TPTP Problem File: SEV665+1.p
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%------------------------------------------------------------------------------
% File : SEV665+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Pythagorean rat pos coo1
% 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 : Pythagorean.rat.pos.coo1.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2987 (1241 unt; 0 def)
% Number of atoms : 9158 (2465 equ)
% Maximal formula atoms : 82 ( 3 avg)
% Number of connectives : 6346 ( 175 ~; 347 |;1326 &)
% ( 969 <=>;3529 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 6 avg)
% Maximal term depth : 23 ( 2 avg)
% Number of predicates : 491 ( 490 usr; 0 prp; 1-23 aty)
% Number of functors : 1622 (1622 usr; 930 con; 0-22 aty)
% Number of variables : 9061 (8556 !; 505 ?)
% 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$2694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__2656__2666__2668__2690___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242694___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),c_24__let__var__var__var__6__r_27__2656__2666__2668__2690___24a1(Vv__CANONICAL__2)) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__2656__2666__2668__2690___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242694___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(c_24__let__var__var__var__6__r_27__2656__2666__2668__2690___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$2700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__2674__2684__2686__2696___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242700___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),c_24__let__var__var__var__6__r_27__2674__2684__2686__2696___24a1(Vv__CANONICAL__2)) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__var__var__6__r_27__2674__2684__2686__2696___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242700___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__1),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(c_24__let__var__var__var__6__r_27__2674__2684__2686__2696___24a1(Vv__CANONICAL__2),Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$74835',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( c_24__type__74836___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__74812__74828___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474835___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__7__down__74810__74826___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) )
| ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__74812__74828___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474835___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__9__z__74812__74828___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$74864',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( c_24__type__74836___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__74841__74857___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474864___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__9__z__74841__74857___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) )
| ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__74841__74857___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474864___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__8__up__74840__74856___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$74902',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( c_24__type__74836___24t(Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__74879__74895___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474902___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__7__down__74877__74893___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) )
| ( happ(Vv__CANONICAL__2,c_24__let__var__9__z__74879__74895___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474902___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__let__var__9__z__74879__74895___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$78081',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__5__r_27__78062__78078___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478081___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__let__var__5__r_27__78062__78078___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__5__r_27__78062__78078___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478081___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(c_24__let__var__5__r_27__78062__78078___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$78089',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__5__r_27__78069__78086___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478089___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__let__var__5__r_27__78069__78086___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(c_24__let__var__5__r_27__78069__78086___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478089___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(c_24__let__var__5__r_27__78069__78086___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.comparison$30477',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eEq
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2430477___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eLt
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2430477___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eGt
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2430477___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$15',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__20] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__20)
& ? [Vvar__3___24Anonymous__21] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__21)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__20,Vvar__3___24Anonymous__21)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( Vvar__3___24Anonymous__21 != cCoq_2eNumbers_2eBinNums_2eZ0
& Vv__CANONICAL__0 = cFermat4_2eArithCompl_2efrac___24a2(Vvar__2___24Anonymous__20,Vvar__3___24Anonymous__21) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$32',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__1)
=> ? [Vvar__2___24Anonymous__37] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__37)
& ? [Vvar__3___24Anonymous__38] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__38)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__37,Vvar__3___24Anonymous__38)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(Vvar__2___24Anonymous__37,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vvar__3___24Anonymous__38,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__2___24Anonymous__37,Vvar__3___24Anonymous__38))
& p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__2___24Anonymous__37,Vvar__3___24Anonymous__38))
& Vv__CANONICAL__0 = cFermat4_2eArithCompl_2efrac___24a2(Vvar__2___24Anonymous__37,Vvar__3___24Anonymous__38) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sig$15484',axiom,
? [Vvar__2__x__15493] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__15493)
& c_24__lam__15479___24a1(Vvar__2__x__15493)
& cCoq_2eReals_2eAltSeries_2eexist__PI = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__15479,Vvar__2__x__15493)
& c_24__case__Coq_2eInit_2eSpecif_2esig_2415484 = Vvar__2__x__15493 ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$38069',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__19)
=> ( ? [Vvar__1___24Anonymous__38072] :
( t(Vvar__1___24Anonymous__38072,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__18516___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__11)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( t(Vvar__1___24Anonymous__38072,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__38072)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__38072),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2438069___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = c_24__let__20__lnum__37765___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18) )
| ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__38072),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2438069___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__37765___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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__19)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__38075] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__38075)
& ? [Vvar__2___24Anonymous__38076] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__38076)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__38075,Vvar__2___24Anonymous__38076)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2438069___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__37765___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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__19)) ) )
| ? [Vvar__1___24Anonymous__38079] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__38079)
& ? [Vvar__2___24Anonymous__38080] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__38080)
& ? [Vvar__3___24Anonymous__38081] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__38081)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__38079,Vvar__2___24Anonymous__38080,Vvar__3___24Anonymous__38081)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2438069___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__37765___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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__19)) ) ) ) ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_2044',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__2044___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_33075',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__33078] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33078)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__33078)
& c_24__let__16__mkpow__33075___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__33079] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33079)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__33079)
& c_24__let__16__mkpow__33075___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__33075___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_33076',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__33076___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__33075___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_33077',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__33077___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__33075___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_1_den_35032',axiom,
! [V0__r] : c_24__let__1__den__35032___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r)) ).
fof('$_def_$_let_20_lnum_37765',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num] : c_24__let__20__lnum__37765___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) ).
fof('$_def_$_let_2_pr_78053',axiom,
! [V0__p] : c_24__let__2__pr__78053___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__p) ).
fof('$_def_$_let_3_qr_78054',axiom,
! [V1__q] : c_24__let__3__qr__78054___24a1(V1__q) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__q) ).
fof('$_def_$_let_4_den_78055',axiom,
! [V0__p,V1__q] : c_24__let__4__den__78055___24a2(V0__p,V1__q) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(c_24__let__2__pr__78053___24a1(V0__p),c_24__let__2__pr__78053___24a1(V0__p)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(c_24__let__3__qr__78054___24a1(V1__q),c_24__let__3__qr__78054___24a1(V1__q))) ).
fof('$_def_$_let_6_lmp_1595',axiom,
! [V2__lpe] : c_24__let__6__lmp__1595___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_6_lmp_20439',axiom,
! [V2__lpe] : c_24__let__6__lmp__20439___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_var_11_x_1268_1318',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1267] : c_24__let__var__11__x__1268__1318___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1267) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1267) ).
fof('$_def_$_let_var_11_x_1271_1319',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1270] : c_24__let__var__11__x__1271__1319___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1270) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1270) ).
fof('$_def_$_let_var_4_r_78061_78077',axiom,
! [V2__b,Vvar__0___24Anonymous__78060] : c_24__let__var__4__r__78061__78077___24a2(V2__b,Vvar__0___24Anonymous__78060) = cCoq_2eZArith_2eZdiv_2eZmod__POS___24a2(Vvar__0___24Anonymous__78060,V2__b) ).
fof('$_def_$_let_var_4_r_78068_78085',axiom,
! [V2__b,Vvar__0___24Anonymous__78067] : c_24__let__var__4__r__78068__78085___24a2(V2__b,Vvar__0___24Anonymous__78067) = cCoq_2eZArith_2eZdiv_2eZmod__POS___24a2(Vvar__0___24Anonymous__78067,V2__b) ).
fof('$_def_$_let_var_5_r\'_78062_78078',axiom,
! [V2__b,Vvar__0___24Anonymous__78060] : c_24__let__var__5__r_27__78062__78078___24a2(V2__b,Vvar__0___24Anonymous__78060) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),c_24__let__var__4__r__78061__78077___24a2(V2__b,Vvar__0___24Anonymous__78060)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_$_let_var_5_r\'_78069_78086',axiom,
! [V2__b,Vvar__0___24Anonymous__78067] : c_24__let__var__5__r_27__78069__78086___24a2(V2__b,Vvar__0___24Anonymous__78067) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),c_24__let__var__4__r__78068__78085___24a2(V2__b,Vvar__0___24Anonymous__78067)) ).
fof('$_def_$_let_var_6_p_31783_31786',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31782] : c_24__let__var__6__p__31783__31786___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31782) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31782) ).
fof('$_def_$_let_var_6_p_31785_31787',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31784] : c_24__let__var__6__p__31785__31787___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31784) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31784) ).
fof('$_def_$_let_var_7_down_74810_74826',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809] : c_24__let__var__7__down__74810__74826___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809) ).
fof('$_def_$_let_var_7_down_74839_74855',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838] : c_24__let__var__7__down__74839__74855___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838) ).
fof('$_def_$_let_var_7_down_74877_74893',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876] : c_24__let__var__7__down__74877__74893___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876) = c_24__fix__74875__0__Dichotomy__lb___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876) ).
fof('$_def_$_let_var_8_up_74811_74827',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809] : c_24__let__var__8__up__74811__74827___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809) = c_24__fix__74808__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809) ).
fof('$_def_$_let_var_8_up_74840_74856',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838] : c_24__let__var__8__up__74840__74856___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838) = c_24__fix__74808__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838) ).
fof('$_def_$_let_var_8_up_74878_74894',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876] : c_24__let__var__8__up__74878__74894___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876) ).
fof('$_def_$_let_var_9_z_74812_74828',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809] : c_24__let__var__9__z__74812__74828___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(c_24__let__var__7__down__74810__74826___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809),c_24__let__var__8__up__74811__74827___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('$_def_$_let_var_9_z_74841_74857',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838] : c_24__let__var__9__z__74841__74857___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(c_24__let__var__7__down__74839__74855___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838),c_24__let__var__8__up__74840__74856___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('$_def_$_let_var_9_z_74879_74895',axiom,
! [V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876] : c_24__let__var__9__z__74879__74895___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(c_24__let__var__7__down__74877__74893___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876),c_24__let__var__8__up__74878__74894___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('$_def_$_let_var_v_CANONICAL_4_48951_48954',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__48950] : c_24__let__var__v__CANONICAL__4__48951__48954___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__48950) = happ(Vv__CANONICAL__1,Vvar__0___24Anonymous__48950) ).
fof('$_def_$_let_var_var_12_x_1226_1229_1299',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223] : c_24__let__var__var__12__x__1226__1229__1299___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223) ).
fof('$_def_$_let_var_var_12_x_1239_1242_1305',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236] : c_24__let__var__var__12__x__1239__1242__1305___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236) ).
fof('$_def_$_let_var_var_12_x_1252_1256_1314',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249] : c_24__let__var__var__12__x__1252__1256__1314___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249) ).
fof('$_def_$_let_var_var_12_x_1276_1280_1326',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273] : c_24__let__var__var__12__x__1276__1280__1326___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273) ).
fof('$_def_$_let_var_var_12_x_1293_1295_1330',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1291] : c_24__let__var__var__12__x__1293__1295__1330___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1291) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1291) ).
fof('$_def_$_let_var_var_13_y_1227_1230_1300',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1224] : c_24__let__var__var__13__y__1227__1230__1300___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1224) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1224) ).
fof('$_def_$_let_var_var_13_y_1240_1243_1306',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1237] : c_24__let__var__var__13__y__1240__1243__1306___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1237) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1237) ).
fof('$_def_$_let_var_var_13_y_1253_1257_1315',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1250] : c_24__let__var__var__13__y__1253__1257__1315___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1250) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1250) ).
fof('$_def_$_let_var_var_13_y_1277_1281_1327',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1274] : c_24__let__var__var__13__y__1277__1281__1327___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1274) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1274) ).
fof('$_def_$_let_var_var_14_s1_1254_1258_1316',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250] : c_24__let__var__var__14__s1__1254__1258__1316___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__1252__1256__1314___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__1253__1257__1315___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1250))) ).
fof('$_def_$_let_var_var_14_s1_1278_1282_1328',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274] : c_24__let__var__var__14__s1__1278__1282__1328___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__1276__1280__1326___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__1277__1281__1327___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1274))) ).
fof('$_def_$_let_var_var_14_s_1228_1231_1301',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224] : c_24__let__var__var__14__s__1228__1231__1301___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__1226__1229__1299___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__1227__1230__1300___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1224))) ).
fof('$_def_$_let_var_var_14_s_1241_1244_1307',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237] : c_24__let__var__var__14__s__1241__1244__1307___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__1239__1242__1305___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__1240__1243__1306___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1237))) ).
fof('$_def_$_let_var_var_15_s2_1255_1259_1317',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250] : c_24__let__var__var__15__s2__1255__1259__1317___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__1253__1257__1315___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1250)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__1252__1256__1314___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249))) ).
fof('$_def_$_let_var_var_15_s2_1279_1283_1329',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274] : c_24__let__var__var__15__s2__1279__1283__1329___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__1276__1280__1326___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__1277__1281__1327___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1274))) ).
fof('$_def_$_let_var_var_var_6_r\'_2656_2666_2668_2690',axiom,
! [Vvar__3___24Anonymous__2664] : c_24__let__var__var__var__6__r_27__2656__2666__2668__2690___24a1(Vvar__3___24Anonymous__2664) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vvar__3___24Anonymous__2664),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_$_let_var_var_var_6_r\'_2674_2684_2686_2696',axiom,
! [Vvar__3___24Anonymous__2682] : c_24__let__var__var__var__6__r_27__2674__2684__2686__2696___24a1(Vvar__3___24Anonymous__2682) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vvar__3___24Anonymous__2682) ).
fof('$_def_Coq.Arith.Compare_dec.le_gt_dec',axiom,
! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V0__n,V1__m) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V0__n,V1__m) ).
fof('$_def_Coq.Arith.Compare_dec.lt_eq_lt_dec',axiom,
! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2elt__eq__lt__dec___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2enat__rec___24a5(c_24__lam__48897,c_24__lam__48904,c_24__lam__48949,V0__n,V1__m) ).
fof('$_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__30666] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30666)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30666)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30666),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__30666)) ) ) ) ).
