,V3__vm)
=> ( ( V3__vm = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V0__A)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = V1__default )
| ? [Vvar__1___24Anonymous__66091] :
( t(Vvar__1___24Anonymous__66091,V0__A)
& V3__vm = cCoq_2emicromega_2eVarMap_2eElt___24a2(V0__A,Vvar__1___24Anonymous__66091)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__1___24Anonymous__66091 )
| ? [Vvar__1___24Anonymous__66093] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__1___24Anonymous__66093)
& ? [Vvar__2___24Anonymous__66094] :
( t(Vvar__2___24Anonymous__66094,V0__A)
& ? [Vvar__3___24Anonymous__66095] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__3___24Anonymous__66095)
& ( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> ( V3__vm = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V0__A,Vvar__1___24Anonymous__66093,Vvar__2___24Anonymous__66094,Vvar__3___24Anonymous__66095)
& ( ? [Vvar__0___24Anonymous__66108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66108)
& V4__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__66108)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,Vvar__3___24Anonymous__66095,Vvar__0___24Anonymous__66108) )
| ? [Vvar__0___24Anonymous__66109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66109)
& V4__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__66109)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,Vvar__1___24Anonymous__66093,Vvar__0___24Anonymous__66109) )
| ( V4__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__2___24Anonymous__66094 ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Zeval_op1',axiom,
! [V0__o] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V0__o)
=> ( ( V0__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__34431 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__34432 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__34433 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V0__o) = c_24__lam__34434 ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.FEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V9__C)
=> ( cType___24t(V11__Cpow)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,V16__pe)
=> ( ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V1__rO )
| ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__20324] :
( t(Vvar__1___24Anonymous__20324,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__20324)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V10__phi,Vvar__1___24Anonymous__20324) )
| ? [Vvar__1___24Anonymous__20326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20326)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__20326)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__20326,V15__l) )
| ? [Vvar__1___24Anonymous__20328] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20328)
& ? [Vvar__2___24Anonymous__20329] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20329)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__20328,Vvar__2___24Anonymous__20329)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__20328)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__20329)) ) )
| ? [Vvar__1___24Anonymous__20332] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20332)
& ? [Vvar__2___24Anonymous__20333] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20333)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__20332,Vvar__2___24Anonymous__20333)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__20332)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__20333)) ) )
| ? [Vvar__1___24Anonymous__20336] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20336)
& ? [Vvar__2___24Anonymous__20337] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20337)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__20336,Vvar__2___24Anonymous__20337)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__20336)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__20337)) ) )
| ? [Vvar__1___24Anonymous__20340] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20340)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__20340)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__20340)) )
| ? [Vvar__1___24Anonymous__20342] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20342)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__20342)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V8__rinv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__20342)) )
| ? [Vvar__1___24Anonymous__20344] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20344)
& ? [Vvar__2___24Anonymous__20345] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__20345)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__20344,Vvar__2___24Anonymous__20345)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__20344)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__20345)) ) )
| ? [Vvar__1___24Anonymous__20348] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__20348)
& ? [Vvar__2___24Anonymous__20349] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__20349)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__20348,Vvar__2___24Anonymous__20349)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V13__rpow,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__20348)),happ(V12__Cp__phi,Vvar__2___24Anonymous__20349)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__36593] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36593)
& ? [Vvar__2___24Anonymous__36594] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__36594)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__36593,Vvar__2___24Anonymous__36594)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__36593),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__36594,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons2',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l] : cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e),V10__l) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fnorm',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,V9__e)
=> ( ( V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ( V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__35411] :
( t(Vvar__1___24Anonymous__35411,V0__C)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V0__C,Vvar__1___24Anonymous__35411)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__35411),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__35413] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__35413)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V0__C,Vvar__1___24Anonymous__35413)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__35413),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__35415] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__35415)
& ? [Vvar__2___24Anonymous__35416] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__35416)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V0__C,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V3__cadd,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__35418__35421__35491___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__35420__35423__35493___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__35419__35422__35492___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35416)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__35420__35423__35493___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416)))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__35420__35423__35493___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416)),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__35420__35423__35493___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__35420__35423__35493___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415,Vvar__2___24Anonymous__35416)))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__35418__35421__35491___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35415)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__35419__35422__35492___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35416)))) ) )
| ? [Vvar__1___24Anonymous__35428] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__35428)
& ? [Vvar__2___24Anonymous__35429] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__35429)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V0__C,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V5__csub,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__35431__35434__35497___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__35433__35436__35499___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__35432__35435__35498___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35429)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__35433__35436__35499___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429)))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__35433__35436__35499___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429)),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__35433__35436__35499___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__35433__35436__35499___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428,Vvar__2___24Anonymous__35429)))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__35431__35434__35497___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35428)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__35432__35435__35498___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35429)))) ) )
| ? [Vvar__1___24Anonymous__35441] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__35441)
& ? [Vvar__2___24Anonymous__35442] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__35442)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V0__C,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s1__35446__35450__35508___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__15__s2__35447__35451__35509___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__15__s2__35447__35451__35509___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__35446__35450__35508___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441,Vvar__2___24Anonymous__35442))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__35444__35448__35506___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35441)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__35445__35449__35507___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35442)))) ) )
| ? [Vvar__1___24Anonymous__35459] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__35459)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V0__C,Vvar__1___24Anonymous__35459)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V6__copp,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__35460__35510___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35459))),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__11__x__35460__35510___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35459)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__35460__35510___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35459))) )
| ? [Vvar__1___24Anonymous__35462] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__35462)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V0__C,Vvar__1___24Anonymous__35462)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__11__x__35463__35511___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35462)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__35463__35511___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35462)),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__35463__35511___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35462)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__35463__35511___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35462)))) )
| ? [Vvar__1___24Anonymous__35465] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__35465)
& ? [Vvar__2___24Anonymous__35466] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__35466)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V0__C,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s1__35470__35474__35520___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__15__s2__35471__35475__35521___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__15__s2__35471__35475__35521___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__35470__35474__35520___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465,Vvar__2___24Anonymous__35466))),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__35469__35473__35519___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35466)),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__35468__35472__35518___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35465)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__35469__35473__35519___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__35466))))) ) )
| ? [Vvar__1___24Anonymous__35483] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__35483)
& ? [Vvar__2___24Anonymous__35484] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__35484)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V0__C,Vvar__1___24Anonymous__35483,Vvar__2___24Anonymous__35484)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__35485__35487__35522___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35483)),Vvar__2___24Anonymous__35484),cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__35485__35487__35522___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35483)),Vvar__2___24Anonymous__35484),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__35485__35487__35522___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__35483))) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__20653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__20653)
& ? [Vvar__2___24Anonymous__20654] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__20654)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__20654)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__20653,Vvar__2___24Anonymous__20654)
& ( ( Vvar__2___24Anonymous__20654 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__20653)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__20665] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__20665)
& ? [Vvar__2___24Anonymous__20666] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__20666)
& Vvar__2___24Anonymous__20654 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__20665,Vvar__2___24Anonymous__20666)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__20653)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__20654) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20640] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20640)
& ? [Vvar__2__denum__20641] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20641)
& ? [Vvar__3__condition__20642] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20642)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20640,Vvar__2__denum__20641,Vvar__3__condition__20642)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__20642 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20631] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20631)
& ? [Vvar__2__denum__20632] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20632)
& ? [Vvar__3__condition__20633] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20633)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20631,Vvar__2__denum__20632,Vvar__3__condition__20633)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__20632 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20620] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20620)
& ? [Vvar__2__denum__20621] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20621)
& ? [Vvar__3__condition__20622] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20622)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20620,Vvar__2__denum__20621,Vvar__3__condition__20622)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__20620 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__13763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13763)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13763)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__13763) )
| ? [Vvar__0___24Anonymous__13764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13764)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13764)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__13764)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.get_signZ',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__31994] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31994)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31994)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__31995] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31995)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31995)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31995)) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__32311] :
( t(Vvar__1___24Anonymous__32311,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__32311)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V8__phi,Vvar__1___24Anonymous__32311) )
| ? [Vvar__1___24Anonymous__32313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32313)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__32313)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__32313,V13__l) )
| ? [Vvar__1___24Anonymous__32315] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32315)
& ? [Vvar__2___24Anonymous__32316] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__32316)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__32315,Vvar__2___24Anonymous__32316)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__32315)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__32316)) ) )
| ? [Vvar__1___24Anonymous__32319] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32319)
& ? [Vvar__2___24Anonymous__32320] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__32320)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__32319,Vvar__2___24Anonymous__32320)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__32319)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__32320)) ) )
| ? [Vvar__1___24Anonymous__32323] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32323)
& ? [Vvar__2___24Anonymous__32324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__32324)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__32323,Vvar__2___24Anonymous__32324)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__32323)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__32324)) ) )
| ? [Vvar__1___24Anonymous__32327] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32327)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__32327)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__32327)) )
| ? [Vvar__1___24Anonymous__32329] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__32329)
& ? [Vvar__2___24Anonymous__32330] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__32330)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__32329,Vvar__2___24Anonymous__32330)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V11__rpow,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__32329)),happ(V10__Cp__phi,Vvar__2___24Anonymous__32330)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Peq',axiom,
! [V0__C,V1__ceqb,V3__P,V4__P_27] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__14128] :
( t(Vvar__1___24Anonymous__14128,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__14128)
& ( ? [Vvar__1___24Anonymous__14138] :
( t(Vvar__1___24Anonymous__14138,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__14138)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__14128),Vvar__1___24Anonymous__14138) )
| ? [Vvar__1___24Anonymous__14140] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14140)
& ? [Vvar__2___24Anonymous__14141] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14141)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__14140,Vvar__2___24Anonymous__14141)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__14144] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14144)
& ? [Vvar__2___24Anonymous__14145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14145)
& ? [Vvar__3___24Anonymous__14146] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14146)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__14144,Vvar__2___24Anonymous__14145,Vvar__3___24Anonymous__14146)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14151] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14151)
& ? [Vvar__2___24Anonymous__14152] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14152)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__14151,Vvar__2___24Anonymous__14152)
& ( ? [Vvar__1___24Anonymous__14172] :
( t(Vvar__1___24Anonymous__14172,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__14172)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__14174] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14174)
& ? [Vvar__2___24Anonymous__14175] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14175)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14151)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14174)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__14174,Vvar__2___24Anonymous__14175)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__14151,Vvar__1___24Anonymous__14174) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__14152,Vvar__2___24Anonymous__14175) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__14151,Vvar__1___24Anonymous__14174) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__14151,Vvar__1___24Anonymous__14174) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14180] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14180)
& ? [Vvar__2___24Anonymous__14181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14181)
& ? [Vvar__3___24Anonymous__14182] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14182)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__14180,Vvar__2___24Anonymous__14181,Vvar__3___24Anonymous__14182)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__14187] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14187)
& ? [Vvar__2___24Anonymous__14188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14188)
& ? [Vvar__3___24Anonymous__14189] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14189)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__14187,Vvar__2___24Anonymous__14188,Vvar__3___24Anonymous__14189)
& ( ? [Vvar__1___24Anonymous__14222] :
( t(Vvar__1___24Anonymous__14222,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__14222)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__14224] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14224)
& ? [Vvar__2___24Anonymous__14225] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__14225)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__14224,Vvar__2___24Anonymous__14225)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__14228] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14228)
& ? [Vvar__2___24Anonymous__14229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14229)
& ? [Vvar__3___24Anonymous__14230] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__14230)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14188)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14229)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__14228,Vvar__2___24Anonymous__14229,Vvar__3___24Anonymous__14230)
& ( ( cType___24t(V0__C)
=> ( c_24__type__14243___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14187)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__14228)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__14188,Vvar__2___24Anonymous__14229) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__14187,Vvar__1___24Anonymous__14228) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__14189,Vvar__3___24Anonymous__14230) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__14187,Vvar__1___24Anonymous__14228) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__14188,Vvar__2___24Anonymous__14229) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__14188,Vvar__2___24Anonymous__14229) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__32944___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__32945___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__32946___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),V15__lpe)
=> ( ( V15__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__32525] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__32525)
& ? [Vvar__2___24Anonymous__32526] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__32526)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__32525)
=> ( V15__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__32525,Vvar__2___24Anonymous__32526)
& ? [Vvar__2___24Anonymous__32544] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__32544)
& ? [Vvar__3___24Anonymous__32545] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__32545)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__32526)
=> ( Vvar__1___24Anonymous__32525 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__32544,Vvar__3___24Anonymous__32545)
& ( ( Vvar__2___24Anonymous__32526 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__32544)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__32545))) ) )
| ? [Vvar__1___24Anonymous__32556] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__32556)
& ? [Vvar__2___24Anonymous__32557] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__32557)
& Vvar__2___24Anonymous__32526 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__32556,Vvar__2___24Anonymous__32557)
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> ( p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__32544)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__32545)))
& cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__32526) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
=> ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__14752] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__14752)
& ? [Vvar__2___24Anonymous__14753] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__2___24Anonymous__14753)
& ( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__14752)
=> ( V10__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__1___24Anonymous__14752,Vvar__2___24Anonymous__14753)
& ? [Vvar__2___24Anonymous__14769] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14769)
& ? [Vvar__3___24Anonymous__14770] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__14770)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__13636___24t(V0__C,V3__cadd)
=> ( c_24__type__13636___24t(V0__C,V4__cmul)
=> ( c_24__type__13636___24t(V0__C,V5__csub)
=> ( c_24__type__13657___24t(V0__C,V6__copp)
=> ( c_24__type__14243___24t(V0__C,V7__ceqb)
=> ( c_24__type__14746___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__14769)
=> ( Vvar__1___24Anonymous__14752 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__14769,Vvar__3___24Anonymous__14770)
& ( ? [Vvar__1___24Anonymous__14778] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__14778)
& cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__14769)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__14778)
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C)),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C),Vvar__1___24Anonymous__14778,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__3___24Anonymous__14770)),cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__14753)) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__14769)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__14753) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__14596___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__14945] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14945)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__14945)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__14945) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__14925] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14925)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__14925)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__14926__14929___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925)),c_24__let__var__6__p__14926__14929___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14925))) )
| ? [Vvar__0___24Anonymous__14927] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14927)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__14927)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__14928__14930___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927)),c_24__let__var__6__p__14928__14930___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14927)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__13206] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13206) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__13241,Vvar__1___24Anonymous__13242,Vvar__0__A__13243] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13241,Vvar__1___24Anonymous__13242) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13243) ).
fof('$_discrim_Coq.Init.Datatypes.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.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__31273,Vvar__1__B__31274,Vvar__2___24Anonymous__31275,Vvar__0__A__31276,Vvar__1__B__31277,Vvar__2___24Anonymous__31278] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31273,Vvar__1__B__31274,Vvar__2___24Anonymous__31275) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31276,Vvar__1__B__31277) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__119,Vvar__1__B__120,Vvar__2___24Anonymous__121,Vvar__0__A__122,Vvar__1__B__123,Vvar__2___24Anonymous__124] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__119,Vvar__1__B__120) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__122,Vvar__1__B__123) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__13183] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13183) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__20] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__6) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7) ).
fof('$_discrim_Coq.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.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__13504,Vvar__1___24Anonymous__13505,Vvar__0__C__13506,Vvar__1___24Anonymous__13507] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13504,Vvar__1___24Anonymous__13505) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13506,Vvar__1___24Anonymous__13507) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__13568,Vvar__1___24Anonymous__13569,Vvar__0__C__13570,Vvar__1___24Anonymous__13571,Vvar__2___24Anonymous__13572] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13568,Vvar__1___24Anonymous__13569) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13570,Vvar__1___24Anonymous__13571,Vvar__2___24Anonymous__13572) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__27460,Vvar__1___24Anonymous__27461,Vvar__0__C__27462,Vvar__1___24Anonymous__27463] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27460,Vvar__1___24Anonymous__27461) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27462,Vvar__1___24Anonymous__27463) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__65456,Vvar__1__TX__65457,Vvar__2__AA__65458,Vvar__3__AF__65459,Vvar__0__TA__65460,Vvar__1__TX__65461,Vvar__2__AA__65462,Vvar__3__AF__65463] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65456,Vvar__1__TX__65457,Vvar__2__AA__65458,Vvar__3__AF__65459) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65460,Vvar__1__TX__65461,Vvar__2__AA__65462,Vvar__3__AF__65463) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__65587,Vvar__0__A__65588,Vvar__1___24Anonymous__65589] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65587) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65588,Vvar__1___24Anonymous__65589) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__20267,Vvar__0__C__20268] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20267) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20268) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__14460,Vvar__0__C__14461] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14460) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14461) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__14102,Vvar__1___24Anonymous__14103,Vvar__0__C__14104,Vvar__1___24Anonymous__14105,Vvar__2___24Anonymous__14106] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14102,Vvar__1___24Anonymous__14103) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14104,Vvar__1___24Anonymous__14105,Vvar__2___24Anonymous__14106) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__14270,Vvar__1___24Anonymous__14271] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14270,Vvar__1___24Anonymous__14271) ).
fof('$_fix_413_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__428)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__428)
& ( ? [Vvar__0___24Anonymous__432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__432)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__432)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__413__1__add__carry___24a2(Vvar__0___24Anonymous__428,Vvar__0___24Anonymous__432)) )
| ? [Vvar__0___24Anonymous__433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__433)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__433)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__413__1__add__carry___24a2(Vvar__0___24Anonymous__428,Vvar__0___24Anonymous__433)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__428)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__434)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__434)
& ( ? [Vvar__0___24Anonymous__438] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__438)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__438)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__413__1__add__carry___24a2(Vvar__0___24Anonymous__434,Vvar__0___24Anonymous__438)) )
| ? [Vvar__0___24Anonymous__439] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__439)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__439)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__434,Vvar__0___24Anonymous__439)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__434)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__440)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__440)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__440)) )
| ? [Vvar__0___24Anonymous__441] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__441)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__441)
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__441)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__413__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__13248,Vvar__0__A__13249] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13248) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13249)
=> Vvar__0__A__13248 = Vvar__0__A__13249 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__13207,Vvar__0___24Anonymous__13208] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13207) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13208)
=> Vvar__0___24Anonymous__13207 = Vvar__0___24Anonymous__13208 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__13244,Vvar__0__A__13245,Vvar__1___24Anonymous__13246,Vvar__1___24Anonymous__13247] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13244,Vvar__1___24Anonymous__13246) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13245,Vvar__1___24Anonymous__13247)
=> ( Vvar__1___24Anonymous__13246 = Vvar__1___24Anonymous__13247
& Vvar__0__A__13244 = Vvar__0__A__13245 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__13329,Vvar__0__A__13330,Vvar__1___24Anonymous__13331,Vvar__1___24Anonymous__13332,Vvar__2___24Anonymous__13333,Vvar__2___24Anonymous__13334] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13329,Vvar__1___24Anonymous__13331,Vvar__2___24Anonymous__13333) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13330,Vvar__1___24Anonymous__13332,Vvar__2___24Anonymous__13334)
=> ( Vvar__2___24Anonymous__13333 = Vvar__2___24Anonymous__13334
& Vvar__1___24Anonymous__13331 = Vvar__1___24Anonymous__13332
& Vvar__0__A__13329 = Vvar__0__A__13330 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__13327,Vvar__0__A__13328] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13327) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13328)
=> Vvar__0__A__13327 = Vvar__0__A__13328 ) ).
fof('$_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.existT',axiom,
! [Vvar__0__A__65093,Vvar__0__A__65094,Vvar__1__P__65095,Vvar__1__P__65096,Vvar__2__x__65097,Vvar__2__x__65098,Vvar__3___24Anonymous__65099,Vvar__3___24Anonymous__65100] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__65093,Vvar__1__P__65095,Vvar__2__x__65097,Vvar__3___24Anonymous__65099) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__65094,Vvar__1__P__65096,Vvar__2__x__65098,Vvar__3___24Anonymous__65100)
=> ( Vvar__3___24Anonymous__65099 = Vvar__3___24Anonymous__65100
& Vvar__2__x__65097 = Vvar__2__x__65098
& Vvar__1__P__65095 = Vvar__1__P__65096
& Vvar__0__A__65093 = Vvar__0__A__65094 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__31279,Vvar__0__A__31280,Vvar__1__B__31281,Vvar__1__B__31282,Vvar__2___24Anonymous__31283,Vvar__2___24Anonymous__31284] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31279,Vvar__1__B__31281,Vvar__2___24Anonymous__31283) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31280,Vvar__1__B__31282,Vvar__2___24Anonymous__31284)
=> ( Vvar__2___24Anonymous__31283 = Vvar__2___24Anonymous__31284
& Vvar__1__B__31281 = Vvar__1__B__31282
& Vvar__0__A__31279 = Vvar__0__A__31280 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__31285,Vvar__0__A__31286,Vvar__1__B__31287,Vvar__1__B__31288,Vvar__2___24Anonymous__31289,Vvar__2___24Anonymous__31290] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31285,Vvar__1__B__31287) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31286,Vvar__1__B__31288)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__31287 = Vvar__1__B__31288
& Vvar__0__A__31285 = Vvar__0__A__31286 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__125,Vvar__0__A__126,Vvar__1__B__127,Vvar__1__B__128,Vvar__2___24Anonymous__129,Vvar__2___24Anonymous__130] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__125,Vvar__1__B__127) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__126,Vvar__1__B__128)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__127 = Vvar__1__B__128
& Vvar__0__A__125 = Vvar__0__A__126 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__131,Vvar__0__A__132,Vvar__1__B__133,Vvar__1__B__134,Vvar__2___24Anonymous__135,Vvar__2___24Anonymous__136] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__131,Vvar__1__B__133) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__132,Vvar__1__B__134)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__133 = Vvar__1__B__134
& Vvar__0__A__131 = Vvar__0__A__132 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__13184,Vvar__0___24Anonymous__13185] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13184) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13185)
=> Vvar__0___24Anonymous__13184 = Vvar__0___24Anonymous__13185 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__23,Vvar__0___24Anonymous__24] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__24)
=> Vvar__0___24Anonymous__23 = Vvar__0___24Anonymous__24 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__21,Vvar__0___24Anonymous__22] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22)
=> Vvar__0___24Anonymous__21 = Vvar__0___24Anonymous__22 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__8,Vvar__0___24Anonymous__9] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9)
=> Vvar__0___24Anonymous__8 = Vvar__0___24Anonymous__9 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__10,Vvar__0___24Anonymous__11] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11)
=> Vvar__0___24Anonymous__10 = Vvar__0___24Anonymous__11 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__13854,Vvar__0__Qnum__13855,Vvar__1__Qden__13856,Vvar__1__Qden__13857] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__13854,Vvar__1__Qden__13856) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__13855,Vvar__1__Qden__13857)
=> ( Vvar__1__Qden__13856 = Vvar__1__Qden__13857
& Vvar__0__Qnum__13854 = Vvar__0__Qnum__13855 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__64821,Vvar__0__pos__64822,Vvar__1__cond__pos__64823,Vvar__1__cond__pos__64824] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__64821) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__64822)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__64821 = Vvar__0__pos__64822 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__32123,Vvar__0__x__32124,Vvar__1__n__32125,Vvar__1__n__32126,Vvar__2___24Anonymous__32127,Vvar__2___24Anonymous__32128] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32123,Vvar__1__n__32125) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32124,Vvar__1__n__32126)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__32125 = Vvar__1__n__32126
& Vvar__0__x__32123 = Vvar__0__x__32124 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__32113,Vvar__0__x__32114,Vvar__1___24Anonymous__32115,Vvar__1___24Anonymous__32116] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32113) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32114)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__32113 = Vvar__0__x__32114 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__32117,Vvar__0__x__32118,Vvar__1__n__32119,Vvar__1__n__32120,Vvar__2___24Anonymous__32121,Vvar__2___24Anonymous__32122] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32117,Vvar__1__n__32119) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32118,Vvar__1__n__32120)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__32119 = Vvar__1__n__32120
& Vvar__0__x__32117 = Vvar__0__x__32118 ) ) ).