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__274] :
( t(Vvar__1___24Anonymous__274,V0__A)
& ? [Vvar__2___24Anonymous__275] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__275)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__274,Vvar__2___24Anonymous__275)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__274,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__275,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__30567] :
( t(Vvar__2___24Anonymous__30567,V0__A)
& ? [Vvar__3___24Anonymous__30568] :
( t(Vvar__3___24Anonymous__30568,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__30567,Vvar__3___24Anonymous__30568)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__30567 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__30579] :
( t(Vvar__1___24Anonymous__30579,V0__A)
& ? [Vvar__2___24Anonymous__30580] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__30580)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__30579,Vvar__2___24Anonymous__30580)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__30580)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__30513___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__30511] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30511)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30511)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__30511),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__30511)) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__2594] :
( t(Vvar__2___24Anonymous__2594,V0__A)
& ? [Vvar__3___24Anonymous__2595] :
( t(Vvar__3___24Anonymous__2595,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__2594,Vvar__3___24Anonymous__2595)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__2595 ) ) ) ) ) ).
fof('$_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__18964] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18964)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18964)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__18964,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__71010] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__71010)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__71010)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__71010)
& ( ( Vvar__0___24Anonymous__71010 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__71013] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__71013)
& Vvar__0___24Anonymous__71010 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__71013)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__71013)) ) ) ) ) ) ) ) ).
fof('$_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__18978] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18978)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18978)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__18981] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18981)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18981)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__18978,Vvar__0___24Anonymous__18981)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__31490] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31490)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31490)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__31490,V2__m)) ) ) ) ).
fof('$_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__31488] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31488)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31488)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__31488 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__31493] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31493)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31493)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__31496] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31496)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31496)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__31493,Vvar__0___24Anonymous__31496) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__25959___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__25953] :
( t(Vvar__2__x__25953,V0__A)
& p(happ(V1__P,Vvar__2__x__25953))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__25953)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__25953 ) ) ) ) ).
fof('$_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.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__51699] :
( t(Vvar__1___24Anonymous__51699,V0__A)
& ? [Vvar__2___24Anonymous__51700] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__51700)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__51699,Vvar__2___24Anonymous__51700)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__51699 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__51700) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__29810] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29810)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29810)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__29813] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29813)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29813)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29810,Vvar__0___24Anonymous__29813)) ) ) ) ) ) ) ) ).
fof('$_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__29848] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29848)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29848)
& ( ( 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__29851] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29851)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29851)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__29848,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__29839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29839)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29839)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__29840] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29840)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29840)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__29843] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29843)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29843)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__29840,Vvar__0___24Anonymous__29843) ) ) ) ) ) ) ) ).
fof('$_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__29825] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29825)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29825)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__29828] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29828)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29828)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29825,Vvar__0___24Anonymous__29828)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__32749] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32749)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32749)
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__32749)) ) ) ) ).
fof('$_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__2517] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2517)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2517)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__2517) ) ) ) ).
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__29864] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29864)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29864)
& ( ? [Vvar__0___24Anonymous__29868] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29868)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29868)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29863__1__add__carry___24a2(Vvar__0___24Anonymous__29864,Vvar__0___24Anonymous__29868)) )
| ? [Vvar__0___24Anonymous__29869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29869)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29869)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29864,Vvar__0___24Anonymous__29869)) )
| ( 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__29864)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29870] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29870)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29870)
& ( ? [Vvar__0___24Anonymous__29874] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29874)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29874)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29870,Vvar__0___24Anonymous__29874)) )
| ? [Vvar__0___24Anonymous__29875] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29875)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29875)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29870,Vvar__0___24Anonymous__29875)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29870) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__29876] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29876)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29876)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29876)) )
| ? [Vvar__0___24Anonymous__29877] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29877)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29877)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29877) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.gcd',axiom,
! [V0__a,V1__b] : cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V0__a,V1__b) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcdn___24a3(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V0__a),cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__b)),V0__a,V1__b) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.ggcd',axiom,
! [V0__a,V1__b] : cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(V0__a,V1__b) = cCoq_2ePArith_2eBinPosDef_2ePos_2eggcdn___24a3(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V0__a),cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__b)),V0__a,V1__b) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__29898] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29898)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29898)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29898,V2__y))) )
| ? [Vvar__0___24Anonymous__29899] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29899)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29899)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29899,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_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__32808] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32808)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32808)
& 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__32808)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__29895] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29895)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29895)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__29895 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.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('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__20112] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__20112)
& ? [Vvar__1__Qden__20113] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__20113)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__20112,Vvar__1__Qden__20113)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__20113 ) ) ) ).
fof('$_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('$_def_Coq.QArith.QArith_base.Qeq_bool',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))) ).
fof('$_def_Coq.QArith.QArith_base.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__20129] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20129)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20129)
& 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__20129) )
| ? [Vvar__0___24Anonymous__20130] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20130)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__20130)
& 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__20130) ) ) ) ).
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__20107] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__20107)
& ? [Vvar__1__Qden__20108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__20108)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__20107,Vvar__1__Qden__20108)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__20107 ) ) ) ).
fof('$_def_Coq.QArith.Qreals.Q2R',axiom,
! [V0__x] : cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x)),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ).
fof('$_def_Coq.Reals.AltSeries.Alt_PI',axiom,
cCoq_2eReals_2eAltSeries_2eAlt__PI = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),c_24__case__Coq_2eInit_2eSpecif_2esig_2415484) ).
fof('$_def_Coq.Reals.AltSeries.PI_tg',axiom,
! [V0__n] : cCoq_2eReals_2eAltSeries_2ePI__tg___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ).
fof('$_def_Coq.Reals.AltSeries.positivity_seq',axiom,
! [V0__Un] :
( cCoq_2eReals_2eAltSeries_2epositivity__seq___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__Un,V1__n))) ) ) ).
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.Cos_plus.Majxy',axiom,
! [V0__x,V1__y,V2__n] : cCoq_2eReals_2eCos__plus_2eMajxy___24a3(V0__x,V1__y,V2__n) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y))),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_2eO)))),cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(V2__n))) ).
fof('$_def_Coq.Reals.Machin.atan_sub',axiom,
! [V0__u,V1__v] : cCoq_2eReals_2eMachin_2eatan__sub___24a2(V0__u,V1__v) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__u,V1__v),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__u,V1__v))) ).
fof('$_def_Coq.Reals.NewtonInt.Newton_integrable',axiom,
! [V0__f,V1__a,V2__b] : cCoq_2eReals_2eNewtonInt_2eNewton__integrable___24a3(V0__f,V1__a,V2__b) = cCoq_2eInit_2eSpecif_2esig___24a2(c_24__type__1601,c_24__lam__31510___24a3(V0__f,V1__a,V2__b)) ).
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.PSeries_reg.CVN_R',axiom,
! [V0__fn] : cCoq_2eReals_2ePSeries__reg_2eCVN__R___24a1(V0__fn) = c_24__type__76347___24a1(V0__fn) ).
fof('$_def_Coq.Reals.PSeries_reg.CVN_r',axiom,
! [V0__fn,V1__r] : cCoq_2eReals_2ePSeries__reg_2eCVN__r___24a2(V0__fn,V1__r) = cCoq_2eInit_2eSpecif_2esigT___24a2(c_24__type__3682,c_24__lam__77001___24a2(V0__fn,V1__r)) ).
fof('$_def_Coq.Reals.PSeries_reg.CVU',axiom,
! [V0__fn,V1__f,V2__x,V3__r] :
( cCoq_2eReals_2ePSeries__reg_2eCVU___24a4(V0__fn,V1__f,V2__x,V3__r)
<=> ! [V4__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V4__eps))
=> ? [V6__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__N)
& ! [V7__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__n)
=> ! [V8__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__y)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V6__N,V7__n))
=> ( cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(V2__x,V3__r,V8__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V1__f,V8__y),happ(happ(V0__fn,V7__n),V8__y))),V4__eps)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.PartSum.SP',axiom,
! [V0__fn,V1__N,V2__x] : cCoq_2eReals_2ePartSum_2eSP___24a3(V0__fn,V1__N,V2__x) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__31516___24a2(V0__fn,V2__x),V1__N) ).
fof('$_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('$_def_Coq.Reals.RIneq.nonneg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__n)
=> ? [Vvar__0__nonneg__71169] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__71169)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__71169))
& V0__n = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__71169)
& cCoq_2eReals_2eRIneq_2enonneg___24a1(V0__n) = Vvar__0__nonneg__71169 ) ) ).
fof('$_def_Coq.Reals.RIneq.nonpos',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V0__n)
=> ? [Vvar__0__nonpos__98168] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__98168)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__98168,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& V0__n = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__98168)
& cCoq_2eReals_2eRIneq_2enonpos___24a1(V0__n) = Vvar__0__nonpos__98168 ) ) ).
fof('$_def_Coq.Reals.RIneq.nonzero',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V0__n)
=> ? [Vvar__0__nonzero__61965] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__61965)
& Vvar__0__nonzero__61965 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V0__n = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__61965)
& cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__n) = Vvar__0__nonzero__61965 ) ) ).
fof('$_def_Coq.Reals.RIneq.pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> ? [Vvar__0__pos__20153] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__20153)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__20153))
& V0__p = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__20153)
& cCoq_2eReals_2eRIneq_2epos___24a1(V0__p) = Vvar__0__pos__20153 ) ) ).
fof('$_def_Coq.Reals.RList.In',axiom,
! [V1__x,V2__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V2__l)
=> ( ( V2__l = cCoq_2eReals_2eRList_2enil
& ( cCoq_2eReals_2eRList_2eIn___24a2(V1__x,V2__l)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__31585] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__31585)
& ? [Vvar__1___24Anonymous__31586] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__31586)
& V2__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__31585,Vvar__1___24Anonymous__31586)
& ( cCoq_2eReals_2eRList_2eIn___24a2(V1__x,V2__l)
<=> ( V1__x = Vvar__0___24Anonymous__31585
| cCoq_2eReals_2eRList_2eIn___24a2(V1__x,Vvar__1___24Anonymous__31586) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.MinRlist',axiom,
! [V1__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eMinRlist___24a1(V1__l) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__76401] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__76401)
& ? [Vvar__1___24Anonymous__76402] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__76402)
& ( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__76402)
=> ( V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__76401,Vvar__1___24Anonymous__76402)
& ( ( Vvar__1___24Anonymous__76402 = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eMinRlist___24a1(V1__l) = Vvar__0___24Anonymous__76401 )
| ? [Vvar__0___24Anonymous__76410] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__76410)
& ? [Vvar__1___24Anonymous__76411] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__76411)
& Vvar__1___24Anonymous__76402 = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__76410,Vvar__1___24Anonymous__76411)
& cCoq_2eReals_2eRList_2eMinRlist___24a1(V1__l) = cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(Vvar__0___24Anonymous__76401,cCoq_2eReals_2eRList_2eMinRlist___24a1(Vvar__1___24Anonymous__76402)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.Rlength',axiom,
! [V1__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eRlength___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__61971] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__61971)
& ? [Vvar__1___24Anonymous__61972] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__61972)
& V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__61971,Vvar__1___24Anonymous__61972)
& cCoq_2eReals_2eRList_2eRlength___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eReals_2eRList_2eRlength___24a1(Vvar__1___24Anonymous__61972)) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.mid_Rlist',axiom,
! [V1__l,V2__x] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2emid__Rlist___24a2(V1__l,V2__x) = cCoq_2eReals_2eRList_2enil )
| ? [Vvar__0___24Anonymous__71220] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__71220)
& ? [Vvar__1___24Anonymous__71221] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__71221)
& V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__71220,Vvar__1___24Anonymous__71221)
& cCoq_2eReals_2eRList_2emid__Rlist___24a2(V1__l,V2__x) = cCoq_2eReals_2eRList_2econs___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__x,Vvar__0___24Anonymous__71220),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRList_2emid__Rlist___24a2(Vvar__1___24Anonymous__71221,Vvar__0___24Anonymous__71220)) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.pos_Rl',axiom,
! [V1__l,V2__i] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__61977] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__61977)
& ? [Vvar__1___24Anonymous__61978] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__61978)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ( V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__61977,Vvar__1___24Anonymous__61978)
& ( ( V2__i = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = Vvar__0___24Anonymous__61977 )
| ? [Vvar__0___24Anonymous__61984] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__61984)
& V2__i = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__61984)
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = cCoq_2eReals_2eRList_2epos__Rl___24a2(Vvar__1___24Anonymous__61978,Vvar__0___24Anonymous__61984) ) ) ) ) ) ) ) ) ).