fof('$_inj_Coq.Reals.Rlimit.Build_Metric_Space',axiom,
! [Vvar__0__Base__65055,Vvar__0__Base__65056,Vvar__1__dist__65057,Vvar__1__dist__65058,Vvar__2__dist__pos__65059,Vvar__2__dist__pos__65060,Vvar__3__dist__sym__65061,Vvar__3__dist__sym__65062,Vvar__4__dist__refl__65063,Vvar__4__dist__refl__65064,Vvar__5__dist__tri__65065,Vvar__5__dist__tri__65066] :
( cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__65055,Vvar__1__dist__65057) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__65056,Vvar__1__dist__65058)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__dist__65057 = Vvar__1__dist__65058
& Vvar__0__Base__65055 = Vvar__0__Base__65056 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__13512,Vvar__0__C__13513,Vvar__1___24Anonymous__13514,Vvar__1___24Anonymous__13515] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13512,Vvar__1___24Anonymous__13514) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13513,Vvar__1___24Anonymous__13515)
=> ( Vvar__1___24Anonymous__13514 = Vvar__1___24Anonymous__13515
& Vvar__0__C__13512 = Vvar__0__C__13513 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__13516,Vvar__0__C__13517,Vvar__1___24Anonymous__13518,Vvar__1___24Anonymous__13519,Vvar__2___24Anonymous__13520,Vvar__2___24Anonymous__13521] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__13516,Vvar__1___24Anonymous__13518,Vvar__2___24Anonymous__13520) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__13517,Vvar__1___24Anonymous__13519,Vvar__2___24Anonymous__13521)
=> ( Vvar__2___24Anonymous__13520 = Vvar__2___24Anonymous__13521
& Vvar__1___24Anonymous__13518 = Vvar__1___24Anonymous__13519
& Vvar__0__C__13516 = Vvar__0__C__13517 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__13508,Vvar__0__C__13509,Vvar__1___24Anonymous__13510,Vvar__1___24Anonymous__13511] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13508,Vvar__1___24Anonymous__13510) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13509,Vvar__1___24Anonymous__13511)
=> ( Vvar__1___24Anonymous__13510 = Vvar__1___24Anonymous__13511
& Vvar__0__C__13508 = Vvar__0__C__13509 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__13528,Vvar__0__C__13529,Vvar__1___24Anonymous__13530,Vvar__1___24Anonymous__13531,Vvar__2___24Anonymous__13532,Vvar__2___24Anonymous__13533] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__13528,Vvar__1___24Anonymous__13530,Vvar__2___24Anonymous__13532) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__13529,Vvar__1___24Anonymous__13531,Vvar__2___24Anonymous__13533)
=> ( Vvar__2___24Anonymous__13532 = Vvar__2___24Anonymous__13533
& Vvar__1___24Anonymous__13530 = Vvar__1___24Anonymous__13531
& Vvar__0__C__13528 = Vvar__0__C__13529 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__13534,Vvar__0__C__13535,Vvar__1___24Anonymous__13536,Vvar__1___24Anonymous__13537] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__13534,Vvar__1___24Anonymous__13536) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__13535,Vvar__1___24Anonymous__13537)
=> ( Vvar__1___24Anonymous__13536 = Vvar__1___24Anonymous__13537
& Vvar__0__C__13534 = Vvar__0__C__13535 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__13538,Vvar__0__C__13539,Vvar__1___24Anonymous__13540,Vvar__1___24Anonymous__13541,Vvar__2___24Anonymous__13542,Vvar__2___24Anonymous__13543] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__13538,Vvar__1___24Anonymous__13540,Vvar__2___24Anonymous__13542) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__13539,Vvar__1___24Anonymous__13541,Vvar__2___24Anonymous__13543)
=> ( Vvar__2___24Anonymous__13542 = Vvar__2___24Anonymous__13543
& Vvar__1___24Anonymous__13540 = Vvar__1___24Anonymous__13541
& Vvar__0__C__13538 = Vvar__0__C__13539 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__13522,Vvar__0__C__13523,Vvar__1___24Anonymous__13524,Vvar__1___24Anonymous__13525,Vvar__2___24Anonymous__13526,Vvar__2___24Anonymous__13527] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__13522,Vvar__1___24Anonymous__13524,Vvar__2___24Anonymous__13526) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__13523,Vvar__1___24Anonymous__13525,Vvar__2___24Anonymous__13527)
=> ( Vvar__2___24Anonymous__13526 = Vvar__2___24Anonymous__13527
& Vvar__1___24Anonymous__13524 = Vvar__1___24Anonymous__13525
& Vvar__0__C__13522 = Vvar__0__C__13523 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__13583,Vvar__0__C__13584,Vvar__1___24Anonymous__13585,Vvar__1___24Anonymous__13586,Vvar__2___24Anonymous__13587,Vvar__2___24Anonymous__13588,Vvar__3___24Anonymous__13589,Vvar__3___24Anonymous__13590] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__13583,Vvar__1___24Anonymous__13585,Vvar__2___24Anonymous__13587,Vvar__3___24Anonymous__13589) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__13584,Vvar__1___24Anonymous__13586,Vvar__2___24Anonymous__13588,Vvar__3___24Anonymous__13590)
=> ( Vvar__3___24Anonymous__13589 = Vvar__3___24Anonymous__13590
& Vvar__2___24Anonymous__13587 = Vvar__2___24Anonymous__13588
& Vvar__1___24Anonymous__13585 = Vvar__1___24Anonymous__13586
& Vvar__0__C__13583 = Vvar__0__C__13584 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__13573,Vvar__0__C__13574,Vvar__1___24Anonymous__13575,Vvar__1___24Anonymous__13576] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13573,Vvar__1___24Anonymous__13575) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13574,Vvar__1___24Anonymous__13576)
=> ( Vvar__1___24Anonymous__13575 = Vvar__1___24Anonymous__13576
& Vvar__0__C__13573 = Vvar__0__C__13574 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__13577,Vvar__0__C__13578,Vvar__1___24Anonymous__13579,Vvar__1___24Anonymous__13580,Vvar__2___24Anonymous__13581,Vvar__2___24Anonymous__13582] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13577,Vvar__1___24Anonymous__13579,Vvar__2___24Anonymous__13581) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13578,Vvar__1___24Anonymous__13580,Vvar__2___24Anonymous__13582)
=> ( Vvar__2___24Anonymous__13581 = Vvar__2___24Anonymous__13582
& Vvar__1___24Anonymous__13579 = Vvar__1___24Anonymous__13580
& Vvar__0__C__13577 = Vvar__0__C__13578 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__64986,Vvar__0__r__64987] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__64986) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__64987)
=> Vvar__0__r__64986 = Vvar__0__r__64987 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__64974,Vvar__0__r1__64975,Vvar__1__r2__64976,Vvar__1__r2__64977] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__64974,Vvar__1__r2__64976) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__64975,Vvar__1__r2__64977)
=> ( Vvar__1__r2__64976 = Vvar__1__r2__64977
& Vvar__0__r1__64974 = Vvar__0__r1__64975 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__64978,Vvar__0__r1__64979,Vvar__1__r2__64980,Vvar__1__r2__64981] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__64978,Vvar__1__r2__64980) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__64979,Vvar__1__r2__64981)
=> ( Vvar__1__r2__64980 = Vvar__1__r2__64981
& Vvar__0__r1__64978 = Vvar__0__r1__64979 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__64988,Vvar__0__r__64989] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__64988) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__64989)
=> Vvar__0__r__64988 = Vvar__0__r__64989 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__64970,Vvar__0__r1__64971,Vvar__1__r2__64972,Vvar__1__r2__64973] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__64970,Vvar__1__r2__64972) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__64971,Vvar__1__r2__64973)
=> ( Vvar__1__r2__64972 = Vvar__1__r2__64973
& Vvar__0__r1__64970 = Vvar__0__r1__64971 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__64982,Vvar__0__r1__64983,Vvar__1__z__64984,Vvar__1__z__64985] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__64982,Vvar__1__z__64984) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__64983,Vvar__1__z__64985)
=> ( Vvar__1__z__64984 = Vvar__1__z__64985
& Vvar__0__r1__64982 = Vvar__0__r1__64983 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__64966,Vvar__0__r__64967] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__64966) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__64967)
=> Vvar__0__r__64966 = Vvar__0__r__64967 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__64968,Vvar__0__r__64969] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__64968) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__64969)
=> Vvar__0__r__64968 = Vvar__0__r__64969 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__27502,Vvar__0__T__27503,Vvar__1__Flhs__27504,Vvar__1__Flhs__27505,Vvar__2__Fop__27506,Vvar__2__Fop__27507,Vvar__3__Frhs__27508,Vvar__3__Frhs__27509] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27502,Vvar__1__Flhs__27504,Vvar__2__Fop__27506,Vvar__3__Frhs__27508) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27503,Vvar__1__Flhs__27505,Vvar__2__Fop__27507,Vvar__3__Frhs__27509)
=> ( Vvar__3__Frhs__27508 = Vvar__3__Frhs__27509
& Vvar__2__Fop__27506 = Vvar__2__Fop__27507
& Vvar__1__Flhs__27504 = Vvar__1__Flhs__27505
& Vvar__0__T__27502 = Vvar__0__T__27503 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__27484,Vvar__0__C__27485,Vvar__1___24Anonymous__27486,Vvar__1___24Anonymous__27487,Vvar__2___24Anonymous__27488,Vvar__2___24Anonymous__27489] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27484,Vvar__1___24Anonymous__27486,Vvar__2___24Anonymous__27488) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27485,Vvar__1___24Anonymous__27487,Vvar__2___24Anonymous__27489)
=> ( Vvar__2___24Anonymous__27488 = Vvar__2___24Anonymous__27489
& Vvar__1___24Anonymous__27486 = Vvar__1___24Anonymous__27487
& Vvar__0__C__27484 = Vvar__0__C__27485 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__27490,Vvar__0__C__27491,Vvar__1___24Anonymous__27492,Vvar__1___24Anonymous__27493] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27490,Vvar__1___24Anonymous__27492) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27491,Vvar__1___24Anonymous__27493)
=> ( Vvar__1___24Anonymous__27492 = Vvar__1___24Anonymous__27493
& Vvar__0__C__27490 = Vvar__0__C__27491 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__27464,Vvar__0__C__27465,Vvar__1___24Anonymous__27466,Vvar__1___24Anonymous__27467] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27464,Vvar__1___24Anonymous__27466) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27465,Vvar__1___24Anonymous__27467)
=> ( Vvar__1___24Anonymous__27466 = Vvar__1___24Anonymous__27467
& Vvar__0__C__27464 = Vvar__0__C__27465 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__27472,Vvar__0__C__27473,Vvar__1___24Anonymous__27474,Vvar__1___24Anonymous__27475,Vvar__2___24Anonymous__27476,Vvar__2___24Anonymous__27477] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27472,Vvar__1___24Anonymous__27474,Vvar__2___24Anonymous__27476) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27473,Vvar__1___24Anonymous__27475,Vvar__2___24Anonymous__27477)
=> ( Vvar__2___24Anonymous__27476 = Vvar__2___24Anonymous__27477
& Vvar__1___24Anonymous__27474 = Vvar__1___24Anonymous__27475
& Vvar__0__C__27472 = Vvar__0__C__27473 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__27478,Vvar__0__C__27479,Vvar__1___24Anonymous__27480,Vvar__1___24Anonymous__27481,Vvar__2___24Anonymous__27482,Vvar__2___24Anonymous__27483] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27478,Vvar__1___24Anonymous__27480,Vvar__2___24Anonymous__27482) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27479,Vvar__1___24Anonymous__27481,Vvar__2___24Anonymous__27483)
=> ( Vvar__2___24Anonymous__27482 = Vvar__2___24Anonymous__27483
& Vvar__1___24Anonymous__27480 = Vvar__1___24Anonymous__27481
& Vvar__0__C__27478 = Vvar__0__C__27479 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__27468,Vvar__0__C__27469,Vvar__1___24Anonymous__27470,Vvar__1___24Anonymous__27471] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27468,Vvar__1___24Anonymous__27470) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27469,Vvar__1___24Anonymous__27471)
=> ( Vvar__1___24Anonymous__27470 = Vvar__1___24Anonymous__27471
& Vvar__0__C__27468 = Vvar__0__C__27469 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__27494,Vvar__0__C__27495] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27494) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27495)
=> Vvar__0__C__27494 = Vvar__0__C__27495 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__65490,Vvar__0__TA__65491,Vvar__1__TX__65492,Vvar__1__TX__65493,Vvar__2__AA__65494,Vvar__2__AA__65495,Vvar__3__AF__65496,Vvar__3__AF__65497,Vvar__4___24Anonymous__65498,Vvar__4___24Anonymous__65499,Vvar__5___24Anonymous__65500,Vvar__5___24Anonymous__65501] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__65490,Vvar__1__TX__65492,Vvar__2__AA__65494,Vvar__3__AF__65496,Vvar__4___24Anonymous__65498,Vvar__5___24Anonymous__65500) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__65491,Vvar__1__TX__65493,Vvar__2__AA__65495,Vvar__3__AF__65497,Vvar__4___24Anonymous__65499,Vvar__5___24Anonymous__65501)
=> ( Vvar__5___24Anonymous__65500 = Vvar__5___24Anonymous__65501
& Vvar__4___24Anonymous__65498 = Vvar__4___24Anonymous__65499
& Vvar__3__AF__65496 = Vvar__3__AF__65497
& Vvar__2__AA__65494 = Vvar__2__AA__65495
& Vvar__1__TX__65492 = Vvar__1__TX__65493
& Vvar__0__TA__65490 = Vvar__0__TA__65491 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__65502,Vvar__0__TA__65503,Vvar__1__TX__65504,Vvar__1__TX__65505,Vvar__2__AA__65506,Vvar__2__AA__65507,Vvar__3__AF__65508,Vvar__3__AF__65509,Vvar__4___24Anonymous__65510,Vvar__4___24Anonymous__65511,Vvar__5___24Anonymous__65512,Vvar__5___24Anonymous__65513] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__65502,Vvar__1__TX__65504,Vvar__2__AA__65506,Vvar__3__AF__65508,Vvar__4___24Anonymous__65510,Vvar__5___24Anonymous__65512) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__65503,Vvar__1__TX__65505,Vvar__2__AA__65507,Vvar__3__AF__65509,Vvar__4___24Anonymous__65511,Vvar__5___24Anonymous__65513)
=> ( Vvar__5___24Anonymous__65512 = Vvar__5___24Anonymous__65513
& Vvar__4___24Anonymous__65510 = Vvar__4___24Anonymous__65511
& Vvar__3__AF__65508 = Vvar__3__AF__65509
& Vvar__2__AA__65506 = Vvar__2__AA__65507
& Vvar__1__TX__65504 = Vvar__1__TX__65505
& Vvar__0__TA__65502 = Vvar__0__TA__65503 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__65514,Vvar__0__TA__65515,Vvar__1__TX__65516,Vvar__1__TX__65517,Vvar__2__AA__65518,Vvar__2__AA__65519,Vvar__3__AF__65520,Vvar__3__AF__65521,Vvar__4___24Anonymous__65522,Vvar__4___24Anonymous__65523,Vvar__5___24Anonymous__65524,Vvar__5___24Anonymous__65525] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__65514,Vvar__1__TX__65516,Vvar__2__AA__65518,Vvar__3__AF__65520,Vvar__4___24Anonymous__65522,Vvar__5___24Anonymous__65524) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__65515,Vvar__1__TX__65517,Vvar__2__AA__65519,Vvar__3__AF__65521,Vvar__4___24Anonymous__65523,Vvar__5___24Anonymous__65525)
=> ( Vvar__5___24Anonymous__65524 = Vvar__5___24Anonymous__65525
& Vvar__4___24Anonymous__65522 = Vvar__4___24Anonymous__65523
& Vvar__3__AF__65520 = Vvar__3__AF__65521
& Vvar__2__AA__65518 = Vvar__2__AA__65519
& Vvar__1__TX__65516 = Vvar__1__TX__65517
& Vvar__0__TA__65514 = Vvar__0__TA__65515 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__65472,Vvar__0__TA__65473,Vvar__1__TX__65474,Vvar__1__TX__65475,Vvar__2__AA__65476,Vvar__2__AA__65477,Vvar__3__AF__65478,Vvar__3__AF__65479] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65472,Vvar__1__TX__65474,Vvar__2__AA__65476,Vvar__3__AF__65478) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65473,Vvar__1__TX__65475,Vvar__2__AA__65477,Vvar__3__AF__65479)
=> ( Vvar__3__AF__65478 = Vvar__3__AF__65479
& Vvar__2__AA__65476 = Vvar__2__AA__65477
& Vvar__1__TX__65474 = Vvar__1__TX__65475
& Vvar__0__TA__65472 = Vvar__0__TA__65473 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__65536,Vvar__0__TA__65537,Vvar__1__TX__65538,Vvar__1__TX__65539,Vvar__2__AA__65540,Vvar__2__AA__65541,Vvar__3__AF__65542,Vvar__3__AF__65543,Vvar__4___24Anonymous__65544,Vvar__4___24Anonymous__65545,Vvar__5___24Anonymous__65546,Vvar__5___24Anonymous__65547,Vvar__6___24Anonymous__65548,Vvar__6___24Anonymous__65549] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__65536,Vvar__1__TX__65538,Vvar__2__AA__65540,Vvar__3__AF__65542,Vvar__4___24Anonymous__65544,Vvar__5___24Anonymous__65546,Vvar__6___24Anonymous__65548) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__65537,Vvar__1__TX__65539,Vvar__2__AA__65541,Vvar__3__AF__65543,Vvar__4___24Anonymous__65545,Vvar__5___24Anonymous__65547,Vvar__6___24Anonymous__65549)
=> ( Vvar__6___24Anonymous__65548 = Vvar__6___24Anonymous__65549
& Vvar__5___24Anonymous__65546 = Vvar__5___24Anonymous__65547
& Vvar__4___24Anonymous__65544 = Vvar__4___24Anonymous__65545
& Vvar__3__AF__65542 = Vvar__3__AF__65543
& Vvar__2__AA__65540 = Vvar__2__AA__65541
& Vvar__1__TX__65538 = Vvar__1__TX__65539
& Vvar__0__TA__65536 = Vvar__0__TA__65537 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__65526,Vvar__0__TA__65527,Vvar__1__TX__65528,Vvar__1__TX__65529,Vvar__2__AA__65530,Vvar__2__AA__65531,Vvar__3__AF__65532,Vvar__3__AF__65533,Vvar__4___24Anonymous__65534,Vvar__4___24Anonymous__65535] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__65526,Vvar__1__TX__65528,Vvar__2__AA__65530,Vvar__3__AF__65532,Vvar__4___24Anonymous__65534) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__65527,Vvar__1__TX__65529,Vvar__2__AA__65531,Vvar__3__AF__65533,Vvar__4___24Anonymous__65535)
=> ( Vvar__4___24Anonymous__65534 = Vvar__4___24Anonymous__65535
& Vvar__3__AF__65532 = Vvar__3__AF__65533
& Vvar__2__AA__65530 = Vvar__2__AA__65531
& Vvar__1__TX__65528 = Vvar__1__TX__65529
& Vvar__0__TA__65526 = Vvar__0__TA__65527 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__65464,Vvar__0__TA__65465,Vvar__1__TX__65466,Vvar__1__TX__65467,Vvar__2__AA__65468,Vvar__2__AA__65469,Vvar__3__AF__65470,Vvar__3__AF__65471] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65464,Vvar__1__TX__65466,Vvar__2__AA__65468,Vvar__3__AF__65470) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65465,Vvar__1__TX__65467,Vvar__2__AA__65469,Vvar__3__AF__65471)
=> ( Vvar__3__AF__65470 = Vvar__3__AF__65471
& Vvar__2__AA__65468 = Vvar__2__AA__65469
& Vvar__1__TX__65466 = Vvar__1__TX__65467
& Vvar__0__TA__65464 = Vvar__0__TA__65465 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__65480,Vvar__0__TA__65481,Vvar__1__TX__65482,Vvar__1__TX__65483,Vvar__2__AA__65484,Vvar__2__AA__65485,Vvar__3__AF__65486,Vvar__3__AF__65487,Vvar__4___24Anonymous__65488,Vvar__4___24Anonymous__65489] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__65480,Vvar__1__TX__65482,Vvar__2__AA__65484,Vvar__3__AF__65486,Vvar__4___24Anonymous__65488) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__65481,Vvar__1__TX__65483,Vvar__2__AA__65485,Vvar__3__AF__65487,Vvar__4___24Anonymous__65489)
=> ( Vvar__4___24Anonymous__65488 = Vvar__4___24Anonymous__65489
& Vvar__3__AF__65486 = Vvar__3__AF__65487
& Vvar__2__AA__65484 = Vvar__2__AA__65485
& Vvar__1__TX__65482 = Vvar__1__TX__65483
& Vvar__0__TA__65480 = Vvar__0__TA__65481 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__65596,Vvar__0__A__65597,Vvar__1___24Anonymous__65598,Vvar__1___24Anonymous__65599,Vvar__2___24Anonymous__65600,Vvar__2___24Anonymous__65601,Vvar__3___24Anonymous__65602,Vvar__3___24Anonymous__65603] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__65596,Vvar__1___24Anonymous__65598,Vvar__2___24Anonymous__65600,Vvar__3___24Anonymous__65602) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__65597,Vvar__1___24Anonymous__65599,Vvar__2___24Anonymous__65601,Vvar__3___24Anonymous__65603)
=> ( Vvar__3___24Anonymous__65602 = Vvar__3___24Anonymous__65603
& Vvar__2___24Anonymous__65600 = Vvar__2___24Anonymous__65601
& Vvar__1___24Anonymous__65598 = Vvar__1___24Anonymous__65599
& Vvar__0__A__65596 = Vvar__0__A__65597 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__65592,Vvar__0__A__65593,Vvar__1___24Anonymous__65594,Vvar__1___24Anonymous__65595] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65592,Vvar__1___24Anonymous__65594) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65593,Vvar__1___24Anonymous__65595)
=> ( Vvar__1___24Anonymous__65594 = Vvar__1___24Anonymous__65595
& Vvar__0__A__65592 = Vvar__0__A__65593 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__65590,Vvar__0__A__65591] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65590) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65591)
=> Vvar__0__A__65590 = Vvar__0__A__65591 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__20271,Vvar__0__C__20272] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20271) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20272)
=> Vvar__0__C__20271 = Vvar__0__C__20272 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__20269,Vvar__0__C__20270] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20269) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20270)
=> Vvar__0__C__20269 = Vvar__0__C__20270 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__20277,Vvar__0__C__20278,Vvar__1___24Anonymous__20279,Vvar__1___24Anonymous__20280] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__20277,Vvar__1___24Anonymous__20279) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__20278,Vvar__1___24Anonymous__20280)
=> ( Vvar__1___24Anonymous__20279 = Vvar__1___24Anonymous__20280
& Vvar__0__C__20277 = Vvar__0__C__20278 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__20281,Vvar__0__C__20282,Vvar__1___24Anonymous__20283,Vvar__1___24Anonymous__20284,Vvar__2___24Anonymous__20285,Vvar__2___24Anonymous__20286] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__20281,Vvar__1___24Anonymous__20283,Vvar__2___24Anonymous__20285) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__20282,Vvar__1___24Anonymous__20284,Vvar__2___24Anonymous__20286)
=> ( Vvar__2___24Anonymous__20285 = Vvar__2___24Anonymous__20286
& Vvar__1___24Anonymous__20283 = Vvar__1___24Anonymous__20284
& Vvar__0__C__20281 = Vvar__0__C__20282 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__20273,Vvar__0__C__20274,Vvar__1___24Anonymous__20275,Vvar__1___24Anonymous__20276] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__20273,Vvar__1___24Anonymous__20275) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__20274,Vvar__1___24Anonymous__20276)
=> ( Vvar__1___24Anonymous__20275 = Vvar__1___24Anonymous__20276
& Vvar__0__C__20273 = Vvar__0__C__20274 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__20307,Vvar__0__C__20308,Vvar__1___24Anonymous__20309,Vvar__1___24Anonymous__20310,Vvar__2___24Anonymous__20311,Vvar__2___24Anonymous__20312] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__20307,Vvar__1___24Anonymous__20309,Vvar__2___24Anonymous__20311) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__20308,Vvar__1___24Anonymous__20310,Vvar__2___24Anonymous__20312)
=> ( Vvar__2___24Anonymous__20311 = Vvar__2___24Anonymous__20312
& Vvar__1___24Anonymous__20309 = Vvar__1___24Anonymous__20310
& Vvar__0__C__20307 = Vvar__0__C__20308 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__20303,Vvar__0__C__20304,Vvar__1___24Anonymous__20305,Vvar__1___24Anonymous__20306] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__20303,Vvar__1___24Anonymous__20305) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__20304,Vvar__1___24Anonymous__20306)
=> ( Vvar__1___24Anonymous__20305 = Vvar__1___24Anonymous__20306
& Vvar__0__C__20303 = Vvar__0__C__20304 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__20293,Vvar__0__C__20294,Vvar__1___24Anonymous__20295,Vvar__1___24Anonymous__20296,Vvar__2___24Anonymous__20297,Vvar__2___24Anonymous__20298] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__20293,Vvar__1___24Anonymous__20295,Vvar__2___24Anonymous__20297) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__20294,Vvar__1___24Anonymous__20296,Vvar__2___24Anonymous__20298)
=> ( Vvar__2___24Anonymous__20297 = Vvar__2___24Anonymous__20298
& Vvar__1___24Anonymous__20295 = Vvar__1___24Anonymous__20296
& Vvar__0__C__20293 = Vvar__0__C__20294 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__20299,Vvar__0__C__20300,Vvar__1___24Anonymous__20301,Vvar__1___24Anonymous__20302] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__20299,Vvar__1___24Anonymous__20301) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__20300,Vvar__1___24Anonymous__20302)
=> ( Vvar__1___24Anonymous__20301 = Vvar__1___24Anonymous__20302
& Vvar__0__C__20299 = Vvar__0__C__20300 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__20313,Vvar__0__C__20314,Vvar__1___24Anonymous__20315,Vvar__1___24Anonymous__20316,Vvar__2___24Anonymous__20317,Vvar__2___24Anonymous__20318] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__20313,Vvar__1___24Anonymous__20315,Vvar__2___24Anonymous__20317) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__20314,Vvar__1___24Anonymous__20316,Vvar__2___24Anonymous__20318)
=> ( Vvar__2___24Anonymous__20317 = Vvar__2___24Anonymous__20318
& Vvar__1___24Anonymous__20315 = Vvar__1___24Anonymous__20316
& Vvar__0__C__20313 = Vvar__0__C__20314 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__20287,Vvar__0__C__20288,Vvar__1___24Anonymous__20289,Vvar__1___24Anonymous__20290,Vvar__2___24Anonymous__20291,Vvar__2___24Anonymous__20292] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__20287,Vvar__1___24Anonymous__20289,Vvar__2___24Anonymous__20291) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__20288,Vvar__1___24Anonymous__20290,Vvar__2___24Anonymous__20292)
=> ( Vvar__2___24Anonymous__20291 = Vvar__2___24Anonymous__20292
& Vvar__1___24Anonymous__20289 = Vvar__1___24Anonymous__20290
& Vvar__0__C__20287 = Vvar__0__C__20288 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__20610,Vvar__0__C__20611,Vvar__1__num__20612,Vvar__1__num__20613,Vvar__2__denum__20614,Vvar__2__denum__20615,Vvar__3__condition__20616,Vvar__3__condition__20617] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20610,Vvar__1__num__20612,Vvar__2__denum__20614,Vvar__3__condition__20616) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20611,Vvar__1__num__20613,Vvar__2__denum__20615,Vvar__3__condition__20617)
=> ( Vvar__3__condition__20616 = Vvar__3__condition__20617
& Vvar__2__denum__20614 = Vvar__2__denum__20615
& Vvar__1__num__20612 = Vvar__1__num__20613
& Vvar__0__C__20610 = Vvar__0__C__20611 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__14464,Vvar__0__C__14465] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14464) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14465)
=> Vvar__0__C__14464 = Vvar__0__C__14465 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__14462,Vvar__0__C__14463] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14462) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14463)
=> Vvar__0__C__14462 = Vvar__0__C__14463 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__14470,Vvar__0__C__14471,Vvar__1___24Anonymous__14472,Vvar__1___24Anonymous__14473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14470,Vvar__1___24Anonymous__14472) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14471,Vvar__1___24Anonymous__14473)
=> ( Vvar__1___24Anonymous__14472 = Vvar__1___24Anonymous__14473
& Vvar__0__C__14470 = Vvar__0__C__14471 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__14474,Vvar__0__C__14475,Vvar__1___24Anonymous__14476,Vvar__1___24Anonymous__14477,Vvar__2___24Anonymous__14478,Vvar__2___24Anonymous__14479] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14474,Vvar__1___24Anonymous__14476,Vvar__2___24Anonymous__14478) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14475,Vvar__1___24Anonymous__14477,Vvar__2___24Anonymous__14479)
=> ( Vvar__2___24Anonymous__14478 = Vvar__2___24Anonymous__14479
& Vvar__1___24Anonymous__14476 = Vvar__1___24Anonymous__14477
& Vvar__0__C__14474 = Vvar__0__C__14475 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__14466,Vvar__0__C__14467,Vvar__1___24Anonymous__14468,Vvar__1___24Anonymous__14469] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14466,Vvar__1___24Anonymous__14468) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14467,Vvar__1___24Anonymous__14469)
=> ( Vvar__1___24Anonymous__14468 = Vvar__1___24Anonymous__14469
& Vvar__0__C__14466 = Vvar__0__C__14467 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__14486,Vvar__0__C__14487,Vvar__1___24Anonymous__14488,Vvar__1___24Anonymous__14489,Vvar__2___24Anonymous__14490,Vvar__2___24Anonymous__14491] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14486,Vvar__1___24Anonymous__14488,Vvar__2___24Anonymous__14490) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14487,Vvar__1___24Anonymous__14489,Vvar__2___24Anonymous__14491)
=> ( Vvar__2___24Anonymous__14490 = Vvar__2___24Anonymous__14491
& Vvar__1___24Anonymous__14488 = Vvar__1___24Anonymous__14489
& Vvar__0__C__14486 = Vvar__0__C__14487 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__14492,Vvar__0__C__14493,Vvar__1___24Anonymous__14494,Vvar__1___24Anonymous__14495] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14492,Vvar__1___24Anonymous__14494) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14493,Vvar__1___24Anonymous__14495)
=> ( Vvar__1___24Anonymous__14494 = Vvar__1___24Anonymous__14495
& Vvar__0__C__14492 = Vvar__0__C__14493 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__14496,Vvar__0__C__14497,Vvar__1___24Anonymous__14498,Vvar__1___24Anonymous__14499,Vvar__2___24Anonymous__14500,Vvar__2___24Anonymous__14501] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14496,Vvar__1___24Anonymous__14498,Vvar__2___24Anonymous__14500) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14497,Vvar__1___24Anonymous__14499,Vvar__2___24Anonymous__14501)
=> ( Vvar__2___24Anonymous__14500 = Vvar__2___24Anonymous__14501
& Vvar__1___24Anonymous__14498 = Vvar__1___24Anonymous__14499
& Vvar__0__C__14496 = Vvar__0__C__14497 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__14480,Vvar__0__C__14481,Vvar__1___24Anonymous__14482,Vvar__1___24Anonymous__14483,Vvar__2___24Anonymous__14484,Vvar__2___24Anonymous__14485] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14480,Vvar__1___24Anonymous__14482,Vvar__2___24Anonymous__14484) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14481,Vvar__1___24Anonymous__14483,Vvar__2___24Anonymous__14485)
=> ( Vvar__2___24Anonymous__14484 = Vvar__2___24Anonymous__14485
& Vvar__1___24Anonymous__14482 = Vvar__1___24Anonymous__14483
& Vvar__0__C__14480 = Vvar__0__C__14481 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__14117,Vvar__0__C__14118,Vvar__1___24Anonymous__14119,Vvar__1___24Anonymous__14120,Vvar__2___24Anonymous__14121,Vvar__2___24Anonymous__14122,Vvar__3___24Anonymous__14123,Vvar__3___24Anonymous__14124] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__14117,Vvar__1___24Anonymous__14119,Vvar__2___24Anonymous__14121,Vvar__3___24Anonymous__14123) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__14118,Vvar__1___24Anonymous__14120,Vvar__2___24Anonymous__14122,Vvar__3___24Anonymous__14124)
=> ( Vvar__3___24Anonymous__14123 = Vvar__3___24Anonymous__14124
& Vvar__2___24Anonymous__14121 = Vvar__2___24Anonymous__14122
& Vvar__1___24Anonymous__14119 = Vvar__1___24Anonymous__14120
& Vvar__0__C__14117 = Vvar__0__C__14118 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__14107,Vvar__0__C__14108,Vvar__1___24Anonymous__14109,Vvar__1___24Anonymous__14110] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14107,Vvar__1___24Anonymous__14109) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14108,Vvar__1___24Anonymous__14110)
=> ( Vvar__1___24Anonymous__14109 = Vvar__1___24Anonymous__14110
& Vvar__0__C__14107 = Vvar__0__C__14108 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__14111,Vvar__0__C__14112,Vvar__1___24Anonymous__14113,Vvar__1___24Anonymous__14114,Vvar__2___24Anonymous__14115,Vvar__2___24Anonymous__14116] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14111,Vvar__1___24Anonymous__14113,Vvar__2___24Anonymous__14115) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14112,Vvar__1___24Anonymous__14114,Vvar__2___24Anonymous__14116)