fof('$_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.Delta',axiom,
! [V0__a,V1__b,V2__c] : cCoq_2eReals_2eR__sqrt_2eDelta___24a3(V0__a,V1__b,V2__c) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__b),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__a)),V2__c)) ).
fof('$_def_Coq.Reals.R_sqrt.Delta_is_pos',axiom,
! [V0__a,V1__b,V2__c] :
( cCoq_2eReals_2eR__sqrt_2eDelta__is__pos___24a3(V0__a,V1__b,V2__c)
<=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2eDelta___24a3(V0__a,V1__b,V2__c))) ) ).
fof('$_def_Coq.Reals.R_sqrt.sol_x1',axiom,
! [V0__a,V1__b,V2__c] : cCoq_2eReals_2eR__sqrt_2esol__x1___24a3(V0__a,V1__b,V2__c) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__b),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eR__sqrt_2eDelta___24a3(V0__a,V1__b,V2__c))),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_2eRIneq_2enonzero___24a1(V0__a))) ).
fof('$_def_Coq.Reals.R_sqrt.sol_x2',axiom,
! [V0__a,V1__b,V2__c] : cCoq_2eReals_2eR__sqrt_2esol__x2___24a3(V0__a,V1__b,V2__c) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__b),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eR__sqrt_2eDelta___24a3(V0__a,V1__b,V2__c))),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__a))) ).
fof('$_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('$_def_Coq.Reals.Ranalysis1.antiderivative',axiom,
! [V0__f,V1__g,V2__a,V3__b] :
( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V0__f,V1__g,V2__a,V3__b)
<=> ( ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__x,V3__b)) )
=> ? [V6__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__g,V4__x,V6__pr)
& happ(V0__f,V4__x) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V4__x,V6__pr) ) ) )
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V3__b)) ) ) ).
fof('$_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('$_def_Coq.Reals.Ranalysis1.constant',axiom,
! [V0__f] :
( cCoq_2eReals_2eRanalysis1_2econstant___24a1(V0__f)
<=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> happ(V0__f,V1__x) = happ(V0__f,V2__y) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.constant_D_eq',axiom,
! [V0__f,V1__D,V2__c] :
( cCoq_2eReals_2eRanalysis1_2econstant__D__eq___24a3(V0__f,V1__D,V2__c)
<=> ! [V3__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__x)
=> ( p(happ(V1__D,V3__x))
=> happ(V0__f,V3__x) = V2__c ) ) ) ).
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('$_def_Coq.Reals.Ranalysis1.decreasing',axiom,
! [V0__f] :
( cCoq_2eReals_2eRanalysis1_2edecreasing___24a1(V0__f)
<=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__x,V2__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__y),happ(V0__f,V1__x))) ) ) ) ) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable',axiom,
! [V0__f] : cCoq_2eReals_2eRanalysis1_2ederivable___24a1(V0__f) = c_24__type__31631___24a1(V0__f) ).
fof('$_def_Coq.Reals.Ranalysis1.derivable_pt',axiom,
! [V0__f,V1__x] : cCoq_2eReals_2eRanalysis1_2ederivable__pt___24a2(V0__f,V1__x) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__31626___24a2(V0__f,V1__x)) ).
fof('$_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__31626___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.increasing',axiom,
! [V0__f] :
( cCoq_2eReals_2eRanalysis1_2eincreasing___24a1(V0__f)
<=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__x,V2__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V1__x),happ(V0__f,V2__y))) ) ) ) ) ).
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.Ranalysis1.opp_fct',axiom,
! [V0__f,V1__x] : cCoq_2eReals_2eRanalysis1_2eopp__fct___24a2(V0__f,V1__x) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(happ(V0__f,V1__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.plus_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.pow_fct',axiom,
! [V0__n,V1__y] : cCoq_2eReals_2eRanalysis1_2epow__fct___24a2(V0__n,V1__y) = cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V0__n) ).
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('$_def_Coq.Reals.Ratan.atan',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__71925] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__71925)
& c_24__lam__71916___24a2(V0__x,Vvar__2__x__71925)
& cCoq_2eReals_2eRatan_2epre__atan___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__71916___24a1(V0__x),Vvar__2__x__71925)
& cCoq_2eReals_2eRatan_2eatan___24a1(V0__x) = Vvar__2__x__71925 ) ) ).
fof('$_def_Coq.Reals.Ratan.pos_half',axiom,
cCoq_2eReals_2eRatan_2epos__half = cCoq_2eReals_2eRIneq_2emkposreal___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRatan_2epos__half__prf) ).
fof('$_def_Coq.Reals.Ratan.ps_atan',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
& ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> ( cCoq_2eReals_2eRatan_2ein__int___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__20372___24a1(V0__x),c_24__prop__20373___24a1(V0__x))
& ? [Vvar__2__x__20365] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__20365)
& c_24__lam__20377___24a2(V0__x,Vvar__2__x__20365)
& cCoq_2eReals_2eRatan_2eps__atan__exists__1___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__20377___24a1(V0__x),Vvar__2__x__20365)
& cCoq_2eReals_2eRatan_2eps__atan___24a1(V0__x) = Vvar__2__x__20365 ) ) ) ) )
| ( ~ ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
& cCoq_2eReals_2eRatan_2ein__int___24a1(V0__x) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__20385___24a1(V0__x),c_24__prop__20386___24a1(V0__x))
& cCoq_2eReals_2eRatan_2eps__atan___24a1(V0__x) = cCoq_2eReals_2eRatan_2eatan___24a1(V0__x) ) ) ) ).
fof('$_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('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__20390] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20390)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20390)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20390)
& ( ( Vvar__0___24Anonymous__20390 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__20393] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20393)
& Vvar__0___24Anonymous__20390 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20393)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__20390),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_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__20417___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__20418___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V0__x ) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmin',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__20406___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V0__x )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__20407___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V1__y ) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IPR',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__76546] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76546)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__76546)
& 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__76546)) )
| ? [Vvar__0___24Anonymous__76547] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76547)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__76547)
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__76547) )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eR1 ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IPR_2',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__20430] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20430)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20430)
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__20430))) )
| ? [Vvar__0___24Anonymous__20431] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20431)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20431)
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1),cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__20431)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V1__p) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eR1) ) ) ) ).
fof('$_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__110] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__110)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__110)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__110) )
| ? [Vvar__0___24Anonymous__111] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__111)) ) ) ) ).
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_in',axiom,
! [V0__f,V1__d,V2__D,V3__x0] :
( cCoq_2eReals_2eRderiv_2eD__in___24a4(V0__f,V1__d,V2__D,V3__x0)
<=> cCoq_2eReals_2eRlimit_2elimit1__in___24a4(c_24__lam__71995___24a2(V0__f,V3__x0),cCoq_2eReals_2eRderiv_2eD__x___24a2(V2__D,V3__x0),happ(V1__d,V3__x0),V3__x0) ) ).
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.Rderiv.continue_in',axiom,
! [V0__f,V1__D,V2__x0] :
( cCoq_2eReals_2eRderiv_2econtinue__in___24a3(V0__f,V1__D,V2__x0)
<=> cCoq_2eReals_2eRlimit_2elimit1__in___24a4(V0__f,cCoq_2eReals_2eRderiv_2eD__x___24a2(V1__D,V2__x0),happ(V0__f,V2__x0),V2__x0) ) ).
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.infinite_sum',axiom,
! [V0__s,V1__l] :
( cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V0__s,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)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__s,V5__n),V1__l),V2__eps)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rfunctions.powerRZ',axiom,
! [V0__x,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__33408] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33408)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__33408)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__33408)) )
| ? [Vvar__0___24Anonymous__33409] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__33409)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__33409)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__33409))) ) ) ) ).
fof('$_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__20448] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20448)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20448)
& 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__20448),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20448))) ) ) ) ).
fof('$_def_Coq.Reals.Rgeom.dist_euc',axiom,
! [V0__x0,V1__y0,V2__x1,V3__y1] : cCoq_2eReals_2eRgeom_2edist__euc___24a4(V0__x0,V1__y0,V2__x1,V3__y1) = cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__x0,V2__x1)),cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__y0,V3__y1)))) ).
fof('$_def_Coq.Reals.RiemannInt.RinvN',axiom,
! [V0__N] : cCoq_2eReals_2eRiemannInt_2eRinvN___24a1(V0__N) = cCoq_2eReals_2eRIneq_2emkposreal___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(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)))),cCoq_2eReals_2eRiemannInt_2eRinvN__pos___24a1(V0__N)) ).
fof('$_def_Coq.Reals.RiemannInt_SF.Int_SF',axiom,
! [V1__l,V2__k] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__72560] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__72560)
& ? [Vvar__1___24Anonymous__72561] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__72561)
& ( cCoq_2eReals_2eRList_2eRlist___24t(V2__k)
=> ( V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__72560,Vvar__1___24Anonymous__72561)
& ( ( V2__k = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__72575] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__72575)
& ? [Vvar__1___24Anonymous__72576] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__72576)
& ( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__72576)
=> ( V2__k = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__72575,Vvar__1___24Anonymous__72576)
& ( ( Vvar__1___24Anonymous__72576 = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__72584] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__72584)
& ? [Vvar__1___24Anonymous__72585] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__72585)
& Vvar__1___24Anonymous__72576 = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__72584,Vvar__1___24Anonymous__72585)
& cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V1__l,V2__k) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(Vvar__0___24Anonymous__72560,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(Vvar__0___24Anonymous__72584,Vvar__0___24Anonymous__72575)),cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(Vvar__1___24Anonymous__72561,cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__72584,Vvar__1___24Anonymous__72585))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.open_interval',axiom,
! [V0__a,V1__b,V2__x] :
( cCoq_2eReals_2eRiemannInt__SF_2eopen__interval___24a3(V0__a,V1__b,V2__x)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V2__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__x,V1__b)) ) ) ).
fof('$_def_Coq.Reals.Rlimit.Base',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ? [Vvar__0__Base__25584] :
( cType___24t(Vvar__0__Base__25584)
& ? [Vvar__1__dist__25585] :
( c_24__type__25665___24t(Vvar__0__Base__25584,Vvar__1__dist__25585)
& ! [Vvar__var__2__x__25591__25593] :
( t(Vvar__var__2__x__25591__25593,Vvar__0__Base__25584)
=> ! [Vvar__var__3__y__25592__25594] :
( t(Vvar__var__3__y__25592__25594,Vvar__0__Base__25584)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__25585,Vvar__var__2__x__25591__25593),Vvar__var__3__y__25592__25594),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__25596__25598] :
( t(Vvar__var__3__x__25596__25598,Vvar__0__Base__25584)
=> ! [Vvar__var__4__y__25597__25599] :
( t(Vvar__var__4__y__25597__25599,Vvar__0__Base__25584)
=> happ(happ(Vvar__1__dist__25585,Vvar__var__3__x__25596__25598),Vvar__var__4__y__25597__25599) = happ(happ(Vvar__1__dist__25585,Vvar__var__4__y__25597__25599),Vvar__var__3__x__25596__25598) ) )
& ! [Vvar__var__4__x__25601__25603] :
( t(Vvar__var__4__x__25601__25603,Vvar__0__Base__25584)
=> ! [Vvar__var__5__y__25602__25604] :
( t(Vvar__var__5__y__25602__25604,Vvar__0__Base__25584)
=> ( happ(happ(Vvar__1__dist__25585,Vvar__var__4__x__25601__25603),Vvar__var__5__y__25602__25604) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__25601__25603 = Vvar__var__5__y__25602__25604 ) ) )
& ! [Vvar__var__5__x__25606__25609] :
( t(Vvar__var__5__x__25606__25609,Vvar__0__Base__25584)
=> ! [Vvar__var__6__y__25607__25610] :
( t(Vvar__var__6__y__25607__25610,Vvar__0__Base__25584)
=> ! [Vvar__var__7__z__25608__25611] :
( t(Vvar__var__7__z__25608__25611,Vvar__0__Base__25584)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__25585,Vvar__var__5__x__25606__25609),Vvar__var__6__y__25607__25610),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__25585,Vvar__var__5__x__25606__25609),Vvar__var__7__z__25608__25611),happ(happ(Vvar__1__dist__25585,Vvar__var__7__z__25608__25611),Vvar__var__6__y__25607__25610)))) ) ) )
& V0__m = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__25584,Vvar__1__dist__25585)
& cCoq_2eReals_2eRlimit_2eBase___24a1(V0__m) = Vvar__0__Base__25584 ) ) ) ).
fof('$_def_Coq.Reals.Rlimit.Dgf',axiom,
! [V0__Df,V1__Dg,V2__f,V3__x] :
( cCoq_2eReals_2eRlimit_2eDgf___24a4(V0__Df,V1__Dg,V2__f,V3__x)
<=> ( p(happ(V0__Df,V3__x))
& p(happ(V1__Dg,happ(V2__f,V3__x))) ) ) ).