=> ( Vvar__2___24Anonymous__14115 = Vvar__2___24Anonymous__14116
& Vvar__1___24Anonymous__14113 = Vvar__1___24Anonymous__14114
& Vvar__0__C__14111 = Vvar__0__C__14112 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__14276,Vvar__0___24Anonymous__14277,Vvar__1___24Anonymous__14278,Vvar__1___24Anonymous__14279] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__14276,Vvar__1___24Anonymous__14278) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__14277,Vvar__1___24Anonymous__14279)
=> ( Vvar__1___24Anonymous__14278 = Vvar__1___24Anonymous__14279
& Vvar__0___24Anonymous__14276 = Vvar__0___24Anonymous__14277 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__14272,Vvar__0___24Anonymous__14273,Vvar__1___24Anonymous__14274,Vvar__1___24Anonymous__14275] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14272,Vvar__1___24Anonymous__14274) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14273,Vvar__1___24Anonymous__14275)
=> ( Vvar__1___24Anonymous__14274 = Vvar__1___24Anonymous__14275
& Vvar__0___24Anonymous__14272 = Vvar__0___24Anonymous__14273 ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__13194,Vvar__1__Q__13195,Vvar__2___24Anonymous__13196] :
( cProp___24t(Vvar__0__P__13194)
=> ( cProp___24t(Vvar__1__Q__13195)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__13196)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__13194,Vvar__1__Q__13195,Vvar__2___24Anonymous__13196)
=> ( ( p(Vvar__0__P__13194)
& Vvar__2___24Anonymous__13196 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__13195)
& Vvar__2___24Anonymous__13196 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__13344,Vvar__1__Plt__13345,Vvar__2__Pgt__13346,Vvar__3___24Anonymous__13347] :
( cProp___24t(Vvar__0__Peq__13344)
=> ( cProp___24t(Vvar__1__Plt__13345)
=> ( cProp___24t(Vvar__2__Pgt__13346)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__13347)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__13344,Vvar__1__Plt__13345,Vvar__2__Pgt__13346,Vvar__3___24Anonymous__13347)
=> ( ( p(Vvar__0__Peq__13344)
& Vvar__3___24Anonymous__13347 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__13345)
& Vvar__3___24Anonymous__13347 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__13346)
& Vvar__3___24Anonymous__13347 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX367] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX367)
=> ( VX367 = cCoq_2eInit_2eDatatypes_2etrue
| VX367 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX394] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX394)
=> ( VX394 = cCoq_2eInit_2eDatatypes_2eEq
| VX394 = cCoq_2eInit_2eDatatypes_2eLt
| VX394 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__13317,VX13318] :
( cType___24t(Vvar__0__A__13317)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13317,VX13318)
=> ( VX13318 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13317)
| ? [Vvar__1___24Anonymous__13321] :
( t(Vvar__1___24Anonymous__13321,Vvar__0__A__13317)
& ? [Vvar__2___24Anonymous__13322] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13317,Vvar__2___24Anonymous__13322)
& VX13318 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13317,Vvar__1___24Anonymous__13321,Vvar__2___24Anonymous__13322) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX13204] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX13204)
=> ( VX13204 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__13205] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13205)
& VX13204 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13205) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__13236,VX13237] :
( cType___24t(Vvar__0__A__13236)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__13236,VX13237)
=> ( ? [Vvar__1___24Anonymous__13239] :
( t(Vvar__1___24Anonymous__13239,Vvar__0__A__13236)
& VX13237 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__13236,Vvar__1___24Anonymous__13239) )
| VX13237 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__13236) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__368,Vvar__1__B__369,VX370] :
( cType___24t(Vvar__0__A__368)
=> ( cType___24t(Vvar__1__B__369)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__368,Vvar__1__B__369,VX370)
=> ? [Vvar__2___24Anonymous__373] :
( t(Vvar__2___24Anonymous__373,Vvar__0__A__368)
& ? [Vvar__3___24Anonymous__374] :
( t(Vvar__3___24Anonymous__374,Vvar__1__B__369)
& VX370 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__368,Vvar__1__B__369,Vvar__2___24Anonymous__373,Vvar__3___24Anonymous__374) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX27] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX27)
=> VX27 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_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.sigT',axiom,
! [Vvar__0__A__65072,Vvar__1__P__65073,VX65076] :
( cType___24t(Vvar__0__A__65072)
=> ( c_24__type__65086___24t(Vvar__0__A__65072,Vvar__1__P__65073,Vvar__1__P__65073)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__65072,Vvar__1__P__65073,VX65076)
=> ? [Vvar__2__x__65081] :
( t(Vvar__2__x__65081,Vvar__0__A__65072)
& ? [Vvar__3___24Anonymous__65082] :
( t(Vvar__3___24Anonymous__65082,happ(Vvar__1__P__65073,Vvar__2__x__65081))
& VX65076 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__65072,Vvar__1__P__65073,Vvar__2__x__65081,Vvar__3___24Anonymous__65082) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__107,Vvar__1__B__108,VX109] :
( cProp___24t(Vvar__0__A__107)
=> ( cProp___24t(Vvar__1__B__108)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__107,Vvar__1__B__108,VX109)
=> ( ( p(Vvar__0__A__107)
& VX109 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__107,Vvar__1__B__108) )
| ( p(Vvar__1__B__108)
& VX109 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__107,Vvar__1__B__108) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__31261,Vvar__1__B__31262,VX31263] :
( cType___24t(Vvar__0__A__31261)
=> ( cProp___24t(Vvar__1__B__31262)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__31261,Vvar__1__B__31262,VX31263)
=> ( ? [Vvar__2___24Anonymous__31266] :
( t(Vvar__2___24Anonymous__31266,Vvar__0__A__31261)
& VX31263 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__31261,Vvar__1__B__31262,Vvar__2___24Anonymous__31266) )
| ( p(Vvar__1__B__31262)
& VX31263 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__31261,Vvar__1__B__31262) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX13181] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX13181)
=> ( VX13181 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__13182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13182)
& VX13181 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13182) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX14] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX14)
=> ( VX14 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__15] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15)
& VX14 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15) )
| ? [Vvar__0___24Anonymous__16] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__16)
& VX14 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1)
=> ( ? [Vvar__0___24Anonymous__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2) )
| ? [Vvar__0___24Anonymous__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3)
& VX1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3) )
| VX1 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX13851] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX13851)
=> ? [Vvar__0__Qnum__13852] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__13852)
& ? [Vvar__1__Qden__13853] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__13853)
& VX13851 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__13852,Vvar__1__Qden__13853) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX64818] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX64818)
=> ? [Vvar__0__pos__64819] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__64819)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__64819))
& VX64818 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__64819) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__32042,Vvar__1___24Anonymous__32043,VX32044] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__32042)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__32043)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__32042,Vvar__1___24Anonymous__32043,VX32044)
=> ( ( Vvar__0__x__32042 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__32043 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX32044 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32042) )
| ? [Vvar__1__n__32048] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__32048)
& Vvar__0__x__32042 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__32048)
& Vvar__1___24Anonymous__32043 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068___24a3(Vvar__0__x__32042,Vvar__1___24Anonymous__32043,Vvar__1__n__32048)
& VX32044 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32042,Vvar__1__n__32048) )
| ? [Vvar__1__n__32053] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__32053)
& Vvar__0__x__32042 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__32053))
& Vvar__1___24Anonymous__32043 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(Vvar__0__x__32042,Vvar__1___24Anonymous__32043,Vvar__1__n__32053)
& VX32044 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32042,Vvar__1__n__32053) ) ) ) ) ) ).
fof('$_inversion_Coq.Reals.Rlimit.Metric_Space',axiom,
! [VX65012] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(VX65012)
=> ? [Vvar__0__Base__65013] :
( cType___24t(Vvar__0__Base__65013)
& ? [Vvar__1__dist__65014] :
( c_24__type__65044___24t(Vvar__0__Base__65013,Vvar__1__dist__65014)
& ! [Vvar__var__2__x__65020__65022] :
( t(Vvar__var__2__x__65020__65022,Vvar__0__Base__65013)
=> ! [Vvar__var__3__y__65021__65023] :
( t(Vvar__var__3__y__65021__65023,Vvar__0__Base__65013)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__65014,Vvar__var__2__x__65020__65022),Vvar__var__3__y__65021__65023),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__65025__65027] :
( t(Vvar__var__3__x__65025__65027,Vvar__0__Base__65013)
=> ! [Vvar__var__4__y__65026__65028] :
( t(Vvar__var__4__y__65026__65028,Vvar__0__Base__65013)
=> happ(happ(Vvar__1__dist__65014,Vvar__var__3__x__65025__65027),Vvar__var__4__y__65026__65028) = happ(happ(Vvar__1__dist__65014,Vvar__var__4__y__65026__65028),Vvar__var__3__x__65025__65027) ) )
& ! [Vvar__var__4__x__65030__65032] :
( t(Vvar__var__4__x__65030__65032,Vvar__0__Base__65013)
=> ! [Vvar__var__5__y__65031__65033] :
( t(Vvar__var__5__y__65031__65033,Vvar__0__Base__65013)
=> ( happ(happ(Vvar__1__dist__65014,Vvar__var__4__x__65030__65032),Vvar__var__5__y__65031__65033) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__65030__65032 = Vvar__var__5__y__65031__65033 ) ) )
& ! [Vvar__var__5__x__65035__65038] :
( t(Vvar__var__5__x__65035__65038,Vvar__0__Base__65013)
=> ! [Vvar__var__6__y__65036__65039] :
( t(Vvar__var__6__y__65036__65039,Vvar__0__Base__65013)
=> ! [Vvar__var__7__z__65037__65040] :
( t(Vvar__var__7__z__65037__65040,Vvar__0__Base__65013)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__65014,Vvar__var__5__x__65035__65038),Vvar__var__6__y__65036__65039),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__65014,Vvar__var__5__x__65035__65038),Vvar__var__7__z__65037__65040),happ(happ(Vvar__1__dist__65014,Vvar__var__7__z__65037__65040),Vvar__var__6__y__65036__65039)))) ) ) )
& VX65012 = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__65013,Vvar__1__dist__65014) ) ) ) ).
fof('$_inversion_Coq.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('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__17013] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__17013)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__17013)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__17013))
& ! [Vvar__var__var__2__n__17018__17020__17022] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__17018__17020__17022)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__17018__17020__17022))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__17018__17020__17022,Vvar__0__p__17013)) )
=> p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__17018__17020__17022,Vvar__0__p__17013)) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__13380,VX13381] :
( cType___24t(Vvar__0__C__13380)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,VX13381)
=> ( ? [Vvar__1___24Anonymous__13383] :
( t(Vvar__1___24Anonymous__13383,Vvar__0__C__13380)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__13380,Vvar__1___24Anonymous__13383) )
| ? [Vvar__1___24Anonymous__13385] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13385)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__13380,Vvar__1___24Anonymous__13385) )
| ? [Vvar__1___24Anonymous__13387] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13387)
& ? [Vvar__2___24Anonymous__13388] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__2___24Anonymous__13388)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13387,Vvar__2___24Anonymous__13388) ) )
| ? [Vvar__1___24Anonymous__13390] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13390)
& ? [Vvar__2___24Anonymous__13391] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__2___24Anonymous__13391)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13390,Vvar__2___24Anonymous__13391) ) )
| ? [Vvar__1___24Anonymous__13393] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13393)
& ? [Vvar__2___24Anonymous__13394] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__2___24Anonymous__13394)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13393,Vvar__2___24Anonymous__13394) ) )
| ? [Vvar__1___24Anonymous__13396] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13396)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__13380,Vvar__1___24Anonymous__13396) )
| ? [Vvar__1___24Anonymous__13398] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__13380,Vvar__1___24Anonymous__13398)
& ? [Vvar__2___24Anonymous__13399] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13399)
& VX13381 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__13380,Vvar__1___24Anonymous__13398,Vvar__2___24Anonymous__13399) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__13544,VX13545] :
( cType___24t(Vvar__0__C__13544)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,VX13545)
=> ( ? [Vvar__1___24Anonymous__13547] :
( t(Vvar__1___24Anonymous__13547,Vvar__0__C__13544)
& VX13545 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__13544,Vvar__1___24Anonymous__13547) )
| ? [Vvar__1___24Anonymous__13549] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13549)
& ? [Vvar__2___24Anonymous__13550] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,Vvar__2___24Anonymous__13550)
& VX13545 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__13544,Vvar__1___24Anonymous__13549,Vvar__2___24Anonymous__13550) ) )
| ? [Vvar__1___24Anonymous__13552] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,Vvar__1___24Anonymous__13552)
& ? [Vvar__2___24Anonymous__13553] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__13553)
& ? [Vvar__3___24Anonymous__13554] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__13544,Vvar__3___24Anonymous__13554)
& VX13545 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__13544,Vvar__1___24Anonymous__13552,Vvar__2___24Anonymous__13553,Vvar__3___24Anonymous__13554) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX64845] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX64845)
=> ( VX64845 = cCoq_2emicromega_2eRMicromega_2eC0
| VX64845 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__64846] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__64846)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__64846) )
| ? [Vvar__0__r__64847] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__64847)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__64847) )
| ? [Vvar__0__r1__64848] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64848)
& ? [Vvar__1__r2__64849] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__64849)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__64848,Vvar__1__r2__64849) ) )
| ? [Vvar__0__r1__64850] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64850)
& ? [Vvar__1__r2__64851] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__64851)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__64850,Vvar__1__r2__64851) ) )
| ? [Vvar__0__r1__64852] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64852)
& ? [Vvar__1__r2__64853] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__64853)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__64852,Vvar__1__r2__64853) ) )
| ? [Vvar__0__r1__64854] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__64854)
& ? [Vvar__1__z__64855] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__64855)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__64854,Vvar__1__z__64855) ) )
| ? [Vvar__0__r__64856] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__64856)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__64856) )
| ? [Vvar__0__r__64857] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__64857)
& VX64845 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__64857) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__27496,VX27497] :
( cType___24t(Vvar__0__T__27496)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__27496,VX27497)
=> ? [Vvar__1__Flhs__27499] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__27496,Vvar__1__Flhs__27499)
& ? [Vvar__2__Fop__27500] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__27500)
& ? [Vvar__3__Frhs__27501] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__27496,Vvar__3__Frhs__27501)
& VX27497 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27496,Vvar__1__Flhs__27499,Vvar__2__Fop__27500,Vvar__3__Frhs__27501) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX32305] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX32305)
=> ( VX32305 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX32305 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX32305 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX32305 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX61428] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX61428)
=> ( VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX61428 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__27350,VX27351] :
( cType___24t(Vvar__0__C__27350)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,VX27351)
=> ( ? [Vvar__1___24Anonymous__27353] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__27353)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27350,Vvar__1___24Anonymous__27353) )
| ? [Vvar__1___24Anonymous__27355] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27355)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27350,Vvar__1___24Anonymous__27355) )
| ? [Vvar__1___24Anonymous__27357] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27357)
& ? [Vvar__2___24Anonymous__27358] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__2___24Anonymous__27358)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27350,Vvar__1___24Anonymous__27357,Vvar__2___24Anonymous__27358) ) )
| ? [Vvar__1___24Anonymous__27360] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27360)
& ? [Vvar__2___24Anonymous__27361] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__2___24Anonymous__27361)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27350,Vvar__1___24Anonymous__27360,Vvar__2___24Anonymous__27361) ) )
| ? [Vvar__1___24Anonymous__27363] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__1___24Anonymous__27363)
& ? [Vvar__2___24Anonymous__27364] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__27350,Vvar__2___24Anonymous__27364)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27350,Vvar__1___24Anonymous__27363,Vvar__2___24Anonymous__27364) ) )
| ? [Vvar__1___24Anonymous__27366] :
( t(Vvar__1___24Anonymous__27366,Vvar__0__C__27350)
& VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27350,Vvar__1___24Anonymous__27366) )
| VX27351 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27350) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,VX65111] :
( cType___24t(Vvar__0__TA__65107)
=> ( cType___24t(Vvar__1__TX__65108)
=> ( cType___24t(Vvar__2__AA__65109)
=> ( cType___24t(Vvar__3__AF__65110)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,VX65111)
=> ( VX65111 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110)
| VX65111 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110)
| ? [Vvar__4___24Anonymous__65124] :
( t(Vvar__4___24Anonymous__65124,Vvar__1__TX__65108)
& VX65111 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65124) )
| ? [Vvar__4___24Anonymous__65129] :
( t(Vvar__4___24Anonymous__65129,Vvar__0__TA__65107)
& ? [Vvar__5___24Anonymous__65130] :
( t(Vvar__5___24Anonymous__65130,Vvar__2__AA__65109)
& VX65111 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65129,Vvar__5___24Anonymous__65130) ) )
| ? [Vvar__4___24Anonymous__65135] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65135)
& ? [Vvar__5___24Anonymous__65136] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__5___24Anonymous__65136)
& VX65111 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65135,Vvar__5___24Anonymous__65136) ) )
| ? [Vvar__4___24Anonymous__65141] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65141)
& ? [Vvar__5___24Anonymous__65142] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__5___24Anonymous__65142)
& VX65111 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65141,Vvar__5___24Anonymous__65142) ) )
| ? [Vvar__4___24Anonymous__65147] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65147)
& VX65111 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65147) )
| ? [Vvar__4___24Anonymous__65152] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65152)
& ? [Vvar__5___24Anonymous__65153] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__65110,Vvar__5___24Anonymous__65153)
& ? [Vvar__6___24Anonymous__65154] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__6___24Anonymous__65154)
& VX65111 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__65107,Vvar__1__TX__65108,Vvar__2__AA__65109,Vvar__3__AF__65110,Vvar__4___24Anonymous__65152,Vvar__5___24Anonymous__65153,Vvar__6___24Anonymous__65154) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__65567,VX65568] :
( cType___24t(Vvar__0__A__65567)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__65567,VX65568)
=> ( VX65568 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__65567)
| ? [Vvar__1___24Anonymous__65571] :
( t(Vvar__1___24Anonymous__65571,Vvar__0__A__65567)
& VX65568 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__65567,Vvar__1___24Anonymous__65571) )
| ? [Vvar__1___24Anonymous__65573] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__65567,Vvar__1___24Anonymous__65573)
& ? [Vvar__2___24Anonymous__65574] :
( t(Vvar__2___24Anonymous__65574,Vvar__0__A__65567)
& ? [Vvar__3___24Anonymous__65575] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__65567,Vvar__3___24Anonymous__65575)
& VX65568 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__65567,Vvar__1___24Anonymous__65573,Vvar__2___24Anonymous__65574,Vvar__3___24Anonymous__65575) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__19992,VX19993] :
( cType___24t(Vvar__0__C__19992)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,VX19993)
=> ( VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19992)
| VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19992)
| ? [Vvar__1___24Anonymous__19997] :
( t(Vvar__1___24Anonymous__19997,Vvar__0__C__19992)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__19997) )
| ? [Vvar__1___24Anonymous__19999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__19999)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__19999) )
| ? [Vvar__1___24Anonymous__20001] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20001)
& ? [Vvar__2___24Anonymous__20002] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20002)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20001,Vvar__2___24Anonymous__20002) ) )
| ? [Vvar__1___24Anonymous__20004] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20004)
& ? [Vvar__2___24Anonymous__20005] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20005)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20004,Vvar__2___24Anonymous__20005) ) )
| ? [Vvar__1___24Anonymous__20007] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20007)
& ? [Vvar__2___24Anonymous__20008] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20008)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20007,Vvar__2___24Anonymous__20008) ) )
| ? [Vvar__1___24Anonymous__20010] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20010)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__20010) )
| ? [Vvar__1___24Anonymous__20012] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20012)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__19992,Vvar__1___24Anonymous__20012) )
| ? [Vvar__1___24Anonymous__20014] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20014)
& ? [Vvar__2___24Anonymous__20015] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__2___24Anonymous__20015)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20014,Vvar__2___24Anonymous__20015) ) )
| ? [Vvar__1___24Anonymous__20017] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__19992,Vvar__1___24Anonymous__20017)
& ? [Vvar__2___24Anonymous__20018] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__20018)
& VX19993 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__19992,Vvar__1___24Anonymous__20017,Vvar__2___24Anonymous__20018) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__20604,VX20605] :
( cType___24t(Vvar__0__C__20604)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__20604,VX20605)
=> ? [Vvar__1__num__20607] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20604,Vvar__1__num__20607)
& ? [Vvar__2__denum__20608] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20604,Vvar__2__denum__20608)
& ? [Vvar__3__condition__20609] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__20604),Vvar__3__condition__20609)
& VX20605 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20604,Vvar__1__num__20607,Vvar__2__denum__20608,Vvar__3__condition__20609) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX14259] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX14259)
=> ( VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__14260] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14260)
& ? [Vvar__1___24Anonymous__14261] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__14261)
& VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__14260,Vvar__1___24Anonymous__14261) ) )
| ? [Vvar__0___24Anonymous__14262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14262)
& ? [Vvar__1___24Anonymous__14263] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__14263)
& VX14259 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__14262,Vvar__1___24Anonymous__14263) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__14280,VX14281] :
( cType___24t(Vvar__0__C__14280)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,VX14281)
=> ( VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__14280)
| VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__14280)
| ? [Vvar__1___24Anonymous__14285] :
( t(Vvar__1___24Anonymous__14285,Vvar__0__C__14280)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__14280,Vvar__1___24Anonymous__14285) )
| ? [Vvar__1___24Anonymous__14287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14287)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__14280,Vvar__1___24Anonymous__14287) )
| ? [Vvar__1___24Anonymous__14289] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14289)
& ? [Vvar__2___24Anonymous__14290] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__2___24Anonymous__14290)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14289,Vvar__2___24Anonymous__14290) ) )
| ? [Vvar__1___24Anonymous__14292] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14292)
& ? [Vvar__2___24Anonymous__14293] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__2___24Anonymous__14293)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14292,Vvar__2___24Anonymous__14293) ) )
| ? [Vvar__1___24Anonymous__14295] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14295)
& ? [Vvar__2___24Anonymous__14296] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__2___24Anonymous__14296)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14295,Vvar__2___24Anonymous__14296) ) )
| ? [Vvar__1___24Anonymous__14298] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14298)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__14280,Vvar__1___24Anonymous__14298) )
| ? [Vvar__1___24Anonymous__14300] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__14280,Vvar__1___24Anonymous__14300)
& ? [Vvar__2___24Anonymous__14301] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14301)
& VX14281 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__14280,Vvar__1___24Anonymous__14300,Vvar__2___24Anonymous__14301) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__14078,VX14079] :
( cType___24t(Vvar__0__C__14078)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,VX14079)
=> ( ? [Vvar__1___24Anonymous__14081] :
( t(Vvar__1___24Anonymous__14081,Vvar__0__C__14078)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__14078,Vvar__1___24Anonymous__14081) )
| ? [Vvar__1___24Anonymous__14083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14083)
& ? [Vvar__2___24Anonymous__14084] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__2___24Anonymous__14084)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__14078,Vvar__1___24Anonymous__14083,Vvar__2___24Anonymous__14084) ) )
| ? [Vvar__1___24Anonymous__14086] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__1___24Anonymous__14086)
& ? [Vvar__2___24Anonymous__14087] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14087)
& ? [Vvar__3___24Anonymous__14088] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__14078,Vvar__3___24Anonymous__14088)
& VX14079 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__14078,Vvar__1___24Anonymous__14086,Vvar__2___24Anonymous__14087,Vvar__3___24Anonymous__14088) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032] :
( cType___24t(Vvar__0__R__31016)
=> ( t(Vvar__1__rI__31017,Vvar__0__R__31016)
=> ( c_24__type__31118___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__2__rmul__31018)
=> ( c_24__type__31162___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__3__req__31023)
=> ( cType___24t(Vvar__4__Cpow__31028)
=> ( c_24__type__31198___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__5__Cp__phi__31029)
=> ( c_24__type__31242___24t(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032,Vvar__6__rpow__31032)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__3__req__31023,Vvar__4__Cpow__31028,Vvar__5__Cp__phi__31029,Vvar__6__rpow__31032)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074] :
( t(Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074,Vvar__0__R__31016)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075)
=> p(happ(happ(Vvar__3__req__31023,happ(happ(Vvar__6__rpow__31032,Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074),happ(Vvar__5__Cp__phi__31029,Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__31016,Vvar__1__rI__31017,Vvar__2__rmul__31018,Vvar__var__var__var__var__var__var__var__7__r__31060__31062__31064__31066__31068__31070__31072__31074,Vvar__var__var__var__var__var__var__var__8__n__31061__31063__31065__31067__31069__31071__31073__31075))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_114204',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__114204___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)),happ(Vv__CANONICAL__0,Vv__CANONICAL__1))) ).
fof('$_lam_114867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__114867___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2eReals_2eRtrigo__def_2eexp___24a1(Vv__CANONICAL__1) ) ).
fof('$_lam_13167',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__13167___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)),happ(Vv__CANONICAL__0,Vv__CANONICAL__1))) ).
fof('$_lam_13172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__13172___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__13174___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_13174',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__13174___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_140',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__140___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_143',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__143___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_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('$_lam_217',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__217___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a3(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eClasses_2eMorphisms_2eiff__flip__impl__subrelation___24a4(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),cCoq_2eZArith_2eBinInt_2eZ_2egt__lt__iff___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__221___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ).
fof('$_lam_22033',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__22033___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_259',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__264] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__264)
& ? [Vvar__3___24Anonymous__265] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__265)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__264,Vvar__3___24Anonymous__265)
& ( c_24__lam__259___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( Vv__CANONICAL__1 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vv__CANONICAL__0,Vvar__2___24Anonymous__264),Vvar__3___24Anonymous__265)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3___24Anonymous__265))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3___24Anonymous__265,Vv__CANONICAL__0)) ) ) ) ) ) ).
fof('$_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('$_lam_31805',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__31805___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_31864',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__31864___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__31805___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_32008',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__32008___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)) ).
fof('$_lam_32010',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__32010___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_32041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__32041___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRaxioms_2eis__lub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_34431',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__34431___24a1(Vv__CANONICAL__0)
<=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_lam_34432',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__34432___24a1(Vv__CANONICAL__0)
<=> Vv__CANONICAL__0 != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_lam_34433',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__34433___24a1(Vv__CANONICAL__0)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__0)) ) ).
fof('$_lam_34434',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__34434___24a1(Vv__CANONICAL__0)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vv__CANONICAL__0)) ) ).
fof('$_lam_529',axiom,
! [Vv__CANONICAL__0] : c_24__lam__529___24a1(Vv__CANONICAL__0) = c_24__type__531___24a1(Vv__CANONICAL__0) ).
fof('$_lam_578',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__lam__578___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__593,c_24__prop__594,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0)) )
| ? [Vvar__0___24Anonymous__579] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__579)
& Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__579)
& c_24__lam__578___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__595___24a1(Vvar__0___24Anonymous__579),c_24__prop__596___24a1(Vvar__0___24Anonymous__579)) )
| ? [Vvar__0___24Anonymous__586] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__586)
& Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__586)
& c_24__lam__578___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__598___24a1(Vvar__0___24Anonymous__586),c_24__prop__599___24a1(Vvar__0___24Anonymous__586)) ) ) ) ).
fof('$_lam_65845',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__65845___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_65922',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__65922___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo1_2ePI),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),Vv__CANONICAL__1))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))
& cCoq_2eReals_2eRtrigo1_2etan___24a1(Vv__CANONICAL__1) = Vv__CANONICAL__0 ) ) ).
fof('$_lam_65958',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__65958___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__65960___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_65960',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__65960___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__1) ).
fof('$_lam_66004',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__66004___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_66019',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__66019___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2esin__in___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_68662',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__68662___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(Vv__CANONICAL__1)),Vv__CANONICAL__0) ).
fof('$_lam_699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__lam__699___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__718___24a1(Vv__CANONICAL__0),c_24__prop__719___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__0___24Anonymous__700] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__700)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__700)
& c_24__lam__699___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(c_24__prop__721___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700),c_24__prop__722___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700),c_24__lam__725___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700),c_24__lam__733___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700),c_24__lam__767___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700),cCoq_2ePArith_2eBinPos_2ePos_2eeq__dec___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700)) )
| ? [Vvar__0___24Anonymous__711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__711)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__711)
& c_24__lam__699___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__771___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__711),c_24__prop__772___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__711)) ) ) ) ).
fof('$_lam_725',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__725___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(c_24__prop__726___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__727___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_733',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__733___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__734___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__735___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eLogic_2eeq__ind__r___24a5(cCoq_2eNumbers_2eBinNums_2epositive,Vv__CANONICAL__1,c_24__lam__738___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1)),Vv__CANONICAL__0)) ).
fof('$_lam_738',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__738___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_lam_767',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__767___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__768___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__769___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_78308',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__78308___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2eexp__in___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_78503',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__78503___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2))
& happ(Vv__CANONICAL__0,Vv__CANONICAL__3) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('$_lam_872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__lam__872___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__891___24a1(Vv__CANONICAL__0),c_24__prop__892___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__0___24Anonymous__873] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__873)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__873)
& c_24__lam__872___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__894___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__873),c_24__prop__895___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__873)) )
| ? [Vvar__0___24Anonymous__880] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__880)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__880)
& c_24__lam__872___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(c_24__prop__897___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880),c_24__prop__898___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880),c_24__lam__901___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880),c_24__lam__909___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880),c_24__lam__943___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880),cCoq_2ePArith_2eBinPos_2ePos_2eeq__dec___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880)) ) ) ) ).
fof('$_lam_901',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__901___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(c_24__prop__902___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__903___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__909___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__910___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__911___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eLogic_2eeq__ind__r___24a5(cCoq_2eNumbers_2eBinNums_2epositive,Vv__CANONICAL__1,c_24__lam__914___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1)),Vv__CANONICAL__0)) ).
fof('$_lam_914',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__914___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1) ) ).
fof('$_lam_943',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__943___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__944___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__945___24a2(Vv__CANONICAL__0,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_137',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__137___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ).
fof('$_prop_16433',axiom,
( p(c_24__prop__16433)
<=> cCoq_2eInit_2eDatatypes_2eEq = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_prop_16434',axiom,
( p(c_24__prop__16434)
<=> cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_prop_16436',axiom,
( p(c_24__prop__16436)
<=> cCoq_2eInit_2eDatatypes_2eLt = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_prop_16437',axiom,
( p(c_24__prop__16437)
<=> cCoq_2eInit_2eDatatypes_2eLt != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_prop_16438',axiom,
( p(c_24__prop__16438)
<=> cCoq_2eInit_2eDatatypes_2eGt = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_prop_16439',axiom,
( p(c_24__prop__16439)
<=> cCoq_2eInit_2eDatatypes_2eGt != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_prop_16444',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__16444___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_17066',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__17066___24a2(V0__a,V1__b))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('$_prop_17067',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__17067___24a2(V0__a,V1__b))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('$_prop_17068',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__17068___24a2(V0__a,V1__b))
<=> ~ p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)) ) ).
fof('$_prop_17143',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__17143___24a2(V0__a,V1__b))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('$_prop_17144',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__17144___24a2(V0__a,V1__b))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ).
fof('$_prop_17145',axiom,
! [V0__a,V1__b] :
( p(c_24__prop__17145___24a2(V0__a,V1__b))
<=> ~ p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)) ) ).
fof('$_prop_17150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__17150___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_19230',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__19230___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_19713',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__19713___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_221',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__221___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__5)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__4,Vv__CANONICAL__5))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__5,Vv__CANONICAL__4)) ) ) ) ) ).
fof('$_prop_35229',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__35229___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_35312',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__35312___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_533',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__533___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_534',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__534___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_593',axiom,
( p(c_24__prop__593)
<=> cCoq_2eNumbers_2eBinNums_2eZ0 = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_594',axiom,
( p(c_24__prop__594)
<=> cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_595',axiom,
! [Vvar__0___24Anonymous__579] :
( p(c_24__prop__595___24a1(Vvar__0___24Anonymous__579))
<=> cCoq_2eNumbers_2eBinNums_2eZ0 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__579) ) ).
fof('$_prop_596',axiom,
! [Vvar__0___24Anonymous__579] :
( p(c_24__prop__596___24a1(Vvar__0___24Anonymous__579))
<=> cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__579) ) ).
fof('$_prop_59731',axiom,
( p(c_24__prop__59731)
<=> cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_prop_59732',axiom,
( p(c_24__prop__59732)
<=> ~ ( cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_prop_59734',axiom,
( p(c_24__prop__59734)
<=> cCoq_2eInit_2eDatatypes_2eLt != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_prop_59735',axiom,
( p(c_24__prop__59735)
<=> ~ ( cCoq_2eInit_2eDatatypes_2eLt != cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_prop_59737',axiom,
( p(c_24__prop__59737)
<=> cCoq_2eInit_2eDatatypes_2eGt != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_prop_59738',axiom,
( p(c_24__prop__59738)
<=> ~ ( cCoq_2eInit_2eDatatypes_2eGt != cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_prop_59743',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__59743___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_598',axiom,
! [Vvar__0___24Anonymous__586] :
( p(c_24__prop__598___24a1(Vvar__0___24Anonymous__586))
<=> cCoq_2eNumbers_2eBinNums_2eZ0 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__586) ) ).
fof('$_prop_599',axiom,
! [Vvar__0___24Anonymous__586] :
( p(c_24__prop__599___24a1(Vvar__0___24Anonymous__586))
<=> cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__586) ) ).
fof('$_prop_60006',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__60006___24a2(V0__x,V1__y))
<=> V1__y = V0__x ) ).
fof('$_prop_60007',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__60007___24a2(V0__x,V1__y))
<=> V1__y = V0__x ) ).
fof('$_prop_64817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__64817___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_65001',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__65001___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_65002',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__65002___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_69021',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__69021___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_718',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__718___24a1(Vv__CANONICAL__0))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_719',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__719___24a1(Vv__CANONICAL__0))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_721',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__700] :
( p(c_24__prop__721___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700))
<=> Vv__CANONICAL__0 = Vvar__0___24Anonymous__700 ) ).
fof('$_prop_722',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__700] :
( p(c_24__prop__722___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__700))
<=> Vv__CANONICAL__0 != Vvar__0___24Anonymous__700 ) ).
fof('$_prop_726',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__726___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_727',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__727___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_734',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__734___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_735',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__735___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_74358',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__74358___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_75281',axiom,
! [V0__x] :
( p(c_24__prop__75281___24a1(V0__x))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x)) ) ).
fof('$_prop_75282',axiom,
! [V0__x] :
( p(c_24__prop__75282___24a1(V0__x))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x)) ) ).
fof('$_prop_768',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__768___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__769___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_771',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__711] :
( p(c_24__prop__771___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__711))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__711) ) ).
fof('$_prop_772',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__711] :
( p(c_24__prop__772___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__711))
<=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__711) ) ).
fof('$_prop_77795',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__77795___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_77796',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__77796___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_891',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__891___24a1(Vv__CANONICAL__0))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_892',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__892___24a1(Vv__CANONICAL__0))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('$_prop_894',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__873] :
( p(c_24__prop__894___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__873))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__873) ) ).
fof('$_prop_895',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__873] :
( p(c_24__prop__895___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__873))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__873) ) ).
fof('$_prop_897',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__880] :
( p(c_24__prop__897___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880))
<=> Vv__CANONICAL__0 = Vvar__0___24Anonymous__880 ) ).
fof('$_prop_898',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__880] :
( p(c_24__prop__898___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__880))
<=> Vv__CANONICAL__0 != Vvar__0___24Anonymous__880 ) ).
fof('$_prop_902',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__902___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__903___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_910',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__910___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_911',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__911___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__944___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__945___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__0) != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vv__CANONICAL__1) ) ).
fof('$_prop_950',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__950___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_951',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__951___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_type_113415',axiom,
! [Vvar__113416] :
( c_24__type__113415___24t(Vvar__113416)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__65958___24a1(Vv__CANONICAL__0),happ(Vvar__113416,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_114864',axiom,
! [Vvar__114865] :
( c_24__type__114864___24t(Vvar__114865)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__0))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__114867___24a1(Vv__CANONICAL__0),happ(Vvar__114865,Vv__CANONICAL__0)) ) ) ) ).
fof('$_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('$_type_118486',axiom,
! [Vvar__118487] :
( c_24__type__118486___24t(Vvar__118487)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__65044___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4) = happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3) ) )
=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ( happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vv__CANONICAL__4 = Vv__CANONICAL__5 ) ) )
=> ( ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__6),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__7),Vv__CANONICAL__6)))) ) ) )
=> cCoq_2eReals_2eRlimit_2eMetric__Space___24t(happ(happ(Vvar__118487,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ) ).
fof('$_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('$_type_122327',axiom,
! [Vvar__122328] :
( c_24__type__122327___24t(Vvar__122328)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__122328,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12714',axiom,
! [Vvar__12715] :
( c_24__type__12714___24t(Vvar__12715)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__12715,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13175',axiom,
! [Vvar__13176] :
( c_24__type__13175___24t(Vvar__13176)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__13176,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13186',axiom,
! [Vvar__13187] :
( c_24__type__13186___24t(Vvar__13187)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__13187,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13189',axiom,
! [Vvar__13190] :
( c_24__type__13189___24t(Vvar__13190)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__13190,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13192',axiom,
! [Vvar__13193] :
( c_24__type__13192___24t(Vvar__13193)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__13193,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13209',axiom,
! [Vvar__13210] :
( c_24__type__13209___24t(Vvar__13210)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__13210,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13253',axiom,
! [Vvar__13254] :
( c_24__type__13253___24t(Vvar__13254)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__13254,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13315',axiom,
! [Vvar__13316] :
( c_24__type__13315___24t(Vvar__13316)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__13316,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_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_13592',axiom,
! [Vvar__13593] :
( c_24__type__13592___24t(Vvar__13593)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__13593,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13636',axiom,
! [Vv__CANONICAL__0,Vvar__13637] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vvar__13637)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13637,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_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('$_type_13754',axiom,
! [Vvar__13755] :
( c_24__type__13754___24t(Vvar__13755)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__13755,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_13849',axiom,
! [Vvar__13850] :
( c_24__type__13849___24t(Vvar__13850)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__13850,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13861',axiom,
! [Vvar__13862] :
( c_24__type__13861___24t(Vvar__13862)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__13862,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13869',axiom,
! [Vvar__13870] :
( c_24__type__13869___24t(Vvar__13870)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__13870,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13871',axiom,
! [Vvar__13872] :
( c_24__type__13871___24t(Vvar__13872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__13872,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13874',axiom,
! [Vvar__13875] :
( c_24__type__13874___24t(Vvar__13875)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__13875,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13879',axiom,
! [Vvar__13880] :
( c_24__type__13879___24t(Vvar__13880)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__13880,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13885',axiom,
! [Vvar__13886] :
( c_24__type__13885___24t(Vvar__13886)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__13886,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13892',axiom,
! [Vvar__13893] :
( c_24__type__13892___24t(Vvar__13893)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__13893,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13938',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13939] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__13939)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__13939,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_14055',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14056] :
( c_24__type__14055___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14056)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14056,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_14067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14068] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14068)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__14068,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_14076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14077] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14077)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__14077,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_14243',axiom,
! [Vv__CANONICAL__0,Vvar__14244] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vvar__14244)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14244,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_14254',axiom,
! [Vvar__14255] :
( c_24__type__14254___24t(Vvar__14255)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__14255,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_14503',axiom,
! [Vvar__14504] :
( c_24__type__14503___24t(Vvar__14504)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__14504,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14506',axiom,
! [Vvar__14507] :
( c_24__type__14506___24t(Vvar__14507)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__14507,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14511',axiom,
! [Vvar__14512] :
( c_24__type__14511___24t(Vvar__14512)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__14512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14520',axiom,
! [Vvar__14521] :
( c_24__type__14520___24t(Vvar__14521)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__14521,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14728',axiom,
! [Vvar__14729] :
( c_24__type__14728___24t(Vvar__14729)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14729,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_14746',axiom,
! [Vv__CANONICAL__0,Vvar__14747] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vvar__14747)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__14747,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_14906',axiom,
! [Vvar__14907] :
( c_24__type__14906___24t(Vvar__14907)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14907,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_14940',axiom,
! [Vvar__14941] :
( c_24__type__14940___24t(Vvar__14941)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__14941,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_14961',axiom,
! [Vvar__14962] :
( c_24__type__14961___24t(Vvar__14962)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__14962,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_16378',axiom,
! [Vvar__16379] :
( c_24__type__16378___24t(Vvar__16379)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__16379,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_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('$_type_16442',axiom,
! [Vvar__16443] :
( c_24__type__16442___24t(Vvar__16443)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__16444___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__16443,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_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('$_type_17148',axiom,
! [Vvar__17149] :
( c_24__type__17148___24t(Vvar__17149)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__17150___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__17149,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_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('$_type_19222',axiom,
! [Vvar__19223] :
( c_24__type__19222___24t(Vvar__19223)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__19223,Vv__CANONICAL__0)) ) ) ).
fof('$_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('$_type_19307',axiom,
! [Vvar__19308] :
( c_24__type__19307___24t(Vvar__19308)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__19308,Vv__CANONICAL__0)) ) ) ).
fof('$_type_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_19377',axiom,
! [Vvar__19378] :
( c_24__type__19377___24t(Vvar__19378)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___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__19378,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
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_20576',axiom,
! [Vvar__20577] :
( c_24__type__20576___24t(Vvar__20577)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__20577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_20627',axiom,
! [Vvar__20628] :
( c_24__type__20627___24t(Vvar__20628)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__20628,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20647',axiom,
! [Vvar__20648] :
( c_24__type__20647___24t(Vvar__20648)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__20648,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20866',axiom,
! [Vvar__20867] :
( c_24__type__20866___24t(Vvar__20867)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__399___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__20867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_21994',axiom,
! [Vvar__21995] :
( c_24__type__21994___24t(Vvar__21995)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21995,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21998',axiom,
! [Vvar__21999] :
( c_24__type__21998___24t(Vvar__21999)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__21999,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22003',axiom,
! [Vvar__22004] :
( c_24__type__22003___24t(Vvar__22004)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__22004,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22008',axiom,
! [Vvar__22009] :
( c_24__type__22008___24t(Vvar__22009)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__22009,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22011',axiom,
! [Vvar__22012] :
( c_24__type__22011___24t(Vvar__22012)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22012,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22019',axiom,
! [Vvar__22020] :
( c_24__type__22019___24t(Vvar__22020)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13871___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__22020,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22029',axiom,
! [Vvar__22030] :
( c_24__type__22029___24t(Vvar__22030)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__22030,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22035',axiom,
! [Vvar__22036] :
( c_24__type__22035___24t(Vvar__22036)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22036,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22038',axiom,
! [Vvar__22039] :
( c_24__type__22038___24t(Vvar__22039)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22040___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22039,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22040',axiom,
! [Vvar__22041] :
( c_24__type__22040___24t(Vvar__22041)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22041,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22042',axiom,
! [Vvar__22043] :
( c_24__type__22042___24t(Vvar__22043)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22040___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22043,Vv__CANONICAL__0)) ) ) ).
fof('$_type_224',axiom,
! [Vvar__225] :
( c_24__type__224___24t(Vvar__225)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__225,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_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_27511',axiom,
! [Vvar__27512] :
( c_24__type__27511___24t(Vvar__27512)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__27512,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27516',axiom,
! [Vvar__27517] :
( c_24__type__27516___24t(Vvar__27517)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__27517,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27524',axiom,
! [Vvar__27525] :
( c_24__type__27524___24t(Vvar__27525)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__27525,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27529',axiom,
! [Vvar__27530] :
( c_24__type__27529___24t(Vvar__27530)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__27530,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_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_31118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31119] :
( c_24__type__31118___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31119)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31119,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31163] :
( c_24__type__31162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31163)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31163,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_31198',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31199] :
( c_24__type__31198___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31199)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__31199,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_31242',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31243] :
( c_24__type__31242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__31243)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__31243,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31256',axiom,
! [Vvar__31257] :
( c_24__type__31256___24t(Vvar__31257)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__31257,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31259',axiom,
! [Vvar__31260] :
( c_24__type__31259___24t(Vvar__31260)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31260,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31271',axiom,
! [Vvar__31272] :
( c_24__type__31271___24t(Vvar__31272)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__31272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31347',axiom,
! [Vvar__31348] :
( c_24__type__31347___24t(Vvar__31348)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__31348,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31996',axiom,
! [Vvar__31997] :
( c_24__type__31996___24t(Vvar__31997)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__31997,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32016',axiom,
! [Vvar__32017] :
( c_24__type__32016___24t(Vvar__32017)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(Vvar__32017,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32019',axiom,
! [Vvar__32020] :
( c_24__type__32019___24t(Vvar__32020)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__32020,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32024',axiom,
! [Vvar__32025] :
( c_24__type__32024___24t(Vvar__32025)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__32025,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32037',axiom,
! [Vvar__32038] :
( c_24__type__32037___24t(Vvar__32038)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22040___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRaxioms_2ebound___24a1(Vv__CANONICAL__0)
=> ( ? [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
& p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) )
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__32041___24a1(Vv__CANONICAL__0),happ(Vvar__32038,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_323',axiom,
! [Vvar__324] :
( c_24__type__323___24t(Vvar__324)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__324,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32497',axiom,
! [Vvar__32498] :
( c_24__type__32497___24t(Vvar__32498)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__32498,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_32757',axiom,
! [Vvar__32758] :
( c_24__type__32757___24t(Vvar__32758)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__399___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__32758,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_33224',axiom,
! [Vvar__33225] :
( c_24__type__33224___24t(Vvar__33225)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__14055___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__13938___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__14067___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__14076___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__33256___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__17)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__33225,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_33256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33257] :
( c_24__type__33256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33257)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__33257,Vv__CANONICAL__3)) ) ) ).
fof('$_type_33358',axiom,
! [Vvar__33359] :
( c_24__type__33358___24t(Vvar__33359)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__33369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__33376___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__33359,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_33362',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33363] :
( c_24__type__33362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33363)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__33363,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33370] :
( c_24__type__33369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33370)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__33370,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_33376',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33377] :
( c_24__type__33376___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33377)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__33377,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_34436',axiom,
! [Vvar__34437] :
( c_24__type__34436___24t(Vvar__34437)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__34437,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34695',axiom,
! [Vvar__34696] :
( c_24__type__34695___24t(Vvar__34696)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__34696,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35250',axiom,
! [Vvar__35251] :
( c_24__type__35250___24t(Vvar__35251)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35251,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35607',axiom,
! [Vvar__35608] :
( c_24__type__35607___24t(Vvar__35608)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__35608,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_36605',axiom,
! [Vvar__36606] :
( c_24__type__36605___24t(Vvar__36606)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36610___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__36606,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36610',axiom,
! [Vv__CANONICAL__0,Vvar__36611] :
( c_24__type__36610___24t(Vv__CANONICAL__0,Vvar__36611)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__36611,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_36732',axiom,
! [Vvar__36733] :
( c_24__type__36732___24t(Vvar__36733)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__13636___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__13657___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__14243___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__14746___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__10)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__36733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_376',axiom,
! [Vvar__377] :
( c_24__type__376___24t(Vvar__377)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__377,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_392',axiom,
! [Vvar__393] :
( c_24__type__392___24t(Vvar__393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_399',axiom,
! [Vv__CANONICAL__0,Vvar__400] :
( c_24__type__399___24t(Vv__CANONICAL__0,Vvar__400)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__400,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_401',axiom,
! [Vvar__402] :
( c_24__type__401___24t(Vvar__402)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__402,Vv__CANONICAL__0)) ) ) ).
fof('$_type_410',axiom,
! [Vvar__411] :
( c_24__type__410___24t(Vvar__411)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__97___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__411,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_443',axiom,
! [Vvar__444] :
( c_24__type__443___24t(Vvar__444)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__444,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45',axiom,
! [Vvar__46] :
( c_24__type__45___24t(Vvar__46)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__46,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_471',axiom,
! [Vvar__472] :
( c_24__type__471___24t(Vvar__472)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__472,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_525',axiom,
! [Vvar__526] :
( c_24__type__525___24t(Vvar__526)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__526,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_531',axiom,
! [Vv__CANONICAL__0,Vvar__532] :
( c_24__type__531___24t(Vv__CANONICAL__0,Vvar__532)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__533___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__534___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__532,Vv__CANONICAL__1)) ) ) ).
fof('$_type_57058',axiom,
! [Vvar__57059] :
( c_24__type__57058___24t(Vvar__57059)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__57059,Vv__CANONICAL__0)) ) ) ).
fof('$_type_57068',axiom,
! [Vvar__57069] :
( c_24__type__57068___24t(Vvar__57069)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__57069,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_57106',axiom,
! [Vvar__57107] :
( c_24__type__57106___24t(Vvar__57107)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,happ(happ(Vvar__57107,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57114',axiom,
! [Vvar__57115] :
( c_24__type__57114___24t(Vvar__57115)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__57115,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_58002',axiom,
! [Vvar__58003] :
( c_24__type__58002___24t(Vvar__58003)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__97___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__58008___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__58020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__58003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_58008',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58009] :
( c_24__type__58008___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58009)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__58009,Vv__CANONICAL__2)) ) ) ).
fof('$_type_58020',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__58021] :
( c_24__type__58020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__58021)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(Vvar__58021,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).