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__25678] :
( cType___24t(Vvar__0__Base__25678)
& ? [Vvar__1__dist__25679] :
( c_24__type__25665___24t(Vvar__0__Base__25678,Vvar__1__dist__25679)
& ! [Vvar__var__2__x__25685__25687] :
( t(Vvar__var__2__x__25685__25687,Vvar__0__Base__25678)
=> ! [Vvar__var__3__y__25686__25688] :
( t(Vvar__var__3__y__25686__25688,Vvar__0__Base__25678)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__25679,Vvar__var__2__x__25685__25687),Vvar__var__3__y__25686__25688),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__25690__25692] :
( t(Vvar__var__3__x__25690__25692,Vvar__0__Base__25678)
=> ! [Vvar__var__4__y__25691__25693] :
( t(Vvar__var__4__y__25691__25693,Vvar__0__Base__25678)
=> happ(happ(Vvar__1__dist__25679,Vvar__var__3__x__25690__25692),Vvar__var__4__y__25691__25693) = happ(happ(Vvar__1__dist__25679,Vvar__var__4__y__25691__25693),Vvar__var__3__x__25690__25692) ) )
& ! [Vvar__var__4__x__25695__25697] :
( t(Vvar__var__4__x__25695__25697,Vvar__0__Base__25678)
=> ! [Vvar__var__5__y__25696__25698] :
( t(Vvar__var__5__y__25696__25698,Vvar__0__Base__25678)
=> ( happ(happ(Vvar__1__dist__25679,Vvar__var__4__x__25695__25697),Vvar__var__5__y__25696__25698) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__25695__25697 = Vvar__var__5__y__25696__25698 ) ) )
& ! [Vvar__var__5__x__25700__25703] :
( t(Vvar__var__5__x__25700__25703,Vvar__0__Base__25678)
=> ! [Vvar__var__6__y__25701__25704] :
( t(Vvar__var__6__y__25701__25704,Vvar__0__Base__25678)
=> ! [Vvar__var__7__z__25702__25705] :
( t(Vvar__var__7__z__25702__25705,Vvar__0__Base__25678)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__25679,Vvar__var__5__x__25700__25703),Vvar__var__6__y__25701__25704),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__25679,Vvar__var__5__x__25700__25703),Vvar__var__7__z__25702__25705),happ(happ(Vvar__1__dist__25679,Vvar__var__7__z__25702__25705),Vvar__var__6__y__25701__25704)))) ) ) )
& V0__m = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__25678,Vvar__1__dist__25679)
& cCoq_2eReals_2eRlimit_2edist___24a1(V0__m) = Vvar__1__dist__25679 ) ) ) ).
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('$_def_Coq.Reals.Rlimit.mul_factor',axiom,
! [V0__l,V1__l_27] : cCoq_2eReals_2eRlimit_2emul__factor___24a2(V0__l,V1__l_27) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__l),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__l_27)))) ).
fof('$_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__2443] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2443)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2443)
& 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__2443)) ) ) ) ).
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.arcsinh',axiom,
! [V0__x] : cCoq_2eReals_2eRpower_2earcsinh___24a1(V0__x) = cCoq_2eReals_2eRpower_2eln___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ).
fof('$_def_Coq.Reals.Rpower.ln',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& cCoq_2eReals_2eRIneq_2eRlt__dec___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x),c_24__prop__25804___24a1(V0__x))
& cCoq_2eReals_2eRpower_2eln___24a1(V0__x) = cCoq_2eReals_2eRpower_2eRln___24a1(cCoq_2eReals_2eRIneq_2emkposreal___24a1(V0__x)) )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& cCoq_2eReals_2eRIneq_2eRlt__dec___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x),c_24__prop__25805___24a1(V0__x))
& cCoq_2eReals_2eRpower_2eln___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('$_def_Coq.Reals.Rprod.prod_f_R0',axiom,
! [V1__f,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,V2__N) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__67678] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__67678)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__67678)
& cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,V2__N) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,Vvar__0___24Anonymous__67678),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__67678))) ) ) ) ).
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.Pser',axiom,
! [V0__An,V1__x,V2__l] :
( cCoq_2eReals_2eRseries_2ePser___24a3(V0__An,V1__x,V2__l)
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(c_24__lam__34302___24a2(V0__An,V1__x),V2__l) ) ).
fof('$_def_Coq.Reals.Rseries.Un_cv',axiom,
! [V0__Un,V1__l] :
( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
<=> ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V4__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__N)
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(happ(V0__Un,V5__n),V1__l),V2__eps)) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Reals.Rsqrt_def.Dichotomy_lb',axiom,
! [V2__x,V3__y,V4__P,V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
=> ( ( V5__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = V2__x )
| ? [Vvar__0___24Anonymous__74809] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74809)
& V5__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74809)
& cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474835___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74809) ) ) ) ).
fof('$_def_Coq.Reals.Rsqrt_def.Rsqrt',axiom,
! [V0__y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__y)
=> ? [Vvar__2__x__34478] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__34478)
& c_24__lam__34482___24a2(V0__y,Vvar__2__x__34478)
& cCoq_2eReals_2eRsqrt__def_2eRsqrt__exists___24a2(cCoq_2eReals_2eRIneq_2enonneg___24a1(V0__y),cCoq_2eReals_2eRIneq_2econd__nonneg___24a1(V0__y)) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__34482___24a1(V0__y),Vvar__2__x__34478)
& cCoq_2eReals_2eRsqrt__def_2eRsqrt___24a1(V0__y) = Vvar__2__x__34478 ) ) ).
fof('$_def_Coq.Reals.Rsqrt_def.cond_positivity',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x),c_24__prop__98319___24a1(V0__x))
& cCoq_2eReals_2eRsqrt__def_2econd__positivity___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2etrue )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x),c_24__prop__98320___24a1(V0__x))
& cCoq_2eReals_2eRsqrt__def_2econd__positivity___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Reals.Rsqrt_def.dicho_lb',axiom,
! [V0__x,V1__y,V2__P,V3__N] : cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a4(V0__x,V1__y,V2__P,V3__N) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V0__x,V1__y,V2__P,V3__N) ).
fof('$_def_Coq.Reals.Rsqrt_def.dicho_up',axiom,
! [V0__x,V1__y,V2__P,V3__N] : cCoq_2eReals_2eRsqrt__def_2edicho__up___24a4(V0__x,V1__y,V2__P,V3__N) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub___24a4(V0__x,V1__y,V2__P,V3__N) ).
fof('$_def_Coq.Reals.Rsqrt_def.pow_2_n',axiom,
! [V0__n] : cCoq_2eReals_2eRsqrt__def_2epow__2__n___24a1(V0__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V0__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.PI2',axiom,
cCoq_2eReals_2eRtrigo1_2ePI2 = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__98355,cCoq_2eReals_2eRtrigo1_2ePI__2__aux) ).
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_alt.cos_approx',axiom,
! [V0__a,V1__n] : cCoq_2eReals_2eRtrigo__alt_2ecos__approx___24a2(V0__a,V1__n) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eRtrigo__alt_2ecos__term___24a1(V0__a),V1__n) ).
fof('$_def_Coq.Reals.Rtrigo_alt.cos_term',axiom,
! [V0__a,V1__i] : cCoq_2eReals_2eRtrigo__alt_2ecos__term___24a2(V0__a,V1__i) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__i),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__a,cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__i)),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__i))))) ).
fof('$_def_Coq.Reals.Rtrigo_alt.sin_approx',axiom,
! [V0__a,V1__n] : cCoq_2eReals_2eRtrigo__alt_2esin__approx___24a2(V0__a,V1__n) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eRtrigo__alt_2esin__term___24a1(V0__a),V1__n) ).
fof('$_def_Coq.Reals.Rtrigo_alt.sin_term',axiom,
! [V0__a,V1__i] : cCoq_2eReals_2eRtrigo__alt_2esin__term___24a2(V0__a,V1__i) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__i),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__a,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__i),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__i),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))) ).
fof('$_def_Coq.Reals.Rtrigo_def.cos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__25821] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__25821)
& c_24__lam__25825___24a2(V0__x,Vvar__2__x__25821)
& 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__25825___24a1(V0__x),Vvar__2__x__25821)
& cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) = Vvar__2__x__25821 ) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.cos_in',axiom,
! [V0__x,V1__l] :
( cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(V0__x,V1__l)
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(c_24__lam__75030___24a1(V0__x),V1__l) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.cos_n',axiom,
! [V0__n] : cCoq_2eReals_2eRtrigo__def_2ecos__n___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n)))) ).
fof('$_def_Coq.Reals.Rtrigo_def.cosh',axiom,
! [V0__x] : cCoq_2eReals_2eRtrigo__def_2ecosh___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('$_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__25812___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2eexist__exp___24a1(V0__x)) ).
fof('$_def_Coq.Reals.Rtrigo_def.exp_in',axiom,
! [V0__x,V1__l] :
( cCoq_2eReals_2eRtrigo__def_2eexp__in___24a2(V0__x,V1__l)
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(c_24__lam__70508___24a1(V0__x),V1__l) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.sin',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ? [Vvar__2__x__67805] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2__x__67805)
& c_24__lam__67809___24a2(V0__x,Vvar__2__x__67805)
& 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__67809___24a1(V0__x),Vvar__2__x__67805)
& cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,Vvar__2__x__67805) ) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.sin_in',axiom,
! [V0__x,V1__l] :
( cCoq_2eReals_2eRtrigo__def_2esin__in___24a2(V0__x,V1__l)
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(c_24__lam__77251___24a1(V0__x),V1__l) ) ).
fof('$_def_Coq.Reals.Rtrigo_def.sinh',axiom,
! [V0__x] : cCoq_2eReals_2eRtrigo__def_2esinh___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
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.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('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_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.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('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_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__29953] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29953)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29953)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29953) )
| ? [Vvar__0___24Anonymous__29954] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29954)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29954)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29954) ) ) ) ).
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__181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__181)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__181)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__185] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__185)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__181,Vvar__0___24Anonymous__185)) )
| ? [Vvar__0___24Anonymous__186] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__186)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__181,Vvar__0___24Anonymous__186) ) ) ) ) )
| ? [Vvar__0___24Anonymous__187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__187)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__187)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__191] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__191)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__191,Vvar__0___24Anonymous__187) )
| ? [Vvar__0___24Anonymous__192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__192)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__192)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__187,Vvar__0___24Anonymous__192)) ) ) ) ) ) ) ) ).
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__213] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__213)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__213)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__214)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__214)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__215] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__215)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__215)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__219] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__219)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__219)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__215,Vvar__0___24Anonymous__219) )
| ? [Vvar__0___24Anonymous__220] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__220)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__220)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__221] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__221)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__221)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__225] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__225)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__225)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__226] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__226)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__226)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__221,Vvar__0___24Anonymous__226)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__2788] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__2788)
& ? [Vvar__3___24Anonymous__2789] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__2789)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__2788,Vvar__3___24Anonymous__2789)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__2788 ) ) ) ) ).