fof('$_type_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('$_type_59300',axiom,
! [Vvar__59301] :
( c_24__type__59300___24t(Vvar__59301)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__59301,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_59305',axiom,
! [Vvar__59306] :
( c_24__type__59305___24t(Vvar__59306)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__59306,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_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('$_type_59741',axiom,
! [Vvar__59742] :
( c_24__type__59741___24t(Vvar__59742)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__59743___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__59742,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_59784',axiom,
! [Vvar__59785] :
( c_24__type__59784___24t(Vvar__59785)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__59785,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60011',axiom,
! [Vvar__60012] :
( c_24__type__60011___24t(Vvar__60012)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( Vv__CANONICAL__0 != Vv__CANONICAL__1
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__60012,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_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_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('$_type_64778',axiom,
! [Vvar__64779] :
( c_24__type__64778___24t(Vvar__64779)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__64779,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64781',axiom,
! [Vvar__64782] :
( c_24__type__64781___24t(Vvar__64782)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__64782,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64786',axiom,
! [Vvar__64787] :
( c_24__type__64786___24t(Vvar__64787)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__64787,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_64789',axiom,
! [Vvar__64790] :
( c_24__type__64789___24t(Vvar__64790)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__64790,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64792',axiom,
! [Vvar__64793] :
( c_24__type__64792___24t(Vvar__64793)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__64793,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64795',axiom,
! [Vvar__64796] :
( c_24__type__64795___24t(Vvar__64796)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__64796,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64800',axiom,
! [Vvar__64801] :
( c_24__type__64800___24t(Vvar__64801)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__64801,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_64803',axiom,
! [Vvar__64804] :
( c_24__type__64803___24t(Vvar__64804)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__64804,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64811',axiom,
! [Vvar__64812] :
( c_24__type__64811___24t(Vvar__64812)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__64812,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_64815',axiom,
! [Vvar__64816] :
( c_24__type__64815___24t(Vvar__64816)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__64817___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__64816,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_64826',axiom,
! [Vvar__64827] :
( c_24__type__64826___24t(Vvar__64827)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eReals_2eRIneq_2eposreal___24t(happ(Vvar__64827,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_64831',axiom,
! [Vvar__64832] :
( c_24__type__64831___24t(Vvar__64832)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__64832,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65004',axiom,
! [Vvar__65005] :
( c_24__type__65004___24t(Vvar__65005)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__65005,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65010',axiom,
! [Vvar__65011] :
( c_24__type__65010___24t(Vvar__65011)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22040___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__65011,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_65044',axiom,
! [Vv__CANONICAL__0,Vvar__65045] :
( c_24__type__65044___24t(Vv__CANONICAL__0,Vvar__65045)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__65045,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_65086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__65087] :
( c_24__type__65086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__65087)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__65087,Vv__CANONICAL__2)) ) ) ).
fof('$_type_65090',axiom,
! [Vvar__65091] :
( c_24__type__65090___24t(Vvar__65091)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__59528___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__65091,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_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('$_type_65161',axiom,
! [Vvar__65162] :
( c_24__type__65161___24t(Vvar__65162)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__65162,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_65565',axiom,
! [Vvar__65566] :
( c_24__type__65565___24t(Vvar__65566)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__65566,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_65680',axiom,
! [Vvar__65681] :
( c_24__type__65680___24t(Vvar__65681)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__1))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(Vv__CANONICAL__0,Vv__CANONICAL__3))) )
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__13167___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__13172___24a1(Vv__CANONICAL__0),happ(happ(Vvar__65681,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_65716',axiom,
! [Vvar__65717] :
( c_24__type__65716___24t(Vvar__65717)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__1))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> happ(Vv__CANONICAL__0,Vv__CANONICAL__3) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__13167___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__13172___24a1(Vv__CANONICAL__0),happ(happ(Vvar__65717,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_65856',axiom,
! [Vvar__65857] :
( c_24__type__65856___24t(Vvar__65857)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12714___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__13172___24a1(Vv__CANONICAL__0),happ(Vvar__65857,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_65878',axiom,
! [Vvar__65879] :
( c_24__type__65878___24t(Vvar__65879)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__65879,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65880',axiom,
! [Vvar__65881] :
( c_24__type__65880___24t(Vvar__65881)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__65881,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65891',axiom,
! [Vvar__65892] :
( c_24__type__65891___24t(Vvar__65892)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__65892,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_65906',axiom,
! [Vvar__65907] :
( c_24__type__65906___24t(Vvar__65907)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eid,Vv__CANONICAL__0,happ(Vvar__65907,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65972',axiom,
! [Vvar__65973] :
( c_24__type__65972___24t(Vvar__65973)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__65973,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_65977',axiom,
! [Vvar__65978] :
( c_24__type__65977___24t(Vvar__65978)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__65978,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_65985',axiom,
! [Vvar__65986] :
( c_24__type__65985___24t(Vvar__65986)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__65986,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_66032',axiom,
! [Vvar__66033] :
( c_24__type__66032___24t(Vvar__66033)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__66033,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_66072',axiom,
! [Vvar__66073] :
( c_24__type__66072___24t(Vvar__66073)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(happ(Vvar__66073,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_66074',axiom,
! [Vvar__66075] :
( c_24__type__66074___24t(Vvar__66075)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(Vvar__66075,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66077',axiom,
! [Vvar__66078] :
( c_24__type__66077___24t(Vvar__66078)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(Vvar__66078,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66085',axiom,
! [Vvar__66086] :
( c_24__type__66085___24t(Vvar__66086)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__66086,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_66116',axiom,
! [Vvar__66117] :
( c_24__type__66116___24t(Vvar__66117)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__66117,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_66151',axiom,
! [Vvar__66152] :
( c_24__type__66151___24t(Vvar__66152)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__66152,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66243',axiom,
! [Vvar__66244] :
( c_24__type__66243___24t(Vvar__66244)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__66244,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66267',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66268] :
( c_24__type__66267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66268)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__66268,Vv__CANONICAL__2)) ) ) ).
fof('$_type_66273',axiom,
! [Vvar__66274] :
( c_24__type__66273___24t(Vvar__66274)
<=> ! [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] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__66274,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_66278',axiom,
! [Vvar__66279] :
( c_24__type__66278___24t(Vvar__66279)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__66279,Vv__CANONICAL__0)) ) ) ).
fof('$_type_68667',axiom,
! [Vvar__68668] :
( c_24__type__68667___24t(Vvar__68668)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__68668,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_68762',axiom,
! [Vvar__68763] :
( c_24__type__68762___24t(Vvar__68763)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__68763,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_68801',axiom,
! [Vvar__68802] :
( c_24__type__68801___24t(Vvar__68802)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),happ(Vvar__68802,Vv__CANONICAL__0)) ) ) ).
fof('$_type_69019',axiom,
! [Vvar__69020] :
( c_24__type__69019___24t(Vvar__69020)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__69021___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__69020,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_71153',axiom,
! [Vvar__71154] :
( c_24__type__71153___24t(Vvar__71154)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__71154,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_74',axiom,
! [Vvar__75] :
( c_24__type__74___24t(Vvar__75)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__75,Vv__CANONICAL__0)) ) ) ).
fof('$_type_75239',axiom,
! [Vvar__75240] :
( c_24__type__75239___24t(Vvar__75240)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75243___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__75247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__75240,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_75243',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75244] :
( c_24__type__75243___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75244)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__1,happ(Vvar__75244,Vv__CANONICAL__2)) ) ) ).
fof('$_type_75247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75248] :
( c_24__type__75247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75248)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__75248,Vv__CANONICAL__2)) ) ) ).
fof('$_type_75256',axiom,
! [Vvar__75257] :
( c_24__type__75256___24t(Vvar__75257)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22040___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__75257,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_77716',axiom,
! [Vv__CANONICAL__0,Vvar__77717] :
( c_24__type__77716___24t(Vv__CANONICAL__0,Vvar__77717)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__77717,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_77723',axiom,
! [Vvar__77724] :
( c_24__type__77723___24t(Vvar__77724)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__77724,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_77817',axiom,
! [Vvar__77818] :
( c_24__type__77817___24t(Vvar__77818)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(Vvar__77818,Vv__CANONICAL__0)) ) ) ).
fof('$_type_78426',axiom,
! [Vvar__78427] :
( c_24__type__78426___24t(Vvar__78427)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__78427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_78459',axiom,
! [Vvar__78460] :
( c_24__type__78459___24t(Vvar__78460)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13871___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ( happ(Vv__CANONICAL__1,Vv__CANONICAL__2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2ediv__fct___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__78460,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_80195',axiom,
! [Vvar__80196] :
( c_24__type__80195___24t(Vvar__80196)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__13871___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__78503___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__80196,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ).
fof('$_type_80536',axiom,
! [Vvar__80537] :
( c_24__type__80536___24t(Vvar__80537)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__0))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__65958___24a1(Vv__CANONICAL__0),happ(Vvar__80537,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('$_type_948',axiom,
! [Vvar__949] :
( c_24__type__948___24t(Vvar__949)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__950___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__951___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__949,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_956',axiom,
! [Vvar__957] :
( c_24__type__956___24t(Vvar__957)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__957,Vv__CANONICAL__0)) ) ) ).
fof('$_type_97',axiom,
! [Vv__CANONICAL__0,Vvar__98] :
( c_24__type__97___24t(Vv__CANONICAL__0,Vvar__98)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__98,Vv__CANONICAL__1)) ) ) ).
fof('$_typeof_ArithCompl.R_p4',axiom,
c_24__type__61___24t(cArithCompl_2eR__p4) ).
fof('$_typeof_ArithCompl.distinct_parity',axiom,
c_24__type__61___24t(cArithCompl_2edistinct__parity) ).
fof('$_typeof_ArithCompl.frac',axiom,
c_24__type__122327___24t(cArithCompl_2efrac) ).
fof('$_typeof_ArithCompl.rel_prime_dec',axiom,
c_24__type__17148___24t(cArithCompl_2erel__prime__dec) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__13209___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__13342___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__13253___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__13209___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__13189___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__35250___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_typeof_Coq.Init.Datatypes.bool',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_typeof_Coq.Init.Datatypes.comparison',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ecomparison) ).
fof('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__13340___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.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.negb',axiom,
c_24__type__13192___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__13335___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__401___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__13189___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__392___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__376___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__13315___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.true',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_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('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__13209___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__13849___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__21994___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__21994___24t(cCoq_2eInit_2ePeano_2egt) ).
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('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__59300___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__59305___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__16386___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__66273___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
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('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__65090___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
c_24__type__58002___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__117___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__33358___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__31271___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__59418___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__13361___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_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('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__34695___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__19157___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__19090___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__31347___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__19160___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_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.mul',axiom,
c_24__type__443___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__66278___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_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.to_nat',axiom,
c_24__type__19222___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__22008___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__22011___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qinv',axiom,
c_24__type__32016___24t(cCoq_2eQArith_2eQArith__base_2eQinv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__21998___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__13861___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__22003___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.QArith.QArith_base.Qpower',axiom,
c_24__type__32024___24t(cCoq_2eQArith_2eQArith__base_2eQpower) ).
fof('$_typeof_Coq.QArith.QArith_base.Qpower_positive',axiom,
c_24__type__32019___24t(cCoq_2eQArith_2eQArith__base_2eQpower__positive) ).
fof('$_typeof_Coq.Reals.Alembert.Alembert_C4',axiom,
c_24__type__65680___24t(cCoq_2eReals_2eAlembert_2eAlembert__C4) ).
fof('$_typeof_Coq.Reals.Alembert.Alembert_C5',axiom,
c_24__type__65716___24t(cCoq_2eReals_2eAlembert_2eAlembert__C5) ).
fof('$_typeof_Coq.Reals.AltSeries.tg_alt',axiom,
c_24__type__13892___24t(cCoq_2eReals_2eAltSeries_2etg__alt) ).
fof('$_typeof_Coq.Reals.PSeries_reg.Boule',axiom,
c_24__type__78426___24t(cCoq_2eReals_2ePSeries__reg_2eBoule) ).
fof('$_typeof_Coq.Reals.PartSum.cv_cauchy_2',axiom,
c_24__type__65856___24t(cCoq_2eReals_2ePartSum_2ecv__cauchy__2) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_dec',axiom,
c_24__type__64815___24t(cCoq_2eReals_2eRIneq_2eRle__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_lt_dec',axiom,
c_24__type__77723___24t(cCoq_2eReals_2eRIneq_2eRle__lt__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.mkposreal',axiom,
c_24__type__64826___24t(cCoq_2eReals_2eRIneq_2emkposreal) ).
fof('$_typeof_Coq.Reals.RIneq.pos',axiom,
c_24__type__64831___24t(cCoq_2eReals_2eRIneq_2epos) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.R_Ifp.Int_part',axiom,
c_24__type__65004___24t(cCoq_2eReals_2eR__Ifp_2eInt__part) ).
fof('$_typeof_Coq.Reals.R_Ifp.frac_part',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eR__Ifp_2efrac__part) ).
fof('$_typeof_Coq.Reals.R_sqrt.sqrt',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eR__sqrt_2esqrt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.comp',axiom,
c_24__type__22019___24t(cCoq_2eReals_2eRanalysis1_2ecomp) ).
fof('$_typeof_Coq.Reals.Ranalysis1.continuity',axiom,
c_24__type__66151___24t(cCoq_2eReals_2eRanalysis1_2econtinuity) ).
fof('$_typeof_Coq.Reals.Ranalysis1.continuity_pt',axiom,
c_24__type__65891___24t(cCoq_2eReals_2eRanalysis1_2econtinuity__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_id',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRanalysis1_2eid,cCoq_2eReals_2eRanalysis1_2ederivable__id) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt',axiom,
c_24__type__22035___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_abs',axiom,
c_24__type__22029___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_const',axiom,
c_24__type__57106___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__const) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_id',axiom,
c_24__type__65906___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__id) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_lim',axiom,
c_24__type__22029___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derive_pt',axiom,
c_24__type__57068___24t(cCoq_2eReals_2eRanalysis1_2ederive__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.div_fct',axiom,
c_24__type__22019___24t(cCoq_2eReals_2eRanalysis1_2ediv__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.fct_cte',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRanalysis1_2efct__cte) ).
fof('$_typeof_Coq.Reals.Ranalysis1.id',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRanalysis1_2eid) ).
fof('$_typeof_Coq.Reals.Ranalysis1.minus_fct',axiom,
c_24__type__22019___24t(cCoq_2eReals_2eRanalysis1_2eminus__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.mult_fct',axiom,
c_24__type__22019___24t(cCoq_2eReals_2eRanalysis1_2emult__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.no_cond',axiom,
c_24__type__22040___24t(cCoq_2eReals_2eRanalysis1_2eno__cond) ).
fof('$_typeof_Coq.Reals.Ranalysis3.derivable_pt_div',axiom,
c_24__type__78459___24t(cCoq_2eReals_2eRanalysis3_2ederivable__pt__div) ).
fof('$_typeof_Coq.Reals.Ratan.Datan_seq',axiom,
c_24__type__31256___24t(cCoq_2eReals_2eRatan_2eDatan__seq) ).
fof('$_typeof_Coq.Reals.Ratan.Ratan_seq',axiom,
c_24__type__31256___24t(cCoq_2eReals_2eRatan_2eRatan__seq) ).
fof('$_typeof_Coq.Reals.Ratan.atan',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRatan_2eatan) ).
fof('$_typeof_Coq.Reals.Ratan.ps_atan_exists_01',axiom,
c_24__type__113415___24t(cCoq_2eReals_2eRatan_2eps__atan__exists__01) ).
fof('$_typeof_Coq.Reals.Ratan.ps_atan_exists_1',axiom,
c_24__type__80536___24t(cCoq_2eReals_2eRatan_2eps__atan__exists__1) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__12714___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Raxioms.bound',axiom,
c_24__type__22042___24t(cCoq_2eReals_2eRaxioms_2ebound) ).
fof('$_typeof_Coq.Reals.Raxioms.completeness',axiom,
c_24__type__32037___24t(cCoq_2eReals_2eRaxioms_2ecompleteness) ).
fof('$_typeof_Coq.Reals.Raxioms.is_lub',axiom,
c_24__type__22038___24t(cCoq_2eReals_2eRaxioms_2eis__lub) ).
fof('$_typeof_Coq.Reals.Raxioms.is_upper_bound',axiom,
c_24__type__22038___24t(cCoq_2eReals_2eRaxioms_2eis__upper__bound) ).
fof('$_typeof_Coq.Reals.Raxioms.total_order_T',axiom,
c_24__type__69019___24t(cCoq_2eReals_2eRaxioms_2etotal__order__T) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rabs',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRbasic__fun_2eRabs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rcase_abs',axiom,
c_24__type__68801___24t(cCoq_2eReals_2eRbasic__fun_2eRcase__abs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmax',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRbasic__fun_2eRmax) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmin',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRbasic__fun_2eRmin) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IPR',axiom,
c_24__type__13879___24t(cCoq_2eReals_2eRdefinitions_2eIPR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IPR_2',axiom,
c_24__type__13879___24t(cCoq_2eReals_2eRdefinitions_2eIPR__2) ).
fof('$_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.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__13874___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__13874___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__13874___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__13874___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__65004___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rderiv.D_x',axiom,
c_24__type__65010___24t(cCoq_2eReals_2eRderiv_2eD__x) ).
fof('$_typeof_Coq.Reals.Rfunctions.R_dist',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRfunctions_2eR__dist) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__16816___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.intP',axiom,
c_24__type__77817___24t(cCoq_2eReals_2eRfunctions_2eintP) ).
fof('$_typeof_Coq.Reals.Rfunctions.powerRZ',axiom,
c_24__type__57114___24t(cCoq_2eReals_2eRfunctions_2epowerRZ) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_f_R0',axiom,
c_24__type__13892___24t(cCoq_2eReals_2eRfunctions_2esum__f__R0) ).
fof('$_typeof_Coq.Reals.Rlimit.Base',axiom,
c_24__type__66243___24t(cCoq_2eReals_2eRlimit_2eBase) ).
fof('$_typeof_Coq.Reals.Rlimit.Build_Metric_Space',axiom,
c_24__type__118486___24t(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space) ).
fof('$_typeof_Coq.Reals.Rlimit.Metric_Space',axiom,
cType___24t(cCoq_2eReals_2eRlimit_2eMetric__Space) ).
fof('$_typeof_Coq.Reals.Rlimit.R_met',axiom,
cCoq_2eReals_2eRlimit_2eMetric__Space___24t(cCoq_2eReals_2eRlimit_2eR__met) ).
fof('$_typeof_Coq.Reals.Rlimit.dist',axiom,
c_24__type__68762___24t(cCoq_2eReals_2eRlimit_2edist) ).
fof('$_typeof_Coq.Reals.Rlimit.limit1_in',axiom,
c_24__type__75256___24t(cCoq_2eReals_2eRlimit_2elimit1__in) ).
fof('$_typeof_Coq.Reals.Rlimit.limit_in',axiom,
c_24__type__75239___24t(cCoq_2eReals_2eRlimit_2elimit__in) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__31256___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Reals.Rpower.Rpower',axiom,
c_24__type__13869___24t(cCoq_2eReals_2eRpower_2eRpower) ).
fof('$_typeof_Coq.Reals.Rpower.ln',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRpower_2eln) ).
fof('$_typeof_Coq.Reals.Rpower.ln_exists1',axiom,
c_24__type__114864___24t(cCoq_2eReals_2eRpower_2eln__exists1) ).
fof('$_typeof_Coq.Reals.Rseries.EUn',axiom,
c_24__type__16378___24t(cCoq_2eReals_2eRseries_2eEUn) ).
fof('$_typeof_Coq.Reals.Rseries.Un_cv',axiom,
c_24__type__16378___24t(cCoq_2eReals_2eRseries_2eUn__cv) ).
fof('$_typeof_Coq.Reals.Rseries.Un_growing',axiom,
c_24__type__31259___24t(cCoq_2eReals_2eRseries_2eUn__growing) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.IVT_cor',axiom,
c_24__type__80195___24t(cCoq_2eReals_2eRsqrt__def_2eIVT__cor) ).
fof('$_typeof_Coq.Reals.Rtrigo1.PI',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRtrigo1_2ePI) ).
fof('$_typeof_Coq.Reals.Rtrigo1.tan',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRtrigo1_2etan) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.cos',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRtrigo__def_2ecos) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.exp',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRtrigo__def_2eexp) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.sin',axiom,
c_24__type__13871___24t(cCoq_2eReals_2eRtrigo__def_2esin) ).
fof('$_typeof_Coq.Reals.SeqProp.Un_decreasing',axiom,
c_24__type__31259___24t(cCoq_2eReals_2eSeqProp_2eUn__decreasing) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__401___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__19818___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq_dec',axiom,
c_24__type__948___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec) ).
fof('$_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.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.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('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_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.div_eucl',axiom,
c_24__type__19459___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.land',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eland) ).
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('$_typeof_Coq.ZArith.BinIntDef.Z.lor',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elor) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
c_24__type__525___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.lxor',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elxor) ).
fof('$_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_div_eucl',axiom,
c_24__type__19377___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl) ).
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('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_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('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__45___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_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_nat',axiom,
c_24__type__19307___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.Wf_Z.natlike_rec',axiom,
c_24__type__16412___24t(cCoq_2eZArith_2eWf__Z_2enatlike__rec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_le_dec',axiom,
c_24__type__59741___24t(cCoq_2eZArith_2eZArith__dec_2eZ__le__dec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_le_gt_dec',axiom,
c_24__type__224___24t(cCoq_2eZArith_2eZArith__dec_2eZ__le__gt__dec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_lt_dec',axiom,
c_24__type__16442___24t(cCoq_2eZArith_2eZArith__dec_2eZ__lt__dec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_lt_ge_dec',axiom,
c_24__type__59784___24t(cCoq_2eZArith_2eZArith__dec_2eZ__lt__ge__dec) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.not_Zeq_inf',axiom,
c_24__type__60011___24t(cCoq_2eZArith_2eZArith__dec_2enot__Zeq__inf) ).
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.Znumtheory.rel_prime',axiom,
c_24__type__61___24t(cCoq_2eZArith_2eZnumtheory_2erel__prime) ).
fof('$_typeof_Coq.ZArith.Znumtheory.rel_prime_dec',axiom,
c_24__type__17148___24t(cCoq_2eZArith_2eZnumtheory_2erel__prime__dec) ).
fof('$_typeof_Coq.ZArith.Zpower.two_p',axiom,
c_24__type__30___24t(cCoq_2eZArith_2eZpower_2etwo__p) ).
fof('$_typeof_Coq.ZArith.Zpower.two_power_pos',axiom,
c_24__type__25___24t(cCoq_2eZArith_2eZpower_2etwo__power__pos) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__64781___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__64786___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__64778___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEmul',axiom,
c_24__type__64786___24t(cCoq_2emicromega_2eEnvRing_2ePEmul) ).
fof('$_typeof_Coq.micromega.EnvRing.PEopp',axiom,
c_24__type__64789___24t(cCoq_2emicromega_2eEnvRing_2ePEopp) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__64786___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__13592___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.QMicromega.QWitness',axiom,
cType___24t(cCoq_2emicromega_2eQMicromega_2eQWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
c_24__type__65880___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__65878___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.RingMicromega.Build_Formula',axiom,
c_24__type__65985___24t(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__65977___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__68667___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__65972___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__65977___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__65565___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__65161___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.I',axiom,
c_24__type__66072___24t(cCoq_2emicromega_2eTauto_2eI) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__66032___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.VarMap.Branch',axiom,
c_24__type__66085___24t(cCoq_2emicromega_2eVarMap_2eBranch) ).
fof('$_typeof_Coq.micromega.VarMap.Elt',axiom,
c_24__type__66077___24t(cCoq_2emicromega_2eVarMap_2eElt) ).
fof('$_typeof_Coq.micromega.VarMap.Empty',axiom,
c_24__type__66074___24t(cCoq_2emicromega_2eVarMap_2eEmpty) ).
fof('$_typeof_Coq.micromega.VarMap.find',axiom,
c_24__type__66116___24t(cCoq_2emicromega_2eVarMap_2efind) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__401___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.Zeval_op1',axiom,
c_24__type__34436___24t(cCoq_2emicromega_2eZMicromega_2eZeval__op1) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__64795___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__64800___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__64792___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__64800___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__20576___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__64803___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__64800___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__64803___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__71153___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__64800___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__36605___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__36732___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fnorm',axiom,
c_24__type__35607___24t(cCoq_2esetoid__ring_2eField__theory_2eFnorm) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__20866___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__20647___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__20627___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__64811___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__20627___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__13754___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__31996___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__14506___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__14511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__14503___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__32497___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__14511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__14520___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__27529___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__14511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__27524___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__27511___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__14254___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__27516___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__401___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__33224___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__32757___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__14906___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__14728___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__14961___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__14940___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('ArithCompl.Rcross_prod',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__c)
=> ! [V3__d] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__d)
=> ( V1__b != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V3__d != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__a,V1__b) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V2__c,V3__d)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__a,V3__d) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__b,V2__c) ) ) ) ) ) ) ) ).
fof('ArithCompl.Zmult_eq_reg_l',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ! [V1__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z1)
=> ! [V2__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z2)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V1__z1) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V2__z2)
=> ( V0__z != cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__z1 = V2__z2 ) ) ) ) ) ).
fof('ArithCompl.Zmult_neq_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
& V1__b != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('ArithCompl.divide_2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__z))
=> ( V0__z != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__z != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__z,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))
=> V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ) ) ).
fof('ArithCompl.frac_eq',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)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cArithCompl_2efrac___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V2__c)) = cArithCompl_2efrac___24a2(V3__d,V2__c)
=> V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V3__d) ) ) ) ) ) ) ) ).
fof('ArithCompl.not_divide1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) ) ) ) ) ) ).
fof('ArithCompl.not_rel_prime1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__x,V1__y))
=> ? [V3__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__d)
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__x,V1__y,V3__d)
& V3__d != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
& V3__d != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ).
fof('ArithCompl.not_rel_prime2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__d] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__d)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__d,V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__d,V1__y)
=> ( V2__d != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V2__d != cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ~ p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__x,V1__y)) ) ) ) ) ) ) ) ).
fof('ArithCompl.sqr_inv',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_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__a),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__b))),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__a),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__b))))) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('ArithCompl.sqr_lt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a))) ) ) ) ).
fof('ArithCompl.sqr_spos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( V0__z != cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z,V0__z),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('ArithCompl.sqr_sum',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,V1__b)) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.Arith.Compare_dec.dec_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Lt.neq_0_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eInit_2eDatatypes_2eO != V0__n
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ) ).
fof('Coq.Arith.Max.le_max_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Max.le_max_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.Peano_dec.dec_eq_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__74358___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Init.Datatypes.CompOpp_iff',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
=> ! [V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__c) = V1__c_27
<=> V0__c = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V1__c_27) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__19822___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__77716___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__65103___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__13363___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.dec_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__35312___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Numbers.BinNums.Z_ind',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V2__p))) )
=> ( ! [V3__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__p))) )
=> ! [V4__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__z)
=> p(happ(V0__P,V4__z)) ) ) ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__13175___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(c_24__prop__19230___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x),cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.Reals.ArithProp.tech8',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__i)) ) ) ).
fof('Coq.Reals.DiscrR.Rlt_R0_R2',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('Coq.Reals.PartSum.cauchy_abs',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ( cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(c_24__lam__65845___24a1(V0__An))
=> cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(V0__An) ) ) ).
fof('Coq.Reals.PartSum.cv_cauchy_1',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1___24Anonymous] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__31864___24a1(V0__An),V1___24Anonymous)
=> cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(V0__An) ) ) ).
fof('Coq.Reals.PartSum.sum_eq',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__12714___24t(V1__Bn)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ! [V3__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__i)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V3__i,V2__N)
=> happ(V0__An,V3__i) = happ(V1__Bn,V3__i) ) )
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V2__N) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__Bn,V2__N) ) ) ) ) ).
fof('Coq.Reals.PartSum.sum_eq_R0',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V1__N)
=> happ(V0__An,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) )
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.PartSum.tech1',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V1__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__An,V2__n))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N))) ) ) ) ).
fof('Coq.Reals.PartSum.tech2',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__n))
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V2__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__m),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__32008___24a2(V0__An,V1__m),cCoq_2eInit_2eNat_2esub___24a2(V2__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))) ) ) ) ) ).
fof('Coq.Reals.PartSum.tech3',axiom,
! [V0__k] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__k)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( V0__k != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__32010___24a1(V0__k),V1__N) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__k,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__N))),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__k)) ) ) ) ).
fof('Coq.Reals.PartSum.tech5',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__N)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N),happ(V0__An,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__N))) ) ) ).
fof('Coq.Reals.PartSum.tech6',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1__k] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__k)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__k))
=> ( ! [V4__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__i)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__An,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__i)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__k,happ(V0__An,V4__i)))) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V2__N),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__An,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__32010___24a1(V1__k),V2__N)))) ) ) ) ) ) ).
fof('Coq.Reals.PartSum.tech7',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 != V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1) != cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.INR_IZR_INZ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.Reals.RIneq.INR_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.INR_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
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.IZR_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_2ege___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_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(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_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_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_neq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 != V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.RField_field_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__fe1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__fe1)
=> ! [V4__fe2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__fe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V2__lpe)
=> ! [V6__lmp] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V6__lmp)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) = V6__lmp
=> ! [V8__nfe1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,V3__fe1) = V8__nfe1
=> ! [V10__nfe2] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,V4__fe2) = V10__nfe2
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,V6__lmp,cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2))),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,V6__lmp,cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1)))) = cCoq_2eInit_2eDatatypes_2etrue
=> ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2)))
=> cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eReals_2eRdefinitions_2eRdiv,cCoq_2eReals_2eRdefinitions_2eRinv,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V3__fe1) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eReals_2eRdefinitions_2eRdiv,cCoq_2eReals_2eRdefinitions_2eRinv,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V4__fe2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.RField_lemma5',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__l)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),V1__l1)
=> ( ! [V2__lock] :
( c_24__type__57058___24t(V2__lock)
=> ( V2__lock = cCoq_2esetoid__ring_2eField__theory_2ePCond___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V0__l)
=> p(happ(V2__lock,cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem),V1__l1,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ))))) ) )
=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V0__l,V1__l1) ) ) ) ).
fof('Coq.Reals.RIneq.RField_ring_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__pe1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__pe1)
=> ! [V4__pe2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__pe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V2__lpe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__32026___24a1(V2__lpe),V3__pe1),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__32026___24a1(V2__lpe),V4__pe2)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V3__pe1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V4__pe2) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rdichotomy',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != V1__r2
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Req_dec',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
| V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Req_le_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_0_lt_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Rinv_1',axiom,
cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.RIneq.Rinv_1_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = V0__r ) ) ).
fof('Coq.Reals.RIneq.Rinv_l_sym',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r),V0__r) ) ) ).
fof('Coq.Reals.RIneq.Rinv_le_contravar',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_mult_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_neq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_simpl_m',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1)) = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_sym',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) ) ) ).
fof('Coq.Reals.RIneq.Rle_0_sqr',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r))) ) ).
fof('Coq.Reals.RIneq.Rle_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_0_plus_1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_refl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rle_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_0_1',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.Reals.RIneq.Rlt_0_sqr',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Rlt_dichotomy_converse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) )
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_gt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rlt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_le_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rminus_diag_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_uniq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_uniq_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_eq_contra',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_not_eq_right',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_1_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = V0__r ) ).
fof('Coq.Reals.RIneq.Rmult_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V1__r1 = V2__r2 ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_ge_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral_contrapositive',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral_contrapositive_currified',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_0_lt_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r3))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r3))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_pos',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_reg_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_reg_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_minus_distr_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V2__r3)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3)) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_opp_opp',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) ) ) ).
fof('Coq.Reals.RIneq.Rmult_plus_distr_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_le_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0',axiom,
cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.Ropp_0_ge_le_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0_gt_lt_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0_le_ge_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_gt_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = V0__r ) ).
fof('Coq.Reals.RIneq.Ropp_le_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_le_ge_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_lt_gt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_minus_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.RIneq.Ropp_mult_distr_l_reverse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),V1__r2) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Ropp_mult_distr_r_reverse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Ropp_plus_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Rplus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_le_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_le_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_le_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_ne',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r
& cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = V0__r ) ) ).
fof('Coq.Reals.RIneq.Rplus_opp_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rtotal_order',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.S_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.Reals.RIneq.Z_R_minus',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Reals.RIneq.cond_pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2epos___24a1(V0__p))) ) ).
fof('Coq.Reals.RIneq.double',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V0__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V0__r1) ) ).
fof('Coq.Reals.RIneq.double_var',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> V0__r1 = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ).
fof('Coq.Reals.RIneq.eq_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.eq_IZR_R0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.Reals.RIneq.le_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(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_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m))) ) ) ) ).
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)
=> ( p(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.le_IZR_R1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ).
fof('Coq.Reals.RIneq.lt_0_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n))) ) ) ).
fof('Coq.Reals.RIneq.lt_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ).
fof('Coq.Reals.RIneq.lt_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.lt_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Reals.RIneq.mult_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.mult_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.not_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.one_IZR_lt1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.Reals.RIneq.one_IZR_r_R1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__n)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__n),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V2__m)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V2__m),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) )
=> V1__n = V2__m ) ) ) ) ) ).
fof('Coq.Reals.RIneq.plus_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.plus_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_2eadd___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.pos_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n))) ) ).
fof('Coq.Reals.RIneq.single_z_r_R1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__n)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__n),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V2__m)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V2__m),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))
=> V1__n = V2__m ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.tech_Rplus',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__s] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__s)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__s))
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__s) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.tech_single_z_r_R1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__n)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__n),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))
=> ( ? [V4__s] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__s)
& V4__s != V1__n
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V4__s)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V4__s),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) )
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Reals.R_Ifp.base_fp',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('Coq.Reals.R_Ifp.plus_Int_part1',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r1),cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V1__r2)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V0__r1),cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V1__r2)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.Reals.R_Ifp.plus_frac_part1',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r1),cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V1__r2)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r1),cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V1__r2)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ).
fof('Coq.Reals.R_Ifp.tech_up',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))
=> V1__z = cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r) ) ) ) ) ).
fof('Coq.Reals.R_Ifp.up_tech',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__z,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__z,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_1',axiom,
cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.R_sqr.Rsqr_incr_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incrst_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incrst_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_inj',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)
=> V0__x = V1__y ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) ) ).
fof('Coq.Reals.R_sqr.Rsqr_pos_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x))) ) ) ).
fof('Coq.Reals.R_sqrt.Rsqr_sqrt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_1',axiom,
cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.R_sqrt.sqrt_Rsqr',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_def',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_eq_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__x = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_le_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_less',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),V0__x)) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_less_alt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),V0__x)) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_lt_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x))) ) ).
fof('Coq.Reals.R_sqrt.sqrt_positivity',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x))) ) ) ).
fof('Coq.Reals.R_sqrt.sqrt_sqrt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x)) = V0__x ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_continuous',axiom,
! [V0__f] :
( c_24__type__13871___24t(V0__f)
=> ! [V1___24Anonymous] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V0__f,V1___24Anonymous)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_continuous_pt',axiom,
! [V0__f] :
( c_24__type__13871___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2___24Anonymous] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V2___24Anonymous)
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V1__x) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_pt_lim_id',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRanalysis1_2eid,V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_eq_0',axiom,
! [V0__f] :
( c_24__type__13871___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l)
=> ! [V3__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V3__pr)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V3__pr) = V2__l ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.pr_nu',axiom,
! [V0__f] :
( c_24__type__13871___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V2__pr1)
=> ! [V3__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V3__pr2)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr1) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V3__pr2) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.pr_nu_var2_interv',axiom,
! [V0__f] :
( c_24__type__13871___24t(V0__f)
=> ! [V1__g] :
( c_24__type__13871___24t(V1__g)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ! [V3__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__ub)
=> ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ! [V5__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V4__x,V5__pr1)
=> ! [V6__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__g,V4__x,V6__pr2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,V3__ub)) )
=> ( ! [V9__h] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__h)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V9__h))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V9__h,V3__ub)) )
=> happ(V0__f,V9__h) = happ(V1__g,V9__h) ) )
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V4__x,V5__pr1) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V4__x,V6__pr2) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.Datan_seq_increasing',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V2__n,cCoq_2eInit_2eDatatypes_2eO)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V0__x,V2__n),cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V1__y,V2__n))) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.Ratan_seq_converging',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.Reals.Ratan.Ratan_seq_decreasing',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V0__x)) ) ) ).
fof('Coq.Reals.Ratan.Ropp_div',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x),V1__y) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.Reals.Ratan.Un_cv_ext',axiom,
! [V0__un] :
( c_24__type__12714___24t(V0__un)
=> ! [V1__vn] :
( c_24__type__12714___24t(V1__vn)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__un,V2__n) = happ(V1__vn,V2__n) )
=> ! [V3__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__un,V3__l)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(V1__vn,V3__l) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.pow_lt_1_compat',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V1__n))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.ps_atanSeq_continuity_pt_1',axiom,
! [V0__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__N)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(c_24__lam__68662___24a1(V0__N),V1__x) ) ) ) ) ).
fof('Coq.Reals.Ratan.tan_is_inj',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo1_2ePI),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo1_2ePI),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),V1__y))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__y,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) )
=> ( cCoq_2eReals_2eRtrigo1_2etan___24a1(V0__x) = cCoq_2eReals_2eRtrigo1_2etan___24a1(V1__y)
=> V0__x = V1__y ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.R1_neq_R0',axiom,
cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Raxioms.Rinv_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.Reals.Raxioms.Rlt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
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.Raxioms.Rmult_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_lt_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_plus_distr_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__r3)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = V0__r ) ).
fof('Coq.Reals.Raxioms.Rplus_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_lt_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_opp_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Raxioms.archimed',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.RRle_abs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_R0',axiom,
cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Rabsolu',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Rinv',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Ropp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_left',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_mult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_no_R0',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos_eq',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) = V0__x ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_right',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_triang',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__a,V1__b)),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__a),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__b)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_l',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y),V0__x)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_r',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y),V1__y)) ) ) ).
fof('Coq.Reals.Rfunctions.INR_fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rfunctions.R_dist_eq',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rfunctions.Rinv_pow',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n)) = cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x),V1__n) ) ) ) ).
fof('Coq.Reals.Rfunctions.Rle_pow',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__m),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n))) ) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.Rlt_pow',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,V2__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__m))) ) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_1_abs',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_R1_Rle',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__k))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_add',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__m)) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_incr',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V2__n))) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_le',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__a,V1__n))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_ne_zero',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rfunctions.pow_nonzero',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.Rpower.Rle_Rpower',axiom,
! [V0__e] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__e)
=> ! [V1__n] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__e))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__n,V2__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpower_2eRpower___24a2(V0__e,V1__n),cCoq_2eReals_2eRpower_2eRpower___24a2(V0__e,V2__m))) ) ) ) ) ) ).
fof('Coq.Reals.Rpower.exp_ineq1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x),cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x))) ) ) ).
fof('Coq.Reals.Rpower.ln_1',axiom,
cCoq_2eReals_2eRpower_2eln___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rseries.Un_cv_crit_lub',axiom,
! [V0__Un] :
( c_24__type__12714___24t(V0__Un)
=> ( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
=> ! [V2__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l)
=> ( cCoq_2eReals_2eRaxioms_2eis__lub___24a2(cCoq_2eReals_2eRseries_2eEUn___24a1(V0__Un),V2__l)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V2__l) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.PI2_RGT_0',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ).
fof('Coq.Reals.Rtrigo1.PI_RGT_0',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ).
fof('Coq.Reals.Rtrigo1.cos_PI2',axiom,
cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo1.cos_eq_0_2PI_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo1_2ePI)))
=> ( ( V0__x = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
| V0__x = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) )
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_gt_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x))) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) = cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) ) ).
fof('Coq.Reals.Rtrigo1.sin_PI',axiom,
cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRtrigo1_2ePI) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo1.sin_eq_O_2PI_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo1_2ePI)))
=> ( cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__x = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
| V0__x = cCoq_2eReals_2eRtrigo1_2ePI
| V0__x = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo1_2ePI) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_eq_O_2PI_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo1_2ePI)))
=> ( ( V0__x = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
| V0__x = cCoq_2eReals_2eRtrigo1_2ePI
| V0__x = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo1_2ePI) )
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_ge_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x))) ) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_gt_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x))) ) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_lb_gt_0',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo1_2esin__lb___24a1(V0__a))) ) ) ) ).
fof('Coq.Reals.Rtrigo_alt.pre_sin_bound',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V0__a,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__n),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__a)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__a),cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V0__a,cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cCoq_2eInit_2eNat_2eadd___24a2(V1__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo_calc.sin_lb_ge_0',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo1_2esin__lb___24a1(V0__a))) ) ) ) ).
fof('Coq.Reals.Rtrigo_def.exp_0',axiom,
cCoq_2eReals_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.Rtrigo_def.pow_i',axiom,
! [V0__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__i)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__i))
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__i) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rtrigo_def.sin_0',axiom,
cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.SeqProp.tech13',axiom,
! [V0__An] :
( c_24__type__12714___24t(V0__An)
=> ! [V1__k] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__k)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__k))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__k,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__114204___24a1(V0__An),V1__k)
=> ? [V4__k0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__k0)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__k,V4__k0))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__k0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
& ? [V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
& ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V5__N,V6__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(happ(V0__An,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n)),happ(V0__An,V6__n))),V4__k0)) ) ) ) ) ) ) ) ) ).
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.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.mul_div_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)),V0__a)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.mod_bound_pos',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b),V1__b)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_NZDiv.div_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_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.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_OrderTac.Tac.eq_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.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.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_case_strong',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__74,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e),V0__P)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__n))
=> p(happ(V0__P,V1__n)) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n))) )
=> p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__n))) ) ) ) ) ) ).
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_pos',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_2eabs___24a1(V0__n)))
<=> V0__n != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_lt_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_lt_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_lt_mono_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_move_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_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V1__m = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_nonneg_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_nonpos_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_opp_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_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_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_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.bit_log2',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_2etestbit___24a2(V0__a,cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ).
fof('Coq.ZArith.BinInt.Z.bits_inj\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n) ) )
=> V0__a = V1__b ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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.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_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_eucl_eq',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
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419752___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_exact',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__b))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V0__a)) ) ) ) ) ).
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_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_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_same',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ).
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_small_iff',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(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_2elt___24a2(V0__a,V1__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,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_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',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(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)
| V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_mul_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_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_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_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_sym_iff',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.gcd_divide_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b),V0__a) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_divide_r',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b),V1__b) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_eq_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
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.ge_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_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)
=> ( p(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',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gt_lt_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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.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_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))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ind',axiom,
! [V0__A] :
( c_24__type__74___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__74,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(happ(V0__A,V2__n))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,V4__m))
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,V5__m))
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_le_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_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_ngt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.le_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_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_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.log2_add_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V1__b)))) ) ) ) ) ).
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_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_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_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_2eBinIntDef_2eZ_2elog2___24a1(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_spec_alt',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___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_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__a)),V2__r)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__r,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)))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.log2_up_add_le',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinInt_2eZ_2elog2__up___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___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_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_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_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_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_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_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_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_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> V0__n != V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_nge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_strorder',axiom,
cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
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.max_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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_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_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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_divide',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V1__b,V0__a) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___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.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_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = V0__a
<=> ( ( 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(V1__b,V0__a))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ) ).
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.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_eq_1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
| V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_id_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = V1__m
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_neg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__p,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_le_mono_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_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_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_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_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_opp_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_opp',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_pos_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_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_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_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_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V1__m) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__45,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__30,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('Coq.ZArith.BinInt.Z.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.neg_pos_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != 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,V0__n)) ) ) ) ).
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_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.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_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_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_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b))))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b))) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b))))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ) ).
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.pos_div_eucl_bound',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2epositive___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_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V0__a,V1__b))))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V0__a,V1__b)),V1__b)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pos_div_eucl_eq',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2epositive___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))
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419737___24a2(V0__a,V1__b) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pos_sub_spec',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V0__p,V1__q) = c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2419712___24a2(V0__p,V1__q) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_0_l\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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_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_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_1',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),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_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b))) ) ) ) ) ).
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_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_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_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_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_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.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_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.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_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_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.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_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.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_iff',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V0__a,V1__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
| ( 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),V1__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_lt_lin',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_2esqrt___24a1(V0__a),V0__a)) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_nonneg',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__a))) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(c_24__let__2__s__19729___24a1(V0__n),c_24__let__2__s__19729___24a1(V0__n)),V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(c_24__let__2__s__19729___24a1(V0__n)),cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(c_24__let__2__s__19729___24a1(V0__n))))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sqrt_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.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_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.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_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_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_2esub___24a2(V2__p,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V2__p,V0__n))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_move_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) = V2__p
<=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_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_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_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_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.Z.zero_pos_neg',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__74,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e),V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V3__n))
=> ( p(happ(V0__P,V3__n))
& p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V3__n))) ) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__n)
=> p(happ(V0__P,V4__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.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.Zabs.Zabs_ind',axiom,
! [V0__P] :
( c_24__type__74___24t(V0__P)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(happ(V0__P,V1__n)) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n))) )
=> p(happ(V0__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__n))) ) ) ) ) ).
fof('Coq.ZArith.Zabs.Zabs_spec',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_2eBinIntDef_2eZ_2eabs___24a1(V0__x) = V0__x )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) ) ) ) ).
fof('Coq.ZArith.Zabs.Zsgn_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( cCoq_2eNumbers_2eBinNums_2eZ0 = V0__x
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__x != V1__y ) ) ) ).
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.Zcase_sign',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__P] :
( cProp___24t(V1__P)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(V1__P) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(V1__P) )
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(V1__P) )
=> p(V1__P) ) ) ) ) ) ).
fof('Coq.ZArith.Zcomplements.sqr_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(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_ge0',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_2ege___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.Zdiv.Z_div_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_2ege___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b),V0__a)) ) ) ) ) ).
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_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_div_same_full',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ).
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.Zmax.Zmax_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__x,V1__y) = V0__x )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__x,V1__y) = V1__y ) ) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_mul',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
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.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))
<=> p(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.inj_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).
fof('Coq.ZArith.Znat.inj_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_minus2',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.Znat.inj_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.positive_nat_Z',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p)) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p) ) ).
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_Zdiv_lt_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_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),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_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,V0__a)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V1__b,V0__a),V1__b)) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zdivide_bounds',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__a,V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b))) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zgcd_is_gcd',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b)) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_ind',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__g] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__g)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V1__b)
=> ( ! [V6__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__x,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__x,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V6__x,V2__g) ) ) )
=> p(V3__P) ) ) )
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__g)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_intro',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__g] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__g)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V1__b)
=> ( ! [V5__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V2__g) ) ) )
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__g) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.Zmult_one',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_aux_subproof',axiom,
! [V0__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__m)) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_aux_subproof0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__x))
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V2__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__x)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_aux_subproof1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__x))
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x)))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V2__n))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_subproof',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V0__p)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__n)) ) ) ) ).
fof('Coq.ZArith.Znumtheory.prime_dec_subproof0',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V0__p)) )
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V0__p)) ) ) ) ).
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)) )
=> 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.prime_intro',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__p))
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V2__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__n,V0__p)) )
=> p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V2__n,V0__p)) ) )
=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V0__p) ) ) ) ).
fof('Coq.ZArith.Zorder.Zle_0_pos',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.Zorder.Zlt_neg_0',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Zmult_gt_0_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_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_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m))) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_ge_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_2ege___24a2(V0__n,V1__m))
=> 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))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.dec_Zge',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_2ege___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.Zorder.not_Zeq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zmult_le_approx',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V2__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n),V2__p)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m)) ) ) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.Fourier_util.Rle_zero_pos_plus1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))) ) ) ).
fof('Coq.micromega.RMicromega.RTautoChecker_sound',axiom,
! [V0__f] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),V0__f)
=> ! [V1__w] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRMicromega_2eRWitness,V1__w)
=> ( cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V0__f,V1__w) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V3__env] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eReals_2eRdefinitions_2eR,V3__env)
=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V3__env),V0__f) ) ) ) ) ).
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.OMEGA19',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.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.OMEGA5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA7',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.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_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.setoid_ring.Field_theory.F_R',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__13636___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__13657___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__399___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.RealField.RField_ring_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__pe1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__pe1)
=> ! [V4__pe2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__pe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V2__lpe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__13887___24a1(V2__lpe),V3__pe1),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__13887___24a1(V2__lpe),V4__pe2)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V3__pe1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V4__pe2) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.RealField.R_power_theory',axiom,
cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__13636___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__13636___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__13657___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__13636___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__13636___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__13636___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__13657___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__399___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.ZArithRing.Zr_ring_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__pe1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__pe1)
=> ! [V4__pe2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__pe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V1__l,V2__lpe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__16424___24a1(V2__lpe),V3__pe1),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__16424___24a1(V2__lpe),V4__pe2)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V1__l,V3__pe1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V1__l,V4__pe2) ) ) ) ) ) ) ) ).
fof('$adef_$_lam_140_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__140,V_24X1),V_24X2),V_24X3) = c_24__lam__140___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Raxioms.bound_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRaxioms_2ebound,V_24X1))
<=> cCoq_2eReals_2eRaxioms_2ebound___24a1(V_24X1) ) ).
fof('$adef_$_lam_31864_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__31864,V_24X1),V_24X2))
<=> c_24__lam__31864___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_59743_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59743,V_24X1),V_24X2) = c_24__prop__59743___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.id_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2eid,V_24X1) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rlimit.Build_Metric_Space_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space,V_24X1),V_24X2) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEmul_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEmul,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.Reals.Rfunctions.R_dist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eR__dist,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.ZMicromega.Zeval_op1_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eZeval__op1,V_24X1) = cCoq_2emicromega_2eZMicromega_2eZeval__op1___24a1(V_24X1) ).
fof('$adef_$_prop_137_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__137,V_24X1),V_24X2) = c_24__prop__137___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_14_s1_35446_35450_35508_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__14__s1__35446__35450__35508,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s1__35446__35450__35508___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_$_prop_898_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__898,V_24X1),V_24X2) = c_24__prop__898___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Specif.sig_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_6_p_14928_14930_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__14928__14930,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__14928__14930___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.powerRZ_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2epowerRZ,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$19752_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419752,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419752___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('$adef_$_lam_114867_$a1',axiom,
! [V_24X1] : happ(c_24__lam__114867,V_24X1) = c_24__lam__114867___24a1(V_24X1) ).
fof('$adef_$_lam_65922_$a1',axiom,
! [V_24X1] : happ(c_24__lam__65922,V_24X1) = c_24__lam__65922___24a1(V_24X1) ).
fof('$adef_$_prop_771_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__771,V_24X1),V_24X2) = c_24__prop__771___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rlimit.limit_in_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eReals_2eRlimit_2elimit__in,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eReals_2eRlimit_2elimit__in___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_lim_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_32010_$a1',axiom,
! [V_24X1] : happ(c_24__lam__32010,V_24X1) = c_24__lam__32010___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_897_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__897,V_24X1),V_24X2) = c_24__prop__897___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_$_lam_914_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__914,V_24X1),V_24X2) = c_24__lam__914___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Logic.False_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eLogic_2eFalse__rec,V_24X1) = cCoq_2eInit_2eLogic_2eFalse__rec___24a1(V_24X1) ).
fof('$adef_$_let_var_6_a0_17037_17124_$a1',axiom,
! [V_24X1] : happ(c_24__let__var__6__a0__17037__17124,V_24X1) = c_24__let__var__6__a0__17037__17124___24a1(V_24X1) ).
fof('$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.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_$_prop_533_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__533,V_24X1),V_24X2) = c_24__prop__533___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_734_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__734,V_24X1),V_24X2) = c_24__prop__734___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.comparison$19712_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2419712,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2419712___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_944_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__944,V_24X1),V_24X2) = c_24__prop__944___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_prop_75281_$a1',axiom,
! [V_24X1] : happ(c_24__prop__75281,V_24X1) = c_24__prop__75281___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.Rle_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2eRle__dec,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons2_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_$_cast_16432_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__cast__16432,V_24X1),V_24X2) = c_24__cast__16432___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.comp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ecomp,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_32041_$a1',axiom,
! [V_24X1] : happ(c_24__lam__32041,V_24X1) = c_24__lam__32041___24a1(V_24X1) ).
fof('$adef_$_lam_32010_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__32010,V_24X1),V_24X2) = c_24__lam__32010___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_769_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__769,V_24X1),V_24X2) = c_24__prop__769___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$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('$adef_$_prop_768_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__768,V_24X1),V_24X2) = c_24__prop__768___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_14_s_35433_35436_35499_$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__var__var__14__s__35433__35436__35499,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s__35433__35436__35499___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
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.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Classes.Morphisms.iff_flip_impl_subrelation_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eiff__flip__impl__subrelation,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2eiff__flip__impl__subrelation___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_66019_$a1',axiom,
! [V_24X1] : happ(c_24__lam__66019,V_24X1) = c_24__lam__66019___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.StrictOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eStrictOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Ranalysis1.derive_pt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederive__pt,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_78503_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__78503,V_24X1),V_24X2),V_24X3) = c_24__lam__78503___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.fct_cte_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2efct__cte,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_772_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__772,V_24X1),V_24X2) = c_24__prop__772___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_var_12_x_35418_35421_35491_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__35418__35421__35491,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__35418__35421__35491___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_lam_65845_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__65845,V_24X1),V_24X2) = c_24__lam__65845___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_6_lmp_16424_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__16424,V_24X1) = c_24__let__6__lmp__16424___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Raxioms.INR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRaxioms_2eINR,V_24X1) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V_24X1) ).
fof('$adef_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_$_let_var_var_12_x_35485_35487_35522_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__35485__35487__35522,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__35485__35487__35522___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_ArithCompl.R_p4_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cArithCompl_2eR__p4,V_24X1),V_24X2))
<=> cArithCompl_2eR__p4___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.SeqProp.Un_decreasing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eSeqProp_2eUn__decreasing,V_24X1))
<=> cCoq_2eReals_2eSeqProp_2eUn__decreasing___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.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_def.cos_in_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtrigo__def_2ecos__in,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_66004_$a1',axiom,
! [V_24X1] : happ(c_24__lam__66004,V_24X1) = c_24__lam__66004___24a1(V_24X1) ).