fof('$_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__29980] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29980)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29980)
& ( ( 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__29984] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29984)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29984)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__29980,Vvar__0___24Anonymous__29984)) )
| ? [Vvar__0___24Anonymous__29985] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29985)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29985)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__29980,Vvar__0___24Anonymous__29985)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29986] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29986)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29986)
& ( ( 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__29990] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29990)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29990)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__29986,Vvar__0___24Anonymous__29990)) )
| ? [Vvar__0___24Anonymous__29991] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29991)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29991)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__29986,Vvar__0___24Anonymous__29991)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.ggcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V1__b))) )
| ? [Vvar__0___24Anonymous__76106] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76106)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__76106)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__a),cCoq_2eNumbers_2eBinNums_2eZ0)) )
| ? [Vvar__0___24Anonymous__76122] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76122)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76106)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76122)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__76122)
& ? [Vvar__2___24Anonymous__76133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76133)
& ? [Vvar__3___24Anonymous__76134] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76134)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76134)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(Vvar__0___24Anonymous__76106,Vvar__0___24Anonymous__76122) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__76133,Vvar__3___24Anonymous__76134)
& ? [Vvar__2___24Anonymous__76146] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76146)
& ? [Vvar__3___24Anonymous__76147] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__76147)
& Vvar__3___24Anonymous__76134 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__76146,Vvar__3___24Anonymous__76147)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__76133),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__76146),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__3___24Anonymous__76147))) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__76149] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76149)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76106)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76149)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__76149)
& ? [Vvar__2___24Anonymous__76160] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76160)
& ? [Vvar__3___24Anonymous__76161] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76161)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76161)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(Vvar__0___24Anonymous__76106,Vvar__0___24Anonymous__76149) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__76160,Vvar__3___24Anonymous__76161)
& ? [Vvar__2___24Anonymous__76173] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76173)
& ? [Vvar__3___24Anonymous__76174] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__76174)
& Vvar__3___24Anonymous__76161 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__76173,Vvar__3___24Anonymous__76174)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__76160),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__76173),cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__3___24Anonymous__76174))) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__76176] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76176)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__76176)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__a),cCoq_2eNumbers_2eBinNums_2eZ0)) )
| ? [Vvar__0___24Anonymous__76192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76192)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76176)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76192)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__76192)
& ? [Vvar__2___24Anonymous__76203] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76203)
& ? [Vvar__3___24Anonymous__76204] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76204)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76204)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(Vvar__0___24Anonymous__76176,Vvar__0___24Anonymous__76192) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__76203,Vvar__3___24Anonymous__76204)
& ? [Vvar__2___24Anonymous__76216] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76216)
& ? [Vvar__3___24Anonymous__76217] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__76217)
& Vvar__3___24Anonymous__76204 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__76216,Vvar__3___24Anonymous__76217)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__76203),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__2___24Anonymous__76216),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__3___24Anonymous__76217))) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__76219] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76219)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76176)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__76219)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__76219)
& ? [Vvar__2___24Anonymous__76230] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76230)
& ? [Vvar__3___24Anonymous__76231] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76231)
& ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__3___24Anonymous__76231)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(Vvar__0___24Anonymous__76176,Vvar__0___24Anonymous__76219) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive),Vvar__2___24Anonymous__76230,Vvar__3___24Anonymous__76231)
& ? [Vvar__2___24Anonymous__76243] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__76243)
& ? [Vvar__3___24Anonymous__76244] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3___24Anonymous__76244)
& Vvar__3___24Anonymous__76231 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive,Vvar__2___24Anonymous__76243,Vvar__3___24Anonymous__76244)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__2___24Anonymous__76230),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__2___24Anonymous__76243),cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__3___24Anonymous__76244))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.ltb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.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__200] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__200)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__204] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__204)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__204)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__200,Vvar__0___24Anonymous__204)) )
| ? [Vvar__0___24Anonymous__205] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__205)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__205)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__200,Vvar__0___24Anonymous__205)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__206] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__206)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__206)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__210] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__210)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__210)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__206,Vvar__0___24Anonymous__210)) )
| ? [Vvar__0___24Anonymous__211] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__211)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__211)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__206,Vvar__0___24Anonymous__211)) ) ) ) ) ) ) ) ).
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__29968] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29968)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29968)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29968) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29965] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29965)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29965)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__29965)) ) ) ) ).
fof('$_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__196] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__196)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__196)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__196) )
| ? [Vvar__0___24Anonymous__197] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__197)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__197)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__197) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pos_div_eucl',axiom,
! [V1__a,V2__b] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__a)
=> ( ? [Vvar__0___24Anonymous__2653] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2653)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2653)
=> ( V1__a = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2653)
& ? [Vvar__2___24Anonymous__2663] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__2663)
& ? [Vvar__3___24Anonymous__2664] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__2664)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2653,V2__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__2663,Vvar__3___24Anonymous__2664)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V1__a,V2__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242694___24a3(V2__b,Vvar__2___24Anonymous__2663,Vvar__3___24Anonymous__2664) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2671] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2671)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__b)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2671)
=> ( V1__a = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2671)
& ? [Vvar__2___24Anonymous__2681] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__2681)
& ? [Vvar__3___24Anonymous__2682] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__2682)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2671,V2__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__2681,Vvar__3___24Anonymous__2682)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl___24a2(V1__a,V2__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242700___24a3(V2__b,Vvar__2___24Anonymous__2681,Vvar__3___24Anonymous__2682) ) ) ) ) ) )
| ( 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__29923] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29923)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29923)
& ( ? [Vvar__0___24Anonymous__29927] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29927)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29927)
& 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__29923,Vvar__0___24Anonymous__29927)) )
| ? [Vvar__0___24Anonymous__29928] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29928)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29928)
& 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__29923,Vvar__0___24Anonymous__29928)) )
| ( 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__29923)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29929] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29929)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29929)
& ( ? [Vvar__0___24Anonymous__29933] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29933)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29933)
& 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__29929,Vvar__0___24Anonymous__29933)) )
| ? [Vvar__0___24Anonymous__29934] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29934)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29934)
& 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__29929,Vvar__0___24Anonymous__29934)) )
| ( 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__29929)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__29935] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29935)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29935)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29935)) )
| ? [Vvar__0___24Anonymous__29936] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29936)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29936)
& 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__29936)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__29943] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29943)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29943)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__29943) )
| ? [Vvar__0___24Anonymous__29944] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29944)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29944)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__2521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2521)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2521)
& ( ( 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__2531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2531)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2521)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2531)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2531)
& ? [Vvar__2___24Anonymous__2539] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2539)
& ? [Vvar__3___24Anonymous__2540] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2540)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2521,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2531)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2539,Vvar__3___24Anonymous__2540)
& 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__2539),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2540)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2542] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2542)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2521)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2542)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2542)
& ? [Vvar__2___24Anonymous__2550] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2550)
& ? [Vvar__3___24Anonymous__2551] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2551)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2521,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2542)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2550,Vvar__3___24Anonymous__2551)
& 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__2550)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2551)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2553] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2553)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2553)
& ( ( 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__2563] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2563)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2553)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2563)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2563)
& ? [Vvar__2___24Anonymous__2571] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2571)
& ? [Vvar__3___24Anonymous__2572] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2572)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2553,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2563)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2571,Vvar__3___24Anonymous__2572)
& 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__2571)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2572))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2574] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2574)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2553)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2574)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2574)
& ? [Vvar__2___24Anonymous__2582] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2582)
& ? [Vvar__3___24Anonymous__2583] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2583)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2553,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2574)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2582,Vvar__3___24Anonymous__2583)
& 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__2582),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2583))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__29978] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29978)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29978)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__29978)) )
| ? [Vvar__0___24Anonymous__29979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29979)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29979)
& 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('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zdiv.Zmod_POS',axiom,
! [V1__a,V2__b] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__a)
=> ( ? [Vvar__0___24Anonymous__78060] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__78060)
& V1__a = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__78060)
& cCoq_2eZArith_2eZdiv_2eZmod__POS___24a2(V1__a,V2__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478081___24a2(V2__b,Vvar__0___24Anonymous__78060) )
| ? [Vvar__0___24Anonymous__78067] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__78067)
& V1__a = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__78067)
& cCoq_2eZArith_2eZdiv_2eZmod__POS___24a2(V1__a,V2__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478089___24a2(V2__b,Vvar__0___24Anonymous__78067) )
| ( 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_2eZdiv_2eZmod__POS___24a2(V1__a,V2__b) = 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_2eZdiv_2eZmod__POS___24a2(V1__a,V2__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ) ).
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.Zpower.Zdiv_rest',axiom,
! [V0__x,V1__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ? [Vvar__2___24Anonymous__75841] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__75841)
& ? [Vvar__3___24Anonymous__75842] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__75842)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eZArith_2eZpower_2eZdiv__rest__aux,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__p) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__75841,Vvar__3___24Anonymous__75842)
& cCoq_2eZArith_2eZpower_2eZdiv__rest___24a2(V0__x,V1__p) = Vvar__2___24Anonymous__75841 ) ) ) ) ).
fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
! [Vvar__20138] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__20138)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__20138) ) ).
fof('$_def_Coq.micromega.RMicromega.INZ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__98627] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98627)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__98627)
& cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98627)) ) ) ) ).
fof('$_def_Coq.micromega.RMicromega.RTautoChecker',axiom,
! [V0__f,V1__w] : cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V0__f,V1__w) = cCoq_2emicromega_2eTauto_2etauto__checker___24a11(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit,cCoq_2emicromega_2eRMicromega_2erunsat,cCoq_2emicromega_2eRMicromega_2erdeduce,cCoq_2emicromega_2eRMicromega_2eRnormalise___24a1(cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRMicromega_2eRnegate___24a1(cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRMicromega_2eRWitness,c_24__lam__20310,cCoq_2emicromega_2eTauto_2emap__bformula___24a7(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2emicromega_2eRingMicromega_2emap__Formula___24a3(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2emicromega_2eRMicromega_2eRcst,cCoq_2emicromega_2eRMicromega_2eQ__of__Rcst),V0__f),V1__w) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.Tauto.BFormula',axiom,
! [V0__A] : cCoq_2emicromega_2eTauto_2eBFormula___24a1(V0__A) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_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__26623] :
( t(Vvar__1___24Anonymous__26623,V0__A)
& V3__vm = cCoq_2emicromega_2eVarMap_2eElt___24a2(V0__A,Vvar__1___24Anonymous__26623)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__1___24Anonymous__26623 )
| ? [Vvar__1___24Anonymous__26625] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__1___24Anonymous__26625)
& ? [Vvar__2___24Anonymous__26626] :
( t(Vvar__2___24Anonymous__26626,V0__A)
& ? [Vvar__3___24Anonymous__26627] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__3___24Anonymous__26627)
& ( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> ( V3__vm = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V0__A,Vvar__1___24Anonymous__26625,Vvar__2___24Anonymous__26626,Vvar__3___24Anonymous__26627)
& ( ? [Vvar__0___24Anonymous__26640] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26640)
& V4__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26640)
& 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__26627,Vvar__0___24Anonymous__26640) )
| ? [Vvar__0___24Anonymous__26641] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26641)
& V4__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26641)
& 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__26625,Vvar__0___24Anonymous__26641) )
| ( V4__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__2___24Anonymous__26626 ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.ZgcdM',axiom,
! [V0__x,V1__y] : cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__x,V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.micromega.ZMicromega.Zgcd_pol',axiom,
! [V1__p] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__p)
=> ( ? [Vvar__1___24Anonymous__34664] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__34664)
& V1__p = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__34664)
& cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__1___24Anonymous__34664) )
| ? [Vvar__1___24Anonymous__34666] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__34666)
& ? [Vvar__2___24Anonymous__34667] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__34667)
& V1__p = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__34666,Vvar__2___24Anonymous__34667)
& cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V1__p) = cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(Vvar__2___24Anonymous__34667) ) )
| ? [Vvar__1___24Anonymous__34670] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__34670)
& ? [Vvar__2___24Anonymous__34671] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__34671)
& ? [Vvar__3___24Anonymous__34672] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__34672)
& ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__34670)
=> ( V1__p = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__34670,Vvar__2___24Anonymous__34671,Vvar__3___24Anonymous__34672)
& ? [Vvar__2___24Anonymous__34698] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__34698)
& ? [Vvar__3___24Anonymous__34699] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__34699)
& ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__34672)
=> ( cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(Vvar__1___24Anonymous__34670) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__34698,Vvar__3___24Anonymous__34699)
& ? [Vvar__2___24Anonymous__34711] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__34711)
& ? [Vvar__3___24Anonymous__34712] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__34712)
& cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(Vvar__3___24Anonymous__34672) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__34711,Vvar__3___24Anonymous__34712)
& cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(Vvar__2___24Anonymous__34698,Vvar__3___24Anonymous__34699),Vvar__2___24Anonymous__34711),Vvar__3___24Anonymous__34712) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.ceiling',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__28020] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__28020)
& ? [Vvar__3___24Anonymous__28021] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__28021)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__28021)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__28020,Vvar__3___24Anonymous__28021)
& ( ( Vvar__3___24Anonymous__28021 = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__28020 )
| ? [Vvar__0___24Anonymous__28029] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28029)
& Vvar__3___24Anonymous__28021 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28029)
& cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(Vvar__2___24Anonymous__28020,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__28030] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28030)
& Vvar__3___24Anonymous__28021 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__28030)
& cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(Vvar__2___24Anonymous__28020,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ) ) ) ) ) ).
fof('$_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__625] :
( t(Vvar__1___24Anonymous__625,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__625)
& 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__625) )
| ? [Vvar__1___24Anonymous__627] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__627)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__627)
& 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__627,V15__l) )
| ? [Vvar__1___24Anonymous__629] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__629)
& ? [Vvar__2___24Anonymous__630] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__630)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__629,Vvar__2___24Anonymous__630)
& 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__629)),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__630)) ) )
| ? [Vvar__1___24Anonymous__633] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__633)
& ? [Vvar__2___24Anonymous__634] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__634)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__633,Vvar__2___24Anonymous__634)
& 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__633)),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__634)) ) )
| ? [Vvar__1___24Anonymous__637] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__637)
& ? [Vvar__2___24Anonymous__638] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__638)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__637,Vvar__2___24Anonymous__638)
& 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__637)),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__638)) ) )
| ? [Vvar__1___24Anonymous__641] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__641)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__641)
& 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__641)) )
| ? [Vvar__1___24Anonymous__643] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__643)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__643)
& 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__643)) )
| ? [Vvar__1___24Anonymous__645] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__645)
& ? [Vvar__2___24Anonymous__646] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__646)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__645,Vvar__2___24Anonymous__646)
& 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__645)),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__646)) ) )
| ? [Vvar__1___24Anonymous__649] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__649)
& ? [Vvar__2___24Anonymous__650] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__650)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__649,Vvar__2___24Anonymous__650)
& 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__649)),happ(V12__Cp__phi,Vvar__2___24Anonymous__650)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__1436] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__1436)
& ? [Vvar__2___24Anonymous__1437] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__1437)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__1436,Vvar__2___24Anonymous__1437)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__1436),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__1437,V4__m)) ) ) ) ) ) ).