fof('$adef_$_lam_909_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__909,V_24X1),V_24X2) = c_24__lam__909___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eup,V_24X1) = cCoq_2eReals_2eRdefinitions_2eup___24a1(V_24X1) ).
fof('$adef_$_let_var_var_var_6_r\'_19349_19359_19361_19371_$a1',axiom,
! [V_24X1] : happ(c_24__let__var__var__var__6__r_27__19349__19359__19361__19371,V_24X1) = c_24__let__var__var__var__6__r_27__19349__19359__19361__19371___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rtrigo_def.exist_exp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexist__exp,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexist__exp___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.sum_f_R0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2esum__f__R0,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.ZArith_dec.Z_le_lt_eq_dec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eZArith_2eZArith__dec_2eZ__le__lt__eq__dec,V_24X1),V_24X2),V_24X3) = cCoq_2eZArith_2eZArith__dec_2eZ__le__lt__eq__dec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rtrigo_alt.sin_approx_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtrigo__alt_2esin__approx,V_24X1),V_24X2) = cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_767_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__767,V_24X1),V_24X2) = c_24__lam__767___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_lt_iff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt__lt__iff,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2egt__lt__iff___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_598_$a1',axiom,
! [V_24X1] : happ(c_24__prop__598,V_24X1) = c_24__prop__598___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('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_$_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.Reals.PartSum.Cauchy_crit_series_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2ePartSum_2eCauchy__crit__series,V_24X1))
<=> cCoq_2eReals_2ePartSum_2eCauchy__crit__series___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.BFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eTauto_2eBFormula,V_24X1) = cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ).
fof('$adef_ArithCompl.frac_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cArithCompl_2efrac,V_24X1),V_24X2) = cArithCompl_2efrac___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEadd_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_prop_891_$a1',axiom,
! [V_24X1] : happ(c_24__prop__891,V_24X1) = c_24__prop__891___24a1(V_24X1) ).
fof('$adef_$_prop_910_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__910,V_24X1),V_24X2) = c_24__prop__910___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_911_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__911,V_24X1),V_24X2) = c_24__prop__911___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_$_prop_69021_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__69021,V_24X1),V_24X2) = c_24__prop__69021___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_721_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__721,V_24X1),V_24X2) = c_24__prop__721___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo_def.sin_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2esin,V_24X1) = cCoq_2eReals_2eRtrigo__def_2esin___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_65922_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__65922,V_24X1),V_24X2))
<=> c_24__lam__65922___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RMicromega.Reval_formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eReval__formula,V_24X1) = cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V_24X1) ).
fof('$adef_$_let_var_var_12_x_35444_35448_35506_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__35444__35448__35506,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__35444__35448__35506___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons2_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.div_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ediv__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ediv__fct___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_725_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__725,V_24X1),V_24X2) = c_24__lam__725___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rpower.ln_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRpower_2eln,V_24X1) = cCoq_2eReals_2eRpower_2eln___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zpower.shift_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eshift__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eshift__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo_def.sin_in_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtrigo__def_2esin__in,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtrigo__def_2esin__in___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_895_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__895,V_24X1),V_24X2) = c_24__prop__895___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_13_y_35419_35422_35492_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__35419__35422__35492,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__35419__35422__35492___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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_$_prop_75282_$a1',axiom,
! [V_24X1] : happ(c_24__prop__75282,V_24X1) = c_24__prop__75282___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.PEsimp_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePEsimp,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons1_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Reals.Rtrigo1.tan_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo1_2etan,V_24X1) = cCoq_2eReals_2eRtrigo1_2etan___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_def.exp_in_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRtrigo__def_2eexp__in,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRtrigo__def_2eexp__in___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_65960_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__65960,V_24X1),V_24X2) = c_24__lam__65960___24a2(V_24X1,V_24X2) ).
fof('$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('$adef_Coq.ZArith.ZArith_dec.Z_le_gt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZArith__dec_2eZ__le__gt__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eZArith__dec_2eZ__le__gt__dec___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.AltSeries.tg_alt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eAltSeries_2etg__alt,V_24X1),V_24X2) = cCoq_2eReals_2eAltSeries_2etg__alt___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.RIneq.Rlt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2eRlt__dec,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2eRlt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_6_lmp_32026_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__32026,V_24X1) = c_24__let__6__lmp__32026___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a1(V_24X1) ).
fof('$adef_$_lam_66019_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__66019,V_24X1),V_24X2))
<=> c_24__lam__66019___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Ranalysis1.minus_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eminus__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2eminus__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_31805_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31805,V_24X1),V_24X2) = c_24__lam__31805___24a2(V_24X1,V_24X2) ).
fof('$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.setoid_ring.Field_theory.Fnorm_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFnorm,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_32944_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__32944,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__32944___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_prop_221_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__221,V_24X1),V_24X2) = c_24__prop__221___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.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.Reals.Ranalysis1.continuity_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2econtinuity,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V_24X1) ) ).
fof('$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.Reals.AltSeries.tg_alt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eAltSeries_2etg__alt,V_24X1) = cCoq_2eReals_2eAltSeries_2etg__alt___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34434_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__34434,V_24X1))
<=> c_24__lam__34434___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Reals.Raxioms.is_lub_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRaxioms_2eis__lub,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRaxioms_2eis__lub___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___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('$adef_$_prop_902_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__902,V_24X1),V_24X2) = c_24__prop__902___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_13172_$a1',axiom,
! [V_24X1] : happ(c_24__lam__13172,V_24X1) = c_24__lam__13172___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.Un_cv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRseries_2eUn__cv,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_140_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__140,V_24X1),V_24X2) = c_24__lam__140___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sig_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rlimit.dist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRlimit_2edist,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRlimit_2edist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$32090_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432090___24a1(V_24X1) ).
fof('$adef_$_let_17_mkopp_pow_32945_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__32945,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__32945___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2erel__prime__dec___24a2(V_24X1,V_24X2) ).
fof('$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('$adef_$_lam_578_$a1',axiom,
! [V_24X1] : happ(c_24__lam__578,V_24X1) = c_24__lam__578___24a1(V_24X1) ).
fof('$adef_$_let_6_lmp_13887_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__13887,V_24X1) = c_24__let__6__lmp__13887___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.Datan_seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRatan_2eDatan__seq,V_24X1),V_24X2) = cCoq_2eReals_2eRatan_2eDatan__seq___24a2(V_24X1,V_24X2) ).
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_$_prop_892_$a1',axiom,
! [V_24X1] : happ(c_24__prop__892,V_24X1) = c_24__prop__892___24a1(V_24X1) ).
fof('$adef_$_prop_951_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__951,V_24X1),V_24X2) = c_24__prop__951___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_17_mkopp_pow_32945_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__32945,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__32945___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_avoid_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_217_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__217,V_24X1),V_24X2) = c_24__lam__217___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_596_$a1',axiom,
! [V_24X1] : happ(c_24__prop__596,V_24X1) = c_24__prop__596___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rlimit.Build_Metric_Space_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_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_$_prop_17066_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__17066,V_24X1),V_24X2) = c_24__prop__17066___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.Un_growing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRseries_2eUn__growing,V_24X1))
<=> cCoq_2eReals_2eRseries_2eUn__growing___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_19230_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__19230,V_24X1),V_24X2) = c_24__prop__19230___24a2(V_24X1,V_24X2) ).
fof('$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.PArith.BinPosDef.Pos.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eland,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_lam_872_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__872,V_24X1),V_24X2) = c_24__lam__872___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('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_lam_78503_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__78503,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__78503___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.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('$adef_$_lam_914_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__914,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__914___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.QArith.QArith_base.Qpower_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQpower,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rmin_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRbasic__fun_2eRmin,V_24X1),V_24X2) = cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Raxioms.is_upper_bound_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRaxioms_2eis__upper__bound,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRaxioms_2eis__upper__bound___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rlimit.limit1_in_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2eRlimit_2elimit1__in,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2eRlimit_2elimit1__in___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_32041_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__32041,V_24X1),V_24X2))
<=> c_24__lam__32041___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_719_$a1',axiom,
! [V_24X1] : happ(c_24__prop__719,V_24X1) = c_24__prop__719___24a1(V_24X1) ).
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('$adef_$_lam_65845_$a1',axiom,
! [V_24X1] : happ(c_24__lam__65845,V_24X1) = c_24__lam__65845___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_common_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__common,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_14_s_35420_35423_35493_$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__var__var__14__s__35420__35423__35493,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s__35420__35423__35493___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_738_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__738,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__738___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.QArith.QArith_base.Qpower_positive_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQpower__positive,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31864_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31864,V_24X1) = c_24__lam__31864___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$19737_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419737,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2419737___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_13167_$a1',axiom,
! [V_24X1] : happ(c_24__lam__13167,V_24X1) = c_24__lam__13167___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rmax_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRbasic__fun_2eRmax,V_24X1),V_24X2) = cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_725_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__725,V_24X1),V_24X2),V_24X3) = c_24__lam__725___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eland,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$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('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmult,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] : 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('$adef_$_lam_114867_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__114867,V_24X1),V_24X2))
<=> c_24__lam__114867___24a2(V_24X1,V_24X2) ) ).
fof('$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_ArithCompl.distinct_parity_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cArithCompl_2edistinct__parity,V_24X1),V_24X2))
<=> cArithCompl_2edistinct__parity___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rtrigo_def.exist_cos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexist__cos,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexist__cos___24a1(V_24X1) ).
fof('$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_$_prop_77795_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__77795,V_24X1),V_24X2) = c_24__prop__77795___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo1.sin_lb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo1_2esin__lb,V_24X1) = cCoq_2eReals_2eRtrigo1_2esin__lb___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.Ratan_seq_decreasing_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eRatan__seq__decreasing,V_24X1) = cCoq_2eReals_2eRatan_2eRatan__seq__decreasing___24a1(V_24X1) ).
fof('$adef_$_lam_65960_$a1',axiom,
! [V_24X1] : happ(c_24__lam__65960,V_24X1) = c_24__lam__65960___24a1(V_24X1) ).
fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_19713_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__19713,V_24X1),V_24X2) = c_24__prop__19713___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_$_prop_718_$a1',axiom,
! [V_24X1] : happ(c_24__prop__718,V_24X1) = c_24__prop__718___24a1(V_24X1) ).
fof('$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_$_lam_32008_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__32008,V_24X1),V_24X2),V_24X3) = c_24__lam__32008___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Numbers.BinNums.Z_rec_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eNumbers_2eBinNums_2eZ__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eNumbers_2eBinNums_2eZ__rec___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.PArith.BinPos.Pos.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eeq__dec,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eeq__dec___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.AltSeries.alternated_series_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eAltSeries_2ealternated__series,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eAltSeries_2ealternated__series___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege__le,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ege__le___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.shiftr_$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('$adef_$_prop_17067_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__17067,V_24X1),V_24X2) = c_24__prop__17067___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.mult_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2emult__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78308_$a1',axiom,
! [V_24X1] : happ(c_24__lam__78308,V_24X1) = c_24__lam__78308___24a1(V_24X1) ).
fof('$adef_$_let_var_var_12_x_35468_35472_35518_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__35468__35472__35518,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__35468__35472__35518___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.PArith.BinPosDef.Pos.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rderiv.continue_in_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRderiv_2econtinue__in,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRderiv_2econtinue__in___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_let_11_subst_l_14524_$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('$adef_Coq.Reals.Rtrigo_def.cos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2ecos,V_24X1) = cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V_24X1) ).
fof('$adef_$_prop_74358_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__74358,V_24X1),V_24X2) = c_24__prop__74358___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Logic.eq_ind_r_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__ind__r,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__ind__r___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_18_mkmult_pow_32946_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__32946,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__32946___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_735_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__735,V_24X1),V_24X2) = c_24__prop__735___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo_def.exp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexp,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V_24X1) ).
fof('$adef_$_prop_17145_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__17145,V_24X1),V_24X2) = c_24__prop__17145___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.ZArith_dec.Z_lt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZArith__dec_2eZ__lt__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eZArith__dec_2eZ__lt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.R_Ifp.frac_part_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__Ifp_2efrac__part,V_24X1) = cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V_24X1) ).
fof('$adef_$_let_var_var_13_y_35469_35473_35519_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__35469__35473__35519,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__35469__35473__35519___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rcase_abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRcase__abs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V_24X1) ).
fof('$adef_$_let_var_var_var_6_r\'_19331_19341_19343_19365_$a1',axiom,
! [V_24X1] : happ(c_24__let__var__var__var__6__r_27__19331__19341__19343__19365,V_24X1) = c_24__let__var__var__var__6__r_27__19331__19341__19343__19365___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_def.exist_sin_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexist__sin,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexist__sin___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_$_lam_738_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__738,V_24X1),V_24X2) = c_24__lam__738___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_945_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__945,V_24X1),V_24X2) = c_24__prop__945___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_$_lam_34432_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__34432,V_24X1))
<=> c_24__lam__34432___24a1(V_24X1) ) ).
fof('$adef_$_let_var_6_p_14926_14929_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__14926__14929,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__14926__14929___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_35312_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35312,V_24X1),V_24X2) = c_24__prop__35312___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.continuity_pt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRanalysis1_2econtinuity__pt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V_24X1,V_24X2) ) ).
fof('$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.Reals.Rlimit.dist_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRlimit_2edist,V_24X1) = cCoq_2eReals_2eRlimit_2edist___24a1(V_24X1) ).
fof('$adef_$_lam_65958_$a1',axiom,
! [V_24X1] : happ(c_24__lam__65958,V_24X1) = c_24__lam__65958___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_$_lam_32008_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__32008,V_24X1),V_24X2) = c_24__lam__32008___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2edouble,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Reals.PSeries_reg.Boule_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2ePSeries__reg_2eBoule,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RMicromega.RTautoChecker_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eRTautoChecker,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_534_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__534,V_24X1),V_24X2) = c_24__prop__534___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rsqrt_def.Rsqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRsqrt__def_2eRsqrt,V_24X1) = cCoq_2eReals_2eRsqrt__def_2eRsqrt___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_17143_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__17143,V_24X1),V_24X2) = c_24__prop__17143___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_4_a0_17034_17122_$a1',axiom,
! [V_24X1] : happ(c_24__let__var__4__a0__17034__17122,V_24X1) = c_24__let__var__4__a0__17034__17122___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEopp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEopp,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_13363_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__13363,V_24X1),V_24X2) = c_24__prop__13363___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_abs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_22033_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__22033,V_24X1),V_24X2) = c_24__lam__22033___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.lor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elor___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78308_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__78308,V_24X1),V_24X2))
<=> c_24__lam__78308___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEsub_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.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_$_let_var_var_14_s1_35470_35474_35520_$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__var__var__14__s1__35470__35474__35520,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s1__35470__35474__35520___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.ZArith.ZArith_dec.Z_le_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZArith__dec_2eZ__le__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eZArith__dec_2eZ__le__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_13174_$a1',axiom,
! [V_24X1] : happ(c_24__lam__13174,V_24X1) = c_24__lam__13174___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_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('$adef_$_lam_22033_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__22033,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__22033___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_903_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__903,V_24X1),V_24X2) = c_24__prop__903___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.R_Ifp.Int_part_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__Ifp_2eInt__part,V_24X1) = cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_$_prop_599_$a1',axiom,
! [V_24X1] : happ(c_24__prop__599,V_24X1) = c_24__prop__599___24a1(V_24X1) ).
fof('$adef_$_prop_894_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__894,V_24X1),V_24X2) = c_24__prop__894___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_11_x_35460_35510_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__35460__35510,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__35460__35510___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_prop_17068_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__17068,V_24X1),V_24X2) = c_24__prop__17068___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_13174_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__13174,V_24X1),V_24X2) = c_24__lam__13174___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_60007_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60007,V_24X1),V_24X2) = c_24__prop__60007___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rlimit.Base_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRlimit_2eBase,V_24X1) = cCoq_2eReals_2eRlimit_2eBase___24a1(V_24X1) ).
fof('$adef_$_prop_17144_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__17144,V_24X1),V_24X2) = c_24__prop__17144___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_943_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__943,V_24X1),V_24X2) = c_24__lam__943___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2epos,V_24X1) = cCoq_2eReals_2eRIneq_2epos___24a1(V_24X1) ).
fof('$adef_$_lam_34431_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__34431,V_24X1))
<=> c_24__lam__34431___24a1(V_24X1) ) ).
fof('$adef_$_let_var_var_13_y_35432_35435_35498_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__35432__35435__35498,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__35432__35435__35498___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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.Reals.Ranalysis1.div_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2ediv__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2ediv__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.get_signZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.ZArith_dec.Z_lt_ge_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZArith__dec_2eZ__lt__ge__dec,V_24X1),V_24X2) = cCoq_2eZArith_2eZArith__dec_2eZ__lt__ge__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_726_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__726,V_24X1),V_24X2) = c_24__prop__726___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.R_sqrt.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__sqrt_2esqrt,V_24X1) = cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEpow_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEpow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_699_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__699,V_24X1),V_24X2) = c_24__lam__699___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.rem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_901_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__901,V_24X1),V_24X2),V_24X3) = c_24__lam__901___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.NArith.BinNatDef.N.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$32085_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432085___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_17150_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__17150,V_24X1),V_24X2) = c_24__prop__17150___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR__2,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V_24X1) ).
fof('$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_$_prop_65002_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__65002,V_24X1),V_24X2) = c_24__prop__65002___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rpower.Rln_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRpower_2eRln,V_24X1) = cCoq_2eReals_2eRpower_2eRln___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.shiftl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.sqrt_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2esqrt__up___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.Ratan_seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRatan_2eRatan__seq,V_24X1),V_24X2) = cCoq_2eReals_2eRatan_2eRatan__seq___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_13167_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__13167,V_24X1),V_24X2) = c_24__lam__13167___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.EUn_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRseries_2eEUn,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRseries_2eEUn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rseries.EUn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRseries_2eEUn,V_24X1) = cCoq_2eReals_2eRseries_2eEUn___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.ZArith_dec.not_Zeq_inf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZArith__dec_2enot__Zeq__inf,V_24X1),V_24X2) = cCoq_2eZArith_2eZArith__dec_2enot__Zeq__inf___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_68662_$a1',axiom,
! [V_24X1] : happ(c_24__lam__68662,V_24X1) = c_24__lam__68662___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_32944_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__32944,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__32944___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Ratan.atan_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eatan,V_24X1) = cCoq_2eReals_2eRatan_2eatan___24a1(V_24X1) ).
fof('$adef_$_let_18_mkmult_pow_32946_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__32946,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__32946___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.VarMap.find_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2efind,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2efind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$19369_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419369,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419369___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_60006_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__60006,V_24X1),V_24X2) = c_24__prop__60006___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_901_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__901,V_24X1),V_24X2) = c_24__lam__901___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$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('$adef_Coq.QArith.QArith_base.Qinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQinv,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.ps_atan_exists_01_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eps__atan__exists__01,V_24X1) = cCoq_2eReals_2eRatan_2eps__atan__exists__01___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rpower.Rpower_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpower_2eRpower,V_24X1),V_24X2) = cCoq_2eReals_2eRpower_2eRpower___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ratan.Ratan_seq_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eRatan__seq,V_24X1) = cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V_24X1) ).
fof('$adef_$_let_var_11_x_35463_35511_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__35463__35511,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__35463__35511___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.NArith.BinNatDef.N.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.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_$_lam_68662_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__68662,V_24X1),V_24X2) = c_24__lam__68662___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.Rge_le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2eRge__le,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2eRge__le___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rabs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRabs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_950_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__950,V_24X1),V_24X2) = c_24__prop__950___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.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_$_lam_34433_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__34433,V_24X1))
<=> c_24__lam__34433___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_16444_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__16444,V_24X1),V_24X2) = c_24__prop__16444___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_77796_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__77796,V_24X1),V_24X2) = c_24__prop__77796___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_var_var_15_s2_35471_35475_35521_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__15__s2__35471__35475__35521,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__15__s2__35471__35475__35521___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_prop_727_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__727,V_24X1),V_24X2) = c_24__prop__727___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_$_let_var_var_12_x_35431_35434_35497_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__35431__35434__35497,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__35431__35434__35497___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.setoid_ring.Field_theory.PCond_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eField__theory_2ePCond___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_$_lam_31805_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31805,V_24X1) = c_24__lam__31805___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_bf_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__bf,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_64817_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__64817,V_24X1),V_24X2) = c_24__prop__64817___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_722_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__722,V_24X1),V_24X2) = c_24__prop__722___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.pre_atan_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2epre__atan,V_24X1) = cCoq_2eReals_2eRatan_2epre__atan___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.left_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$32068_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432068___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_66004_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__66004,V_24X1),V_24X2))
<=> c_24__lam__66004___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Ranalysis1.fct_cte_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2efct__cte,V_24X1) = cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_65958_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__65958,V_24X1),V_24X2))
<=> c_24__lam__65958___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_114204_$a1',axiom,
! [V_24X1] : happ(c_24__lam__114204,V_24X1) = c_24__lam__114204___24a1(V_24X1) ).
fof('$adef_$_lam_143_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__143,V_24X1),V_24X2) = c_24__lam__143___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_65001_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__65001,V_24X1),V_24X2) = c_24__prop__65001___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_13_y_35445_35449_35507_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__35445__35449__35507,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__35445__35449__35507___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_cast_59730_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__cast__59730,V_24X1),V_24X2) = c_24__cast__59730___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_15_s2_35447_35451_35509_$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__var__var__15__s2__35447__35451__35509,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__15__s2__35447__35451__35509___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Arith.Factorial.fact_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2eFactorial_2efact,V_24X1) = cCoq_2eArith_2eFactorial_2efact___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_595_$a1',axiom,
! [V_24X1] : happ(c_24__prop__595,V_24X1) = c_24__prop__595___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$19375_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419375,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2419375___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ratan.Ratan_seq_converging_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eRatan__seq__converging,V_24X1) = cCoq_2eReals_2eRatan_2eRatan__seq__converging___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.right_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eright___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rderiv.D_x_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRderiv_2eD__x,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRderiv_2eD__x___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.PreOrder_$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('$adef_$_lam_529_$a1',axiom,
! [V_24X1] : happ(c_24__lam__529,V_24X1) = c_24__lam__529___24a1(V_24X1) ).
fof('$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_$_lam_733_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__733,V_24X1),V_24X2) = c_24__lam__733___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_13172_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__13172,V_24X1),V_24X2))
<=> c_24__lam__13172___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_114204_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__114204,V_24X1),V_24X2) = c_24__lam__114204___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.no_cond_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2eno__cond,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2eno__cond___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_113415',axiom,
! [V_24Y] :
( c_24__type__113415___24t(V_24Y)
<=> t(V_24Y,c_24__type__113415) ) ).
fof('$tdef_$_type_66032',axiom,
! [V_24Y] :
( c_24__type__66032___24t(V_24Y)
<=> t(V_24Y,c_24__type__66032) ) ).
fof('$tdef_$_type_64795',axiom,
! [V_24Y] :
( c_24__type__64795___24t(V_24Y)
<=> t(V_24Y,c_24__type__64795) ) ).
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('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22040',axiom,
! [V_24Y] :
( c_24__type__22040___24t(V_24Y)
<=> t(V_24Y,c_24__type__22040) ) ).
fof('$tdef_$_type_13361',axiom,
! [V_24Y] :
( c_24__type__13361___24t(V_24Y)
<=> t(V_24Y,c_24__type__13361) ) ).
fof('$tdef_Coq.Reals.Rlimit.Metric_Space',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRlimit_2eMetric__Space) ) ).
fof('$tdef_$_type_65565',axiom,
! [V_24Y] :
( c_24__type__65565___24t(V_24Y)
<=> t(V_24Y,c_24__type__65565) ) ).
fof('$tdef_$_type_21998',axiom,
! [V_24Y] :
( c_24__type__21998___24t(V_24Y)
<=> t(V_24Y,c_24__type__21998) ) ).
fof('$tdef_$_type_531',axiom,
! [V_24X1,V_24Y] :
( c_24__type__531___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__531___24a1(V_24X1)) ) ).
fof('$tdef_$_type_66151',axiom,
! [V_24Y] :
( c_24__type__66151___24t(V_24Y)
<=> t(V_24Y,c_24__type__66151) ) ).
fof('$tdef_$_type_410',axiom,
! [V_24Y] :
( c_24__type__410___24t(V_24Y)
<=> t(V_24Y,c_24__type__410) ) ).
fof('$tdef_$_type_12',axiom,
! [V_24Y] :
( c_24__type__12___24t(V_24Y)
<=> t(V_24Y,c_24__type__12) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22038',axiom,
! [V_24Y] :
( c_24__type__22038___24t(V_24Y)
<=> t(V_24Y,c_24__type__22038) ) ).
fof('$tdef_$_type_16378',axiom,
! [V_24Y] :
( c_24__type__16378___24t(V_24Y)
<=> t(V_24Y,c_24__type__16378) ) ).
fof('$tdef_$_type_59418',axiom,
! [V_24Y] :
( c_24__type__59418___24t(V_24Y)
<=> t(V_24Y,c_24__type__59418) ) ).
fof('$tdef_$_type_19295',axiom,
! [V_24Y] :
( c_24__type__19295___24t(V_24Y)
<=> t(V_24Y,c_24__type__19295) ) ).
fof('$tdef_$_type_32757',axiom,
! [V_24Y] :
( c_24__type__32757___24t(V_24Y)
<=> t(V_24Y,c_24__type__32757) ) ).
fof('$tdef_$_type_64815',axiom,
! [V_24Y] :
( c_24__type__64815___24t(V_24Y)
<=> t(V_24Y,c_24__type__64815) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_59741',axiom,
! [V_24Y] :
( c_24__type__59741___24t(V_24Y)
<=> t(V_24Y,c_24__type__59741) ) ).
fof('$tdef_$_type_16391',axiom,
! [V_24Y] :
( c_24__type__16391___24t(V_24Y)
<=> t(V_24Y,c_24__type__16391) ) ).
fof('$tdef_$_type_20866',axiom,
! [V_24Y] :
( c_24__type__20866___24t(V_24Y)
<=> t(V_24Y,c_24__type__20866) ) ).
fof('$tdef_$_type_16412',axiom,
! [V_24Y] :
( c_24__type__16412___24t(V_24Y)
<=> t(V_24Y,c_24__type__16412) ) ).
fof('$tdef_$_type_956',axiom,
! [V_24Y] :
( c_24__type__956___24t(V_24Y)
<=> t(V_24Y,c_24__type__956) ) ).
fof('$tdef_$_type_66077',axiom,
! [V_24Y] :
( c_24__type__66077___24t(V_24Y)
<=> t(V_24Y,c_24__type__66077) ) ).
fof('$tdef_$_type_19822',axiom,
! [V_24Y] :
( c_24__type__19822___24t(V_24Y)
<=> t(V_24Y,c_24__type__19822) ) ).
fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).
fof('$tdef_$_type_27524',axiom,
! [V_24Y] :
( c_24__type__27524___24t(V_24Y)
<=> t(V_24Y,c_24__type__27524) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_75247',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__75247___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__75247___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13592',axiom,
! [V_24Y] :
( c_24__type__13592___24t(V_24Y)
<=> t(V_24Y,c_24__type__13592) ) ).
fof('$tdef_Coq.Reals.Ranalysis1.derivable',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRanalysis1_2ederivable___24a1(V_24X1)) ) ).
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_114864',axiom,
! [V_24Y] :
( c_24__type__114864___24t(V_24Y)
<=> t(V_24Y,c_24__type__114864) ) ).
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_14961',axiom,
! [V_24Y] :
( c_24__type__14961___24t(V_24Y)
<=> t(V_24Y,c_24__type__14961) ) ).
fof('$tdef_$_type_75239',axiom,
! [V_24Y] :
( c_24__type__75239___24t(V_24Y)
<=> t(V_24Y,c_24__type__75239) ) ).
fof('$tdef_$_type_66085',axiom,
! [V_24Y] :
( c_24__type__66085___24t(V_24Y)
<=> t(V_24Y,c_24__type__66085) ) ).
fof('$tdef_$_type_32497',axiom,
! [V_24Y] :
( c_24__type__32497___24t(V_24Y)
<=> t(V_24Y,c_24__type__32497) ) ).
fof('$tdef_$_type_16442',axiom,
! [V_24Y] :
( c_24__type__16442___24t(V_24Y)
<=> t(V_24Y,c_24__type__16442) ) ).
fof('$tdef_$_type_20576',axiom,
! [V_24Y] :
( c_24__type__20576___24t(V_24Y)
<=> t(V_24Y,c_24__type__20576) ) ).
fof('$tdef_$_type_13849',axiom,
! [V_24Y] :
( c_24__type__13849___24t(V_24Y)
<=> t(V_24Y,c_24__type__13849) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_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('$tdef_$_type_68667',axiom,
! [V_24Y] :
( c_24__type__68667___24t(V_24Y)
<=> t(V_24Y,c_24__type__68667) ) ).
fof('$tdef_$_type_66074',axiom,
! [V_24Y] :
( c_24__type__66074___24t(V_24Y)
<=> t(V_24Y,c_24__type__66074) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_59305',axiom,
! [V_24Y] :
( c_24__type__59305___24t(V_24Y)
<=> t(V_24Y,c_24__type__59305) ) ).
fof('$tdef_$_type_31256',axiom,
! [V_24Y] :
( c_24__type__31256___24t(V_24Y)
<=> t(V_24Y,c_24__type__31256) ) ).
fof('$tdef_$_type_33362',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33362___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33362___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_65004',axiom,
! [V_24Y] :
( c_24__type__65004___24t(V_24Y)
<=> t(V_24Y,c_24__type__65004) ) ).
fof('$tdef_$_type_77817',axiom,
! [V_24Y] :
( c_24__type__77817___24t(V_24Y)
<=> t(V_24Y,c_24__type__77817) ) ).
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_$_type_65906',axiom,
! [V_24Y] :
( c_24__type__65906___24t(V_24Y)
<=> t(V_24Y,c_24__type__65906) ) ).
fof('$tdef_$_type_13657',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13657___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13657___24a1(V_24X1)) ) ).
fof('$tdef_$_type_68801',axiom,
! [V_24Y] :
( c_24__type__68801___24t(V_24Y)
<=> t(V_24Y,c_24__type__68801) ) ).
fof('$tdef_$_type_71153',axiom,
! [V_24Y] :
( c_24__type__71153___24t(V_24Y)
<=> t(V_24Y,c_24__type__71153) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_Coq.micromega.Tauto.BFormula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_399',axiom,
! [V_24X1,V_24Y] :
( c_24__type__399___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__399___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13892',axiom,
! [V_24Y] :
( c_24__type__13892___24t(V_24Y)
<=> t(V_24Y,c_24__type__13892) ) ).
fof('$tdef_$_type_117',axiom,
! [V_24Y] :
( c_24__type__117___24t(V_24Y)
<=> t(V_24Y,c_24__type__117) ) ).
fof('$tdef_$_type_65044',axiom,
! [V_24X1,V_24Y] :
( c_24__type__65044___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__65044___24a1(V_24X1)) ) ).
fof('$tdef_$_type_65878',axiom,
! [V_24Y] :
( c_24__type__65878___24t(V_24Y)
<=> t(V_24Y,c_24__type__65878) ) ).
fof('$tdef_$_type_118486',axiom,
! [V_24Y] :
( c_24__type__118486___24t(V_24Y)
<=> t(V_24Y,c_24__type__118486) ) ).
fof('$tdef_$_type_31259',axiom,
! [V_24Y] :
( c_24__type__31259___24t(V_24Y)
<=> t(V_24Y,c_24__type__31259) ) ).
fof('$tdef_$_type_45',axiom,
! [V_24Y] :
( c_24__type__45___24t(V_24Y)
<=> t(V_24Y,c_24__type__45) ) ).
fof('$tdef_$_type_471',axiom,
! [V_24Y] :
( c_24__type__471___24t(V_24Y)
<=> t(V_24Y,c_24__type__471) ) ).
fof('$tdef_$_type_36732',axiom,
! [V_24Y] :
( c_24__type__36732___24t(V_24Y)
<=> t(V_24Y,c_24__type__36732) ) ).
fof('$tdef_$_type_17148',axiom,
! [V_24Y] :
( c_24__type__17148___24t(V_24Y)
<=> t(V_24Y,c_24__type__17148) ) ).
fof('$tdef_$_type_32016',axiom,
! [V_24Y] :
( c_24__type__32016___24t(V_24Y)
<=> t(V_24Y,c_24__type__32016) ) ).
fof('$tdef_$_type_22035',axiom,
! [V_24Y] :
( c_24__type__22035___24t(V_24Y)
<=> t(V_24Y,c_24__type__22035) ) ).
fof('$tdef_$_type_20627',axiom,
! [V_24Y] :
( c_24__type__20627___24t(V_24Y)
<=> t(V_24Y,c_24__type__20627) ) ).
fof('$tdef_$_type_58008',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__58008___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__58008___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_323',axiom,
! [V_24Y] :
( c_24__type__323___24t(V_24Y)
<=> t(V_24Y,c_24__type__323) ) ).
fof('$tdef_$_type_32019',axiom,
! [V_24Y] :
( c_24__type__32019___24t(V_24Y)
<=> t(V_24Y,c_24__type__32019) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20647',axiom,
! [V_24Y] :
( c_24__type__20647___24t(V_24Y)
<=> t(V_24Y,c_24__type__20647) ) ).
fof('$tdef_$_type_65880',axiom,
! [V_24Y] :
( c_24__type__65880___24t(V_24Y)
<=> t(V_24Y,c_24__type__65880) ) ).
fof('$tdef_$_type_14906',axiom,
! [V_24Y] :
( c_24__type__14906___24t(V_24Y)
<=> t(V_24Y,c_24__type__14906) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_65716',axiom,
! [V_24Y] :
( c_24__type__65716___24t(V_24Y)
<=> t(V_24Y,c_24__type__65716) ) ).
fof('$tdef_$_type_61',axiom,
! [V_24Y] :
( c_24__type__61___24t(V_24Y)
<=> t(V_24Y,c_24__type__61) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_65680',axiom,
! [V_24Y] :
( c_24__type__65680___24t(V_24Y)
<=> t(V_24Y,c_24__type__65680) ) ).
fof('$tdef_$_type_13209',axiom,
! [V_24Y] :
( c_24__type__13209___24t(V_24Y)
<=> t(V_24Y,c_24__type__13209) ) ).
fof('$tdef_$_type_57114',axiom,
! [V_24Y] :
( c_24__type__57114___24t(V_24Y)
<=> t(V_24Y,c_24__type__57114) ) ).
fof('$tdef_$_type_14067',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14067___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14067___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16422',axiom,
! [V_24X1,V_24Y] :
( c_24__type__16422___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__16422___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22029',axiom,
! [V_24Y] :
( c_24__type__22029___24t(V_24Y)
<=> t(V_24Y,c_24__type__22029) ) ).
fof('$tdef_$_type_19318',axiom,
! [V_24Y] :
( c_24__type__19318___24t(V_24Y)
<=> t(V_24Y,c_24__type__19318) ) ).
fof('$tdef_$_type_16816',axiom,
! [V_24Y] :
( c_24__type__16816___24t(V_24Y)
<=> t(V_24Y,c_24__type__16816) ) ).
fof('$tdef_$_type_19818',axiom,
! [V_24Y] :
( c_24__type__19818___24t(V_24Y)
<=> t(V_24Y,c_24__type__19818) ) ).
fof('$tdef_$_type_80195',axiom,
! [V_24Y] :
( c_24__type__80195___24t(V_24Y)
<=> t(V_24Y,c_24__type__80195) ) ).
fof('$tdef_$_type_30',axiom,
! [V_24Y] :
( c_24__type__30___24t(V_24Y)
<=> t(V_24Y,c_24__type__30) ) ).
fof('$tdef_$_type_13754',axiom,
! [V_24Y] :
( c_24__type__13754___24t(V_24Y)
<=> t(V_24Y,c_24__type__13754) ) ).
fof('$tdef_$_type_64826',axiom,
! [V_24Y] :
( c_24__type__64826___24t(V_24Y)
<=> t(V_24Y,c_24__type__64826) ) ).
fof('$tdef_$_type_401',axiom,
! [V_24Y] :
( c_24__type__401___24t(V_24Y)
<=> t(V_24Y,c_24__type__401) ) ).
fof('$tdef_$_type_64789',axiom,
! [V_24Y] :
( c_24__type__64789___24t(V_24Y)
<=> t(V_24Y,c_24__type__64789) ) ).
fof('$tdef_$_type_33369',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33369___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33369___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_19377',axiom,
! [V_24Y] :
( c_24__type__19377___24t(V_24Y)
<=> t(V_24Y,c_24__type__19377) ) ).
fof('$tdef_$_type_14940',axiom,
! [V_24Y] :
( c_24__type__14940___24t(V_24Y)
<=> t(V_24Y,c_24__type__14940) ) ).
fof('$tdef_Coq.Reals.Rlimit.Base',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRlimit_2eBase___24a1(V_24X1)) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_75256',axiom,
! [V_24Y] :
( c_24__type__75256___24t(V_24Y)
<=> t(V_24Y,c_24__type__75256) ) ).
fof('$tdef_$_type_35250',axiom,
! [V_24Y] :
( c_24__type__35250___24t(V_24Y)
<=> t(V_24Y,c_24__type__35250) ) ).
fof('$tdef_$_type_22042',axiom,
! [V_24Y] :
( c_24__type__22042___24t(V_24Y)
<=> t(V_24Y,c_24__type__22042) ) ).
fof('$tdef_$_type_22019',axiom,
! [V_24Y] :
( c_24__type__22019___24t(V_24Y)
<=> t(V_24Y,c_24__type__22019) ) ).
fof('$tdef_$_type_14055',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14055___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14055___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34436',axiom,
! [V_24Y] :
( c_24__type__34436___24t(V_24Y)
<=> t(V_24Y,c_24__type__34436) ) ).
fof('$tdef_$_type_27516',axiom,
! [V_24Y] :
( c_24__type__27516___24t(V_24Y)
<=> t(V_24Y,c_24__type__27516) ) ).
fof('$tdef_$_type_31271',axiom,
! [V_24Y] :
( c_24__type__31271___24t(V_24Y)
<=> t(V_24Y,c_24__type__31271) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).
fof('$tdef_$_type_58002',axiom,
! [V_24Y] :
( c_24__type__58002___24t(V_24Y)
<=> t(V_24Y,c_24__type__58002) ) ).
fof('$tdef_$_type_90',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__90___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__90___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_68762',axiom,
! [V_24Y] :
( c_24__type__68762___24t(V_24Y)
<=> t(V_24Y,c_24__type__68762) ) ).
fof('$tdef_$_type_36610',axiom,
! [V_24X1,V_24Y] :
( c_24__type__36610___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__36610___24a1(V_24X1)) ) ).
fof('$tdef_$_type_78459',axiom,
! [V_24Y] :
( c_24__type__78459___24t(V_24Y)
<=> t(V_24Y,c_24__type__78459) ) ).
fof('$tdef_$_type_22011',axiom,
! [V_24Y] :
( c_24__type__22011___24t(V_24Y)
<=> t(V_24Y,c_24__type__22011) ) ).
fof('$tdef_$_type_21994',axiom,
! [V_24Y] :
( c_24__type__21994___24t(V_24Y)
<=> t(V_24Y,c_24__type__21994) ) ).
fof('$tdef_$_type_65161',axiom,
! [V_24Y] :
( c_24__type__65161___24t(V_24Y)
<=> t(V_24Y,c_24__type__65161) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_286',axiom,
! [V_24Y] :
( c_24__type__286___24t(V_24Y)
<=> t(V_24Y,c_24__type__286) ) ).
fof('$tdef_$_type_31996',axiom,
! [V_24Y] :
( c_24__type__31996___24t(V_24Y)
<=> t(V_24Y,c_24__type__31996) ) ).
fof('$tdef_$_type_443',axiom,
! [V_24Y] :
( c_24__type__443___24t(V_24Y)
<=> t(V_24Y,c_24__type__443) ) ).
fof('$tdef_$_type_13186',axiom,
! [V_24Y] :
( c_24__type__13186___24t(V_24Y)
<=> t(V_24Y,c_24__type__13186) ) ).
fof('$tdef_$_type_13175',axiom,
! [V_24Y] :
( c_24__type__13175___24t(V_24Y)
<=> t(V_24Y,c_24__type__13175) ) ).
fof('$tdef_$_type_12714',axiom,
! [V_24Y] :
( c_24__type__12714___24t(V_24Y)
<=> t(V_24Y,c_24__type__12714) ) ).
fof('$tdef_$_type_22008',axiom,
! [V_24Y] :
( c_24__type__22008___24t(V_24Y)
<=> t(V_24Y,c_24__type__22008) ) ).
fof('$tdef_$_type_31118',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31118___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31118___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_66072',axiom,
! [V_24Y] :
( c_24__type__66072___24t(V_24Y)
<=> t(V_24Y,c_24__type__66072) ) ).
fof('$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_66116',axiom,
! [V_24Y] :
( c_24__type__66116___24t(V_24Y)
<=> t(V_24Y,c_24__type__66116) ) ).
fof('$tdef_$_type_392',axiom,
! [V_24Y] :
( c_24__type__392___24t(V_24Y)
<=> t(V_24Y,c_24__type__392) ) ).
fof('$tdef_$_type_13879',axiom,
! [V_24Y] :
( c_24__type__13879___24t(V_24Y)
<=> t(V_24Y,c_24__type__13879) ) ).
fof('$tdef_$_type_948',axiom,
! [V_24Y] :
( c_24__type__948___24t(V_24Y)
<=> t(V_24Y,c_24__type__948) ) ).
fof('$tdef_$_type_14076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14076___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14076___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_36605',axiom,
! [V_24Y] :
( c_24__type__36605___24t(V_24Y)
<=> t(V_24Y,c_24__type__36605) ) ).
fof('$tdef_$_type_22003',axiom,
! [V_24Y] :
( c_24__type__22003___24t(V_24Y)
<=> t(V_24Y,c_24__type__22003) ) ).
fof('$tdef_$_type_65972',axiom,
! [V_24Y] :
( c_24__type__65972___24t(V_24Y)
<=> t(V_24Y,c_24__type__65972) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_59784',axiom,
! [V_24Y] :
( c_24__type__59784___24t(V_24Y)
<=> t(V_24Y,c_24__type__59784) ) ).
fof('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_64786',axiom,
! [V_24Y] :
( c_24__type__64786___24t(V_24Y)
<=> t(V_24Y,c_24__type__64786) ) ).
fof('$tdef_$_type_33224',axiom,
! [V_24Y] :
( c_24__type__33224___24t(V_24Y)
<=> t(V_24Y,c_24__type__33224) ) ).
fof('$tdef_$_type_27511',axiom,
! [V_24Y] :
( c_24__type__27511___24t(V_24Y)
<=> t(V_24Y,c_24__type__27511) ) ).
fof('$tdef_$_type_19222',axiom,
! [V_24Y] :
( c_24__type__19222___24t(V_24Y)
<=> t(V_24Y,c_24__type__19222) ) ).
fof('$tdef_$_type_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_122327',axiom,
! [V_24Y] :
( c_24__type__122327___24t(V_24Y)
<=> t(V_24Y,c_24__type__122327) ) ).
fof('$tdef_$_type_66273',axiom,
! [V_24Y] :
( c_24__type__66273___24t(V_24Y)
<=> t(V_24Y,c_24__type__66273) ) ).
fof('$tdef_$_type_224',axiom,
! [V_24Y] :
( c_24__type__224___24t(V_24Y)
<=> t(V_24Y,c_24__type__224) ) ).
fof('$tdef_$_type_69019',axiom,
! [V_24Y] :
( c_24__type__69019___24t(V_24Y)
<=> t(V_24Y,c_24__type__69019) ) ).
fof('$tdef_$_type_16414',axiom,
! [V_24Y] :
( c_24__type__16414___24t(V_24Y)
<=> t(V_24Y,c_24__type__16414) ) ).
fof('$tdef_Coq.micromega.EnvRing.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_65010',axiom,
! [V_24Y] :
( c_24__type__65010___24t(V_24Y)
<=> t(V_24Y,c_24__type__65010) ) ).
fof('$tdef_$_type_31162',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31162___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31162___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_14506',axiom,
! [V_24Y] :
( c_24__type__14506___24t(V_24Y)
<=> t(V_24Y,c_24__type__14506) ) ).
fof('$tdef_$_type_13636',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13636___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13636___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13938',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__13938___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__13938___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32037',axiom,
! [V_24Y] :
( c_24__type__32037___24t(V_24Y)
<=> t(V_24Y,c_24__type__32037) ) ).
fof('$tdef_$_type_19307',axiom,
! [V_24Y] :
( c_24__type__19307___24t(V_24Y)
<=> t(V_24Y,c_24__type__19307) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_64831',axiom,
! [V_24Y] :
( c_24__type__64831___24t(V_24Y)
<=> t(V_24Y,c_24__type__64831) ) ).
fof('$tdef_$_type_58020',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__58020___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__58020___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_75243',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__75243___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__75243___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13253',axiom,
! [V_24Y] :
( c_24__type__13253___24t(V_24Y)
<=> t(V_24Y,c_24__type__13253) ) ).
fof('$tdef_$_type_31347',axiom,
! [V_24Y] :
( c_24__type__31347___24t(V_24Y)
<=> t(V_24Y,c_24__type__31347) ) ).
fof('$tdef_$_type_65891',axiom,
! [V_24Y] :
( c_24__type__65891___24t(V_24Y)
<=> t(V_24Y,c_24__type__65891) ) ).
fof('$tdef_$_type_64803',axiom,
! [V_24Y] :
( c_24__type__64803___24t(V_24Y)
<=> t(V_24Y,c_24__type__64803) ) ).
fof('$tdef_$_type_33256',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33256___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33256___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_13342',axiom,
! [V_24Y] :
( c_24__type__13342___24t(V_24Y)
<=> t(V_24Y,c_24__type__13342) ) ).
fof('$tdef_$_type_78426',axiom,
! [V_24Y] :
( c_24__type__78426___24t(V_24Y)
<=> t(V_24Y,c_24__type__78426) ) ).
fof('$tdef_$_type_94',axiom,
! [V_24Y] :
( c_24__type__94___24t(V_24Y)
<=> t(V_24Y,c_24__type__94) ) ).
fof('$tdef_$_type_65090',axiom,
! [V_24Y] :
( c_24__type__65090___24t(V_24Y)
<=> t(V_24Y,c_24__type__65090) ) ).
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_$_type_27529',axiom,
! [V_24Y] :
( c_24__type__27529___24t(V_24Y)
<=> t(V_24Y,c_24__type__27529) ) ).
fof('$tdef_$_type_65856',axiom,
! [V_24Y] :
( c_24__type__65856___24t(V_24Y)
<=> t(V_24Y,c_24__type__65856) ) ).
fof('$tdef_$_type_59300',axiom,
! [V_24Y] :
( c_24__type__59300___24t(V_24Y)
<=> t(V_24Y,c_24__type__59300) ) ).
fof('$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_57058',axiom,
! [V_24Y] :
( c_24__type__57058___24t(V_24Y)
<=> t(V_24Y,c_24__type__57058) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_60011',axiom,
! [V_24Y] :
( c_24__type__60011___24t(V_24Y)
<=> t(V_24Y,c_24__type__60011) ) ).
fof('$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_$_type_14520',axiom,
! [V_24Y] :
( c_24__type__14520___24t(V_24Y)
<=> t(V_24Y,c_24__type__14520) ) ).
fof('$tdef_$_type_14511',axiom,
! [V_24Y] :
( c_24__type__14511___24t(V_24Y)
<=> t(V_24Y,c_24__type__14511) ) ).
fof('$tdef_$_type_64792',axiom,
! [V_24Y] :
( c_24__type__64792___24t(V_24Y)
<=> t(V_24Y,c_24__type__64792) ) ).
fof('$tdef_$_type_64781',axiom,
! [V_24Y] :
( c_24__type__64781___24t(V_24Y)
<=> t(V_24Y,c_24__type__64781) ) ).
fof('$tdef_$_type_65086',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__65086___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__65086___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19090',axiom,
! [V_24Y] :
( c_24__type__19090___24t(V_24Y)
<=> t(V_24Y,c_24__type__19090) ) ).
fof('$tdef_$_type_57068',axiom,
! [V_24Y] :
( c_24__type__57068___24t(V_24Y)
<=> t(V_24Y,c_24__type__57068) ) ).
fof('$tdef_$_type_31198',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31198___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31198___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33376',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33376___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33376___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_66267',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__66267___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__66267___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35607',axiom,
! [V_24Y] :
( c_24__type__35607___24t(V_24Y)
<=> t(V_24Y,c_24__type__35607) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31242',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__31242___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__31242___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_33358',axiom,
! [V_24Y] :
( c_24__type__33358___24t(V_24Y)
<=> t(V_24Y,c_24__type__33358) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_64800',axiom,
! [V_24Y] :
( c_24__type__64800___24t(V_24Y)
<=> t(V_24Y,c_24__type__64800) ) ).
fof('$tdef_$_type_65977',axiom,
! [V_24Y] :
( c_24__type__65977___24t(V_24Y)
<=> t(V_24Y,c_24__type__65977) ) ).
fof('$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_$_type_32024',axiom,
! [V_24Y] :
( c_24__type__32024___24t(V_24Y)
<=> t(V_24Y,c_24__type__32024) ) ).
fof('$tdef_$_type_64811',axiom,
! [V_24Y] :
( c_24__type__64811___24t(V_24Y)
<=> t(V_24Y,c_24__type__64811) ) ).
fof('$tdef_$_type_66278',axiom,
! [V_24Y] :
( c_24__type__66278___24t(V_24Y)
<=> t(V_24Y,c_24__type__66278) ) ).
fof('$tdef_$_type_19157',axiom,
! [V_24Y] :
( c_24__type__19157___24t(V_24Y)
<=> t(V_24Y,c_24__type__19157) ) ).
fof('$tdef_$_type_77716',axiom,
! [V_24X1,V_24Y] :
( c_24__type__77716___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__77716___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13861',axiom,
! [V_24Y] :
( c_24__type__13861___24t(V_24Y)
<=> t(V_24Y,c_24__type__13861) ) ).
fof('$tdef_$_type_97',axiom,
! [V_24X1,V_24Y] :
( c_24__type__97___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__97___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13315',axiom,
! [V_24Y] :
( c_24__type__13315___24t(V_24Y)
<=> t(V_24Y,c_24__type__13315) ) ).
fof('$tdef_$_type_14243',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14243___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14243___24a1(V_24X1)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_Coq.Reals.Ranalysis1.derivable_pt',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34695',axiom,
! [V_24Y] :
( c_24__type__34695___24t(V_24Y)
<=> t(V_24Y,c_24__type__34695) ) ).
fof('$tdef_$_type_66243',axiom,
! [V_24Y] :
( c_24__type__66243___24t(V_24Y)
<=> t(V_24Y,c_24__type__66243) ) ).
fof('$tdef_$_type_14503',axiom,
! [V_24Y] :
( c_24__type__14503___24t(V_24Y)
<=> t(V_24Y,c_24__type__14503) ) ).
fof('$tdef_$_type_77723',axiom,
! [V_24Y] :
( c_24__type__77723___24t(V_24Y)
<=> t(V_24Y,c_24__type__77723) ) ).
fof('$tdef_$_type_80536',axiom,
! [V_24Y] :
( c_24__type__80536___24t(V_24Y)
<=> t(V_24Y,c_24__type__80536) ) ).
fof('$tdef_$_type_60500',axiom,
! [V_24Y] :
( c_24__type__60500___24t(V_24Y)
<=> t(V_24Y,c_24__type__60500) ) ).
fof('$tdef_$_type_64778',axiom,
! [V_24Y] :
( c_24__type__64778___24t(V_24Y)
<=> t(V_24Y,c_24__type__64778) ) ).
fof('$tdef_$_type_16386',axiom,
! [V_24Y] :
( c_24__type__16386___24t(V_24Y)
<=> t(V_24Y,c_24__type__16386) ) ).
fof('$tdef_$_type_57106',axiom,
! [V_24Y] :
( c_24__type__57106___24t(V_24Y)
<=> t(V_24Y,c_24__type__57106) ) ).
fof('$tdef_$_type_13335',axiom,
! [V_24Y] :
( c_24__type__13335___24t(V_24Y)
<=> t(V_24Y,c_24__type__13335) ) ).
fof('$tdef_$_type_525',axiom,
! [V_24Y] :
( c_24__type__525___24t(V_24Y)
<=> t(V_24Y,c_24__type__525) ) ).
fof('$tdef_$_type_25',axiom,
! [V_24Y] :
( c_24__type__25___24t(V_24Y)
<=> t(V_24Y,c_24__type__25) ) ).
fof('$tdef_$_type_14254',axiom,
! [V_24Y] :
( c_24__type__14254___24t(V_24Y)
<=> t(V_24Y,c_24__type__14254) ) ).
fof('$tdef_$_type_65985',axiom,
! [V_24Y] :
( c_24__type__65985___24t(V_24Y)
<=> t(V_24Y,c_24__type__65985) ) ).
fof('$tdef_$_type_245',axiom,
! [V_24Y] :
( c_24__type__245___24t(V_24Y)
<=> t(V_24Y,c_24__type__245) ) ).
fof('_HAMMER_GOAL',conjecture,
! [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_2eReals_2eRdefinitions_2eRge___24a2(cArithCompl_2efrac___24a2(V0__a,V1__b),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cArithCompl_2efrac___24a2(V0__a,V1__b),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__b,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__a,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_2ele___24a2(V1__b,V0__a)) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------