fof('$_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__1219] :
( t(Vvar__1___24Anonymous__1219,V0__C)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V0__C,Vvar__1___24Anonymous__1219)
& 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__1219),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__1221] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1221)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V0__C,Vvar__1___24Anonymous__1221)
& 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__1221),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__1223] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__1223)
& ? [Vvar__2___24Anonymous__1224] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__1224)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V0__C,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224)
& 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__1226__1229__1299___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__1228__1231__1301___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224))),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__1227__1230__1300___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1224)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__1228__1231__1301___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224)))),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__1228__1231__1301___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224)),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__1228__1231__1301___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__1228__1231__1301___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223,Vvar__2___24Anonymous__1224)))),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__1226__1229__1299___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1223)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__1227__1230__1300___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1224)))) ) )
| ? [Vvar__1___24Anonymous__1236] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__1236)
& ? [Vvar__2___24Anonymous__1237] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__1237)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V0__C,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237)
& 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__1239__1242__1305___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__1241__1244__1307___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237))),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__1240__1243__1306___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1237)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__1241__1244__1307___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237)))),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__1241__1244__1307___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237)),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__1241__1244__1307___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__1241__1244__1307___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236,Vvar__2___24Anonymous__1237)))),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__1239__1242__1305___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1236)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__1240__1243__1306___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1237)))) ) )
| ? [Vvar__1___24Anonymous__1249] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__1249)
& ? [Vvar__2___24Anonymous__1250] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__1250)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V0__C,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250)
& 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__1254__1258__1316___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__15__s2__1255__1259__1317___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250))),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__1255__1259__1317___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__1254__1258__1316___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250))),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__1252__1256__1314___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1249)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__1253__1257__1315___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1250)))) ) )
| ? [Vvar__1___24Anonymous__1267] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__1267)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V0__C,Vvar__1___24Anonymous__1267)
& 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__1268__1318___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1267))),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__11__x__1268__1318___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1267)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__1268__1318___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1267))) )
| ? [Vvar__1___24Anonymous__1270] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__1270)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V0__C,Vvar__1___24Anonymous__1270)
& 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__1271__1319___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1270)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__1271__1319___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1270)),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__1271__1319___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1270)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__1271__1319___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1270)))) )
| ? [Vvar__1___24Anonymous__1273] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__1273)
& ? [Vvar__2___24Anonymous__1274] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__1274)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V0__C,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274)
& 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__1278__1282__1328___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__15__s2__1279__1283__1329___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274))),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__1279__1283__1329___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__1278__1282__1328___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274))),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__1277__1281__1327___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1274)),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__1276__1280__1326___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1273)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__1277__1281__1327___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__1274))))) ) )
| ? [Vvar__1___24Anonymous__1291] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__1291)
& ? [Vvar__2___24Anonymous__1292] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__1292)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V0__C,Vvar__1___24Anonymous__1291,Vvar__2___24Anonymous__1292)
& 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__1293__1295__1330___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1291)),Vvar__2___24Anonymous__1292),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__1293__1295__1330___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1291)),Vvar__2___24Anonymous__1292),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__1293__1295__1330___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__1291))) ) ) ) ) ) ).
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__972] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__972)
& ? [Vvar__2___24Anonymous__973] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__973)
& ( 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__973)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__972,Vvar__2___24Anonymous__973)
& ( ( Vvar__2___24Anonymous__973 = 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__972)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__984] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__984)
& ? [Vvar__2___24Anonymous__985] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__985)
& Vvar__2___24Anonymous__973 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__984,Vvar__2___24Anonymous__985)
& ( 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__972)),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__973) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__959] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__959)
& ? [Vvar__2__denum__960] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__960)
& ? [Vvar__3__condition__961] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__961)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__959,Vvar__2__denum__960,Vvar__3__condition__961)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__961 ) ) ) ) ) ).
fof('$_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__950] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__950)
& ? [Vvar__2__denum__951] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__951)
& ? [Vvar__3__condition__952] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__952)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__950,Vvar__2__denum__951,Vvar__3__condition__952)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__951 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den] : cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2438069___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) ).
fof('$_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__939] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__939)
& ? [Vvar__2__denum__940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__940)
& ? [Vvar__3__condition__941] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__941)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__939,Vvar__2__denum__940,Vvar__3__condition__941)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__939 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__32906] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__32906)
& ? [Vvar__2__rsplit__common__32907] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__32907)
& ? [Vvar__3__rsplit__right__32908] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__32908)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__32906,Vvar__2__rsplit__common__32907,Vvar__3__rsplit__right__32908)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__32906 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__32917] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__32917)
& ? [Vvar__2__rsplit__common__32918] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__32918)
& ? [Vvar__3__rsplit__right__32919] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__32919)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__32917,Vvar__2__rsplit__common__32918,Vvar__3__rsplit__right__32919)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__32919 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.split',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2] : cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,cCoq_2eNumbers_2eBinNums_2exH,V6__e2) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__31426] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31426)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31426)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__31426))) )
| ? [Vvar__0___24Anonymous__31427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31427)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31427)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__31427)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__18886] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18886)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18886)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__18886) )
| ? [Vvar__0___24Anonymous__18887] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18887)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18887)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__18887)) ) ) ) ) ).
fof('$_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__32969] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32969)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32969)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__32970] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32970)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32970)
& 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__32970)) ) ) ) ).
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__21283] :
( t(Vvar__1___24Anonymous__21283,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__21283)
& 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__21283) )
| ? [Vvar__1___24Anonymous__21285] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__21285)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__21285)
& 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__21285,V13__l) )
| ? [Vvar__1___24Anonymous__21287] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__21287)
& ? [Vvar__2___24Anonymous__21288] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__21288)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__21287,Vvar__2___24Anonymous__21288)
& 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__21287)),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__21288)) ) )
| ? [Vvar__1___24Anonymous__21291] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__21291)
& ? [Vvar__2___24Anonymous__21292] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__21292)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__21291,Vvar__2___24Anonymous__21292)
& 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__21291)),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__21292)) ) )
| ? [Vvar__1___24Anonymous__21295] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__21295)
& ? [Vvar__2___24Anonymous__21296] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__21296)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__21295,Vvar__2___24Anonymous__21296)
& 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__21295)),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__21296)) ) )
| ? [Vvar__1___24Anonymous__21299] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__21299)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__21299)
& 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__21299)) )
| ? [Vvar__1___24Anonymous__21301] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__21301)
& ? [Vvar__2___24Anonymous__21302] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21302)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__21301,Vvar__2___24Anonymous__21302)
& 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__21301)),happ(V10__Cp__phi,Vvar__2___24Anonymous__21302)) ) ) ) ) ) ) ) ).
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__1656] :
( t(Vvar__1___24Anonymous__1656,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__1656)
& ( ? [Vvar__1___24Anonymous__1666] :
( t(Vvar__1___24Anonymous__1666,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1666)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__1656),Vvar__1___24Anonymous__1666) )
| ? [Vvar__1___24Anonymous__1668] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1668)
& ? [Vvar__2___24Anonymous__1669] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1669)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1668,Vvar__2___24Anonymous__1669)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__1672] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1672)
& ? [Vvar__2___24Anonymous__1673] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1673)
& ? [Vvar__3___24Anonymous__1674] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1674)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1672,Vvar__2___24Anonymous__1673,Vvar__3___24Anonymous__1674)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__1679] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1679)
& ? [Vvar__2___24Anonymous__1680] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1680)
& ( 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__1679,Vvar__2___24Anonymous__1680)
& ( ? [Vvar__1___24Anonymous__1700] :
( t(Vvar__1___24Anonymous__1700,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1700)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__1702] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1702)
& ? [Vvar__2___24Anonymous__1703] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1703)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1679)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1702)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1702,Vvar__2___24Anonymous__1703)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__1679,Vvar__1___24Anonymous__1702) = 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__1680,Vvar__2___24Anonymous__1703) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__1679,Vvar__1___24Anonymous__1702) = 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__1679,Vvar__1___24Anonymous__1702) = 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__1708] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1708)
& ? [Vvar__2___24Anonymous__1709] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1709)
& ? [Vvar__3___24Anonymous__1710] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1710)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1708,Vvar__2___24Anonymous__1709,Vvar__3___24Anonymous__1710)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__1715] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1715)
& ? [Vvar__2___24Anonymous__1716] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1716)
& ? [Vvar__3___24Anonymous__1717] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1717)
& ( 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__1715,Vvar__2___24Anonymous__1716,Vvar__3___24Anonymous__1717)
& ( ? [Vvar__1___24Anonymous__1750] :
( t(Vvar__1___24Anonymous__1750,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1750)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__1752] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1752)
& ? [Vvar__2___24Anonymous__1753] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1753)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1752,Vvar__2___24Anonymous__1753)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__1756] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1756)
& ? [Vvar__2___24Anonymous__1757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1757)
& ? [Vvar__3___24Anonymous__1758] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1758)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1716)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1757)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1756,Vvar__2___24Anonymous__1757,Vvar__3___24Anonymous__1758)
& ( ( cType___24t(V0__C)
=> ( c_24__type__1430___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1715)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1756)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__1716,Vvar__2___24Anonymous__1757) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__1715,Vvar__1___24Anonymous__1756) = 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__1717,Vvar__3___24Anonymous__1758) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__1715,Vvar__1___24Anonymous__1756) = 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__1716,Vvar__2___24Anonymous__1757) = 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__1716,Vvar__2___24Anonymous__1757) = 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('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__33075___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__33076___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__33077___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_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__21497] :
( 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__21497)
& ? [Vvar__2___24Anonymous__21498] :
( 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__21498)
& ( 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__21497)
=> ( 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__21497,Vvar__2___24Anonymous__21498)
& ? [Vvar__2___24Anonymous__21516] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__21516)
& ? [Vvar__3___24Anonymous__21517] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__21517)
& ( 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__21498)
=> ( Vvar__1___24Anonymous__21497 = 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__21516,Vvar__3___24Anonymous__21517)
& ( ( Vvar__2___24Anonymous__21498 = 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__21516)),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__21517))) ) )
| ? [Vvar__1___24Anonymous__21528] :
( 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__21528)
& ? [Vvar__2___24Anonymous__21529] :
( 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__21529)
& Vvar__2___24Anonymous__21498 = 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__21528,Vvar__2___24Anonymous__21529)
& ( 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__21516)),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__21517)))
& 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__21498) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__2270] :
( 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__2270)
& ? [Vvar__2___24Anonymous__2271] :
( 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__2271)
& ( 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__2270)
=> ( 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__2270,Vvar__2___24Anonymous__2271)
& ? [Vvar__2___24Anonymous__2287] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__2287)
& ? [Vvar__3___24Anonymous__2288] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__2288)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__882___24t(V0__C,V3__cadd)
=> ( c_24__type__882___24t(V0__C,V4__cmul)
=> ( c_24__type__882___24t(V0__C,V5__csub)
=> ( c_24__type__891___24t(V0__C,V6__copp)
=> ( c_24__type__1430___24t(V0__C,V7__ceqb)
=> ( c_24__type__1593___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__2287)
=> ( Vvar__1___24Anonymous__2270 = 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__2287,Vvar__3___24Anonymous__2288)
& ( ? [Vvar__1___24Anonymous__2296] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__2296)
& 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__2287)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__2296)
& 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__2296,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__2288)),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__2271)) )
| ( 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__2287)) = 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__2271) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__2116___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__21814] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21814)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21814)
& 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__21814) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__31782] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31782)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31782)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__31783__31786___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31782)),c_24__let__var__6__p__31783__31786___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31782))) )
| ? [Vvar__0___24Anonymous__31784] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31784)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31784)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__31785__31787___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31784)),c_24__let__var__6__p__31785__31787___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__31784)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_Fermat4.ArithCompl.frac',axiom,
! [V0__a,V1__b] : cFermat4_2eArithCompl_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('$_def_Fermat4.ArithCompl.is_rat',axiom,
! [V0__r] :
( cFermat4_2eArithCompl_2eis__rat___24a1(V0__r)
<=> ? [V1__pq] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,V1__pq)
& c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415___24a2(V0__r,V1__pq) ) ) ).
fof('$_def_Fermat4.ArithCompl.is_ratp',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__c)
=> ? [Vvar__2___24Anonymous__34816] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__2___24Anonymous__34816)
& ? [Vvar__3___24Anonymous__34817] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__3___24Anonymous__34817)
& V0__c = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,Vvar__2___24Anonymous__34816,Vvar__3___24Anonymous__34817)
& ( cFermat4_2eArithCompl_2eis__ratp___24a1(V0__c)
<=> ( cFermat4_2eArithCompl_2eis__rat___24a1(Vvar__2___24Anonymous__34816)
& cFermat4_2eArithCompl_2eis__rat___24a1(Vvar__3___24Anonymous__34817) ) ) ) ) ) ).
fof('$_def_Pythagorean.D_r',axiom,
! [V0__r,V1__x,V2__y] :
( cPythagorean_2eD__r___24a3(V0__r,V1__x,V2__y)
<=> V2__y = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ).
fof('$_def_Pythagorean.cond_pqb',axiom,
! [V0__p,V1__q] :
( cPythagorean_2econd__pqb___24a2(V0__p,V1__q)
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__q,cCoq_2eNumbers_2eBinNums_2eZ0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__p,V1__q))
& p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__p,V1__q)) ) ) ).
fof('$_def_Pythagorean.eqp',axiom,
! [V0__p1,V1__p2] :
( cPythagorean_2eeqp___24a2(V0__p1,V1__p2)
<=> ( cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__p1) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V1__p2)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__p1) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V1__p2) ) ) ).
fof('$_def_Pythagorean.in_ucirc',axiom,
! [V0__x,V1__y] :
( cPythagorean_2ein__ucirc___24a2(V0__x,V1__y)
<=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V0__x),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__y,V1__y)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('$_def_Pythagorean.in_ucp_setb',axiom,
! [V0__x,V1__y] :
( cPythagorean_2ein__ucp__setb___24a2(V0__x,V1__y)
<=> ? [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
& ? [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
& V0__x = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cPythagorean_2eucp___24a2(V2__p,V3__q))
& V1__y = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cPythagorean_2eucp___24a2(V2__p,V3__q))
& cPythagorean_2econd__pqb___24a2(V2__p,V3__q) ) ) ) ).
fof('$_def_Pythagorean.interCDr',axiom,
! [V0__r,V1__x,V2__y] :
( cPythagorean_2einterCDr___24a3(V0__r,V1__x,V2__y)
<=> ( cPythagorean_2ein__ucirc___24a2(V1__x,V2__y)
& cPythagorean_2eD__r___24a3(V0__r,V1__x,V2__y) ) ) ).
fof('$_def_Pythagorean.is_posp',axiom,
! [V0__c] :
( cPythagorean_2eis__posp___24a1(V0__c)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__c),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__c),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('$_def_Pythagorean.is_ucp',axiom,
! [V0__c] :
( cPythagorean_2eis__ucp___24a1(V0__c)
<=> ( cPythagorean_2ein__ucirc___24a2(cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__c),cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__c))
& cFermat4_2eArithCompl_2eis__ratp___24a1(V0__c)
& cPythagorean_2eis__posp___24a1(V0__c) ) ) ).
fof('$_def_Pythagorean.p1',axiom,
cPythagorean_2ep1 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ).
fof('$_def_Pythagorean.p2',axiom,
! [V0__r] : cPythagorean_2ep2___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,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_2eRdefinitions_2eRmult___24a2(V0__r,V0__r)),c_24__let__1__den__35032___24a1(V0__r)),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(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__r),c_24__let__1__den__35032___24a1(V0__r))) ).
fof('$_def_Pythagorean.ucp',axiom,
! [V0__p,V1__q] : cPythagorean_2eucp___24a2(V0__p,V1__q) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(c_24__let__3__qr__78054___24a1(V1__q),c_24__let__3__qr__78054___24a1(V1__q)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(c_24__let__2__pr__78053___24a1(V0__p),c_24__let__2__pr__78053___24a1(V0__p))),c_24__let__4__den__78055___24a2(V0__p,V1__q)),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),c_24__let__2__pr__78053___24a1(V0__p)),c_24__let__3__qr__78054___24a1(V1__q)),c_24__let__4__den__78055___24a2(V0__p,V1__q))) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__240] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__240) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__15565,Vvar__1___24Anonymous__15566,Vvar__0__A__15567] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__15565,Vvar__1___24Anonymous__15566) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__15567) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__30545,Vvar__1__B__30546,Vvar__2___24Anonymous__30547,Vvar__0__A__30548,Vvar__1__B__30549,Vvar__2___24Anonymous__30550] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__30545,Vvar__1__B__30546,Vvar__2___24Anonymous__30547) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__30548,Vvar__1__B__30549,Vvar__2___24Anonymous__30550) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__251,Vvar__0__A__252,Vvar__1___24Anonymous__253,Vvar__2___24Anonymous__254] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__251) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__252,Vvar__1___24Anonymous__253,Vvar__2___24Anonymous__254) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2459,Vvar__1__B__2460,Vvar__2___24Anonymous__2461,Vvar__0__A__2462,Vvar__1__B__2463,Vvar__2___24Anonymous__2464] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2459,Vvar__1__B__2460,Vvar__2___24Anonymous__2461) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2462,Vvar__1__B__2463) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__126,Vvar__1__B__127,Vvar__2___24Anonymous__128,Vvar__0__A__129,Vvar__1__B__130,Vvar__2___24Anonymous__131] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__126,Vvar__1__B__127) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__129,Vvar__1__B__130) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__15503] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__15503) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__57] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__57) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__45,Vvar__0___24Anonymous__46] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__32762] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__32762) ).
fof('$_discrim_Coq.Reals.RList.nil$Coq.Reals.RList.cons',axiom,
! [Vvar__0___24Anonymous__31575,Vvar__1___24Anonymous__31576] : cCoq_2eReals_2eRList_2enil != cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__31575,Vvar__1___24Anonymous__31576) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__15724,Vvar__1___24Anonymous__15725,Vvar__0__C__15726,Vvar__1___24Anonymous__15727] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__15724,Vvar__1___24Anonymous__15725) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__15726,Vvar__1___24Anonymous__15727) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__30626,Vvar__1___24Anonymous__30627,Vvar__0__C__30628,Vvar__1___24Anonymous__30629,Vvar__2___24Anonymous__30630] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30626,Vvar__1___24Anonymous__30627) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30628,Vvar__1___24Anonymous__30629,Vvar__2___24Anonymous__30630) ).
fof('$_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$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__21149,Vvar__1___24Anonymous__21150,Vvar__0__C__21151,Vvar__1___24Anonymous__21152] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21149,Vvar__1___24Anonymous__21150) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21151,Vvar__1___24Anonymous__21152) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__26445,Vvar__1__TX__26446,Vvar__2__AA__26447,Vvar__3__AF__26448,Vvar__0__TA__26449,Vvar__1__TX__26450,Vvar__2__AA__26451,Vvar__3__AF__26452] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__26445,Vvar__1__TX__26446,Vvar__2__AA__26447,Vvar__3__AF__26448) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__26449,Vvar__1__TX__26450,Vvar__2__AA__26451,Vvar__3__AF__26452) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__26599,Vvar__0__A__26600,Vvar__1___24Anonymous__26601] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__26599) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__26600,Vvar__1___24Anonymous__26601) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__557,Vvar__0__C__558] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__557) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__558) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__1986,Vvar__0__C__1987] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1986) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1987) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1630,Vvar__1___24Anonymous__1631,Vvar__0__C__1632,Vvar__1___24Anonymous__1633,Vvar__2___24Anonymous__1634] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1630,Vvar__1___24Anonymous__1631) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1632,Vvar__1___24Anonymous__1633,Vvar__2___24Anonymous__1634) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__1796,Vvar__1___24Anonymous__1797] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1796,Vvar__1___24Anonymous__1797) ).
fof('$_fix_29863_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__29878] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29878)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29878)
& ( ? [Vvar__0___24Anonymous__29882] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29882)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29882)
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__29863__1__add__carry___24a2(Vvar__0___24Anonymous__29878,Vvar__0___24Anonymous__29882)) )
| ? [Vvar__0___24Anonymous__29883] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29883)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29883)
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29863__1__add__carry___24a2(Vvar__0___24Anonymous__29878,Vvar__0___24Anonymous__29883)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29878)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29884] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29884)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29884)
& ( ? [Vvar__0___24Anonymous__29888] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29888)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29888)
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29863__1__add__carry___24a2(Vvar__0___24Anonymous__29884,Vvar__0___24Anonymous__29888)) )
| ? [Vvar__0___24Anonymous__29889] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29889)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29889)
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29884,Vvar__0___24Anonymous__29889)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29884)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__29890] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29890)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29890)
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29890)) )
| ? [Vvar__0___24Anonymous__29891] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29891)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29891)
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29891)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__29863__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_74808_1_Dichotomy_ub',axiom,
! [V2__x,V3__y,V4__P,V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
=> ( ( V5__N = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__74808__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,V5__N) = V3__y )
| ? [Vvar__0___24Anonymous__74838] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74838)
& V5__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74838)
& c_24__fix__74808__1__Dichotomy__ub___24a4(V2__x,V3__y,V4__P,V5__N) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474864___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74838) ) ) ) ).
fof('$_fix_74875_0_Dichotomy_lb',axiom,
! [V2__x,V3__y,V4__P,V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
=> ( ( V5__N = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__74875__0__Dichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = V2__x )
| ? [Vvar__0___24Anonymous__74876] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74876)
& V5__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74876)
& c_24__fix__74875__0__Dichotomy__lb___24a4(V2__x,V3__y,V4__P,V5__N) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474902___24a4(V2__x,V3__y,V4__P,Vvar__0___24Anonymous__74876) ) ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__15572,Vvar__0__A__15573] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__15572) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__15573)
=> Vvar__0__A__15572 = Vvar__0__A__15573 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__241,Vvar__0___24Anonymous__242] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__241) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__242)
=> Vvar__0___24Anonymous__241 = Vvar__0___24Anonymous__242 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__15568,Vvar__0__A__15569,Vvar__1___24Anonymous__15570,Vvar__1___24Anonymous__15571] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__15568,Vvar__1___24Anonymous__15570) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__15569,Vvar__1___24Anonymous__15571)
=> ( Vvar__1___24Anonymous__15570 = Vvar__1___24Anonymous__15571
& Vvar__0__A__15568 = Vvar__0__A__15569 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__257,Vvar__0__A__258,Vvar__1___24Anonymous__259,Vvar__1___24Anonymous__260,Vvar__2___24Anonymous__261,Vvar__2___24Anonymous__262] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__257,Vvar__1___24Anonymous__259,Vvar__2___24Anonymous__261) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__258,Vvar__1___24Anonymous__260,Vvar__2___24Anonymous__262)
=> ( Vvar__2___24Anonymous__261 = Vvar__2___24Anonymous__262
& Vvar__1___24Anonymous__259 = Vvar__1___24Anonymous__260
& Vvar__0__A__257 = Vvar__0__A__258 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__30551,Vvar__0__A__30552,Vvar__1__B__30553,Vvar__1__B__30554,Vvar__2___24Anonymous__30555,Vvar__2___24Anonymous__30556] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__30551,Vvar__1__B__30553,Vvar__2___24Anonymous__30555) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__30552,Vvar__1__B__30554,Vvar__2___24Anonymous__30556)
=> ( Vvar__2___24Anonymous__30555 = Vvar__2___24Anonymous__30556
& Vvar__1__B__30553 = Vvar__1__B__30554
& Vvar__0__A__30551 = Vvar__0__A__30552 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__30557,Vvar__0__A__30558,Vvar__1__B__30559,Vvar__1__B__30560,Vvar__2___24Anonymous__30561,Vvar__2___24Anonymous__30562] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__30557,Vvar__1__B__30559,Vvar__2___24Anonymous__30561) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__30558,Vvar__1__B__30560,Vvar__2___24Anonymous__30562)
=> ( Vvar__2___24Anonymous__30561 = Vvar__2___24Anonymous__30562
& Vvar__1__B__30559 = Vvar__1__B__30560
& Vvar__0__A__30557 = Vvar__0__A__30558 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__255,Vvar__0__A__256] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__255) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__256)
=> Vvar__0__A__255 = Vvar__0__A__256 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__74,Vvar__0__A__75,Vvar__1__B__76,Vvar__1__B__77,Vvar__2___24Anonymous__78,Vvar__2___24Anonymous__79,Vvar__3___24Anonymous__80,Vvar__3___24Anonymous__81] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__74,Vvar__1__B__76,Vvar__2___24Anonymous__78,Vvar__3___24Anonymous__80) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__75,Vvar__1__B__77,Vvar__2___24Anonymous__79,Vvar__3___24Anonymous__81)
=> ( Vvar__3___24Anonymous__80 = Vvar__3___24Anonymous__81
& Vvar__2___24Anonymous__78 = Vvar__2___24Anonymous__79
& Vvar__1__B__76 = Vvar__1__B__77
& Vvar__0__A__74 = Vvar__0__A__75 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__25927,Vvar__0__A__25928,Vvar__1__P__25929,Vvar__1__P__25930,Vvar__2__x__25931,Vvar__2__x__25932,Vvar__3___24Anonymous__25933,Vvar__3___24Anonymous__25934] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__25927,Vvar__1__P__25929,Vvar__2__x__25931) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__25928,Vvar__1__P__25930,Vvar__2__x__25932)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__25931 = Vvar__2__x__25932
& Vvar__1__P__25929 = Vvar__1__P__25930
& Vvar__0__A__25927 = Vvar__0__A__25928 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__32390,Vvar__0__A__32391,Vvar__1__P__32392,Vvar__1__P__32393,Vvar__2__x__32394,Vvar__2__x__32395,Vvar__3___24Anonymous__32396,Vvar__3___24Anonymous__32397] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__32390,Vvar__1__P__32392,Vvar__2__x__32394,Vvar__3___24Anonymous__32396) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__32391,Vvar__1__P__32393,Vvar__2__x__32395,Vvar__3___24Anonymous__32397)
=> ( Vvar__3___24Anonymous__32396 = Vvar__3___24Anonymous__32397
& Vvar__2__x__32394 = Vvar__2__x__32395
& Vvar__1__P__32392 = Vvar__1__P__32393
& Vvar__0__A__32390 = Vvar__0__A__32391 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__2465,Vvar__0__A__2466,Vvar__1__B__2467,Vvar__1__B__2468,Vvar__2___24Anonymous__2469,Vvar__2___24Anonymous__2470] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2465,Vvar__1__B__2467,Vvar__2___24Anonymous__2469) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2466,Vvar__1__B__2468,Vvar__2___24Anonymous__2470)
=> ( Vvar__2___24Anonymous__2469 = Vvar__2___24Anonymous__2470
& Vvar__1__B__2467 = Vvar__1__B__2468
& Vvar__0__A__2465 = Vvar__0__A__2466 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2471,Vvar__0__A__2472,Vvar__1__B__2473,Vvar__1__B__2474,Vvar__2___24Anonymous__2475,Vvar__2___24Anonymous__2476] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2471,Vvar__1__B__2473) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2472,Vvar__1__B__2474)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2473 = Vvar__1__B__2474
& Vvar__0__A__2471 = Vvar__0__A__2472 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__132,Vvar__0__A__133,Vvar__1__B__134,Vvar__1__B__135,Vvar__2___24Anonymous__136,Vvar__2___24Anonymous__137] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__132,Vvar__1__B__134) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__133,Vvar__1__B__135)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__134 = Vvar__1__B__135
& Vvar__0__A__132 = Vvar__0__A__133 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__138,Vvar__0__A__139,Vvar__1__B__140,Vvar__1__B__141,Vvar__2___24Anonymous__142,Vvar__2___24Anonymous__143] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__138,Vvar__1__B__140) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__139,Vvar__1__B__141)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__140 = Vvar__1__B__141
& Vvar__0__A__138 = Vvar__0__A__139 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__15504,Vvar__0___24Anonymous__15505] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__15504) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__15505)
=> Vvar__0___24Anonymous__15504 = Vvar__0___24Anonymous__15505 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__60,Vvar__0___24Anonymous__61] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__60) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__61)
=> Vvar__0___24Anonymous__60 = Vvar__0___24Anonymous__61 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__58,Vvar__0___24Anonymous__59] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__58) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__59)
=> Vvar__0___24Anonymous__58 = Vvar__0___24Anonymous__59 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__47,Vvar__0___24Anonymous__48] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__47) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__48)
=> Vvar__0___24Anonymous__47 = Vvar__0___24Anonymous__48 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__49,Vvar__0___24Anonymous__50] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__49) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__50)
=> Vvar__0___24Anonymous__49 = Vvar__0___24Anonymous__50 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__32763,Vvar__0___24Anonymous__32764] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__32763) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__32764)
=> Vvar__0___24Anonymous__32763 = Vvar__0___24Anonymous__32764 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__20100,Vvar__0__Qnum__20101,Vvar__1__Qden__20102,Vvar__1__Qden__20103] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__20100,Vvar__1__Qden__20102) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__20101,Vvar__1__Qden__20103)
=> ( Vvar__1__Qden__20102 = Vvar__1__Qden__20103
& Vvar__0__Qnum__20100 = Vvar__0__Qnum__20101 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__31535,Vvar__0__nonneg__31536,Vvar__1__cond__nonneg__31537,Vvar__1__cond__nonneg__31538] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__31535) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__31536)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__31535 = Vvar__0__nonneg__31536 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__31565,Vvar__0__nonzero__31566,Vvar__1__cond__nonzero__31567,Vvar__1__cond__nonzero__31568] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__31565) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__31566)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__31565 = Vvar__0__nonzero__31566 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__20146,Vvar__0__pos__20147,Vvar__1__cond__pos__20148,Vvar__1__cond__pos__20149] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__20146) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__20147)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__20146 = Vvar__0__pos__20147 ) ) ).
fof('$_inj_Coq.Reals.RList.cons',axiom,
! [Vvar__0___24Anonymous__31577,Vvar__0___24Anonymous__31578,Vvar__1___24Anonymous__31579,Vvar__1___24Anonymous__31580] :
( cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__31577,Vvar__1___24Anonymous__31579) = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__31578,Vvar__1___24Anonymous__31580)
=> ( Vvar__1___24Anonymous__31579 = Vvar__1___24Anonymous__31580
& Vvar__0___24Anonymous__31577 = Vvar__0___24Anonymous__31578 ) ) ).
fof('$_inj_Coq.Reals.Rlimit.Build_Metric_Space',axiom,
! [Vvar__0__Base__32341,Vvar__0__Base__32342,Vvar__1__dist__32343,Vvar__1__dist__32344,Vvar__2__dist__pos__32345,Vvar__2__dist__pos__32346,Vvar__3__dist__sym__32347,Vvar__3__dist__sym__32348,Vvar__4__dist__refl__32349,Vvar__4__dist__refl__32350,Vvar__5__dist__tri__32351,Vvar__5__dist__tri__32352] :
( cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__32341,Vvar__1__dist__32343) = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__32342,Vvar__1__dist__32344)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__dist__32343 = Vvar__1__dist__32344
& Vvar__0__Base__32341 = Vvar__0__Base__32342 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__15732,Vvar__0__C__15733,Vvar__1___24Anonymous__15734,Vvar__1___24Anonymous__15735] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__15732,Vvar__1___24Anonymous__15734) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__15733,Vvar__1___24Anonymous__15735)
=> ( Vvar__1___24Anonymous__15734 = Vvar__1___24Anonymous__15735
& Vvar__0__C__15732 = Vvar__0__C__15733 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__15736,Vvar__0__C__15737,Vvar__1___24Anonymous__15738,Vvar__1___24Anonymous__15739,Vvar__2___24Anonymous__15740,Vvar__2___24Anonymous__15741] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__15736,Vvar__1___24Anonymous__15738,Vvar__2___24Anonymous__15740) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__15737,Vvar__1___24Anonymous__15739,Vvar__2___24Anonymous__15741)
=> ( Vvar__2___24Anonymous__15740 = Vvar__2___24Anonymous__15741
& Vvar__1___24Anonymous__15738 = Vvar__1___24Anonymous__15739
& Vvar__0__C__15736 = Vvar__0__C__15737 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__15728,Vvar__0__C__15729,Vvar__1___24Anonymous__15730,Vvar__1___24Anonymous__15731] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__15728,Vvar__1___24Anonymous__15730) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__15729,Vvar__1___24Anonymous__15731)
=> ( Vvar__1___24Anonymous__15730 = Vvar__1___24Anonymous__15731
& Vvar__0__C__15728 = Vvar__0__C__15729 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__15748,Vvar__0__C__15749,Vvar__1___24Anonymous__15750,Vvar__1___24Anonymous__15751,Vvar__2___24Anonymous__15752,Vvar__2___24Anonymous__15753] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__15748,Vvar__1___24Anonymous__15750,Vvar__2___24Anonymous__15752) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__15749,Vvar__1___24Anonymous__15751,Vvar__2___24Anonymous__15753)
=> ( Vvar__2___24Anonymous__15752 = Vvar__2___24Anonymous__15753
& Vvar__1___24Anonymous__15750 = Vvar__1___24Anonymous__15751
& Vvar__0__C__15748 = Vvar__0__C__15749 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__15754,Vvar__0__C__15755,Vvar__1___24Anonymous__15756,Vvar__1___24Anonymous__15757] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__15754,Vvar__1___24Anonymous__15756) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__15755,Vvar__1___24Anonymous__15757)
=> ( Vvar__1___24Anonymous__15756 = Vvar__1___24Anonymous__15757
& Vvar__0__C__15754 = Vvar__0__C__15755 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__15758,Vvar__0__C__15759,Vvar__1___24Anonymous__15760,Vvar__1___24Anonymous__15761,Vvar__2___24Anonymous__15762,Vvar__2___24Anonymous__15763] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__15758,Vvar__1___24Anonymous__15760,Vvar__2___24Anonymous__15762) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__15759,Vvar__1___24Anonymous__15761,Vvar__2___24Anonymous__15763)
=> ( Vvar__2___24Anonymous__15762 = Vvar__2___24Anonymous__15763
& Vvar__1___24Anonymous__15760 = Vvar__1___24Anonymous__15761
& Vvar__0__C__15758 = Vvar__0__C__15759 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__15742,Vvar__0__C__15743,Vvar__1___24Anonymous__15744,Vvar__1___24Anonymous__15745,Vvar__2___24Anonymous__15746,Vvar__2___24Anonymous__15747] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__15742,Vvar__1___24Anonymous__15744,Vvar__2___24Anonymous__15746) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__15743,Vvar__1___24Anonymous__15745,Vvar__2___24Anonymous__15747)
=> ( Vvar__2___24Anonymous__15746 = Vvar__2___24Anonymous__15747
& Vvar__1___24Anonymous__15744 = Vvar__1___24Anonymous__15745
& Vvar__0__C__15742 = Vvar__0__C__15743 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__30641,Vvar__0__C__30642,Vvar__1___24Anonymous__30643,Vvar__1___24Anonymous__30644,Vvar__2___24Anonymous__30645,Vvar__2___24Anonymous__30646,Vvar__3___24Anonymous__30647,Vvar__3___24Anonymous__30648] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__30641,Vvar__1___24Anonymous__30643,Vvar__2___24Anonymous__30645,Vvar__3___24Anonymous__30647) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__30642,Vvar__1___24Anonymous__30644,Vvar__2___24Anonymous__30646,Vvar__3___24Anonymous__30648)
=> ( Vvar__3___24Anonymous__30647 = Vvar__3___24Anonymous__30648
& Vvar__2___24Anonymous__30645 = Vvar__2___24Anonymous__30646
& Vvar__1___24Anonymous__30643 = Vvar__1___24Anonymous__30644
& Vvar__0__C__30641 = Vvar__0__C__30642 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__30631,Vvar__0__C__30632,Vvar__1___24Anonymous__30633,Vvar__1___24Anonymous__30634] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30631,Vvar__1___24Anonymous__30633) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30632,Vvar__1___24Anonymous__30634)
=> ( Vvar__1___24Anonymous__30633 = Vvar__1___24Anonymous__30634
& Vvar__0__C__30631 = Vvar__0__C__30632 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__30635,Vvar__0__C__30636,Vvar__1___24Anonymous__30637,Vvar__1___24Anonymous__30638,Vvar__2___24Anonymous__30639,Vvar__2___24Anonymous__30640] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30635,Vvar__1___24Anonymous__30637,Vvar__2___24Anonymous__30639) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30636,Vvar__1___24Anonymous__30638,Vvar__2___24Anonymous__30640)
=> ( Vvar__2___24Anonymous__30639 = Vvar__2___24Anonymous__30640
& Vvar__1___24Anonymous__30637 = Vvar__1___24Anonymous__30638
& Vvar__0__C__30635 = Vvar__0__C__30636 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__20299,Vvar__0__r__20300] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__20299) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__20300)
=> Vvar__0__r__20299 = Vvar__0__r__20300 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__20287,Vvar__0__r1__20288,Vvar__1__r2__20289,Vvar__1__r2__20290] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__20287,Vvar__1__r2__20289) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__20288,Vvar__1__r2__20290)
=> ( Vvar__1__r2__20289 = Vvar__1__r2__20290
& Vvar__0__r1__20287 = Vvar__0__r1__20288 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__20291,Vvar__0__r1__20292,Vvar__1__r2__20293,Vvar__1__r2__20294] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__20291,Vvar__1__r2__20293) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__20292,Vvar__1__r2__20294)
=> ( Vvar__1__r2__20293 = Vvar__1__r2__20294
& Vvar__0__r1__20291 = Vvar__0__r1__20292 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__20301,Vvar__0__r__20302] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__20301) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__20302)
=> Vvar__0__r__20301 = Vvar__0__r__20302 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__20283,Vvar__0__r1__20284,Vvar__1__r2__20285,Vvar__1__r2__20286] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__20283,Vvar__1__r2__20285) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__20284,Vvar__1__r2__20286)
=> ( Vvar__1__r2__20285 = Vvar__1__r2__20286
& Vvar__0__r1__20283 = Vvar__0__r1__20284 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__20295,Vvar__0__r1__20296,Vvar__1__z__20297,Vvar__1__z__20298] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__20295,Vvar__1__z__20297) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__20296,Vvar__1__z__20298)
=> ( Vvar__1__z__20297 = Vvar__1__z__20298
& Vvar__0__r1__20295 = Vvar__0__r1__20296 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__20279,Vvar__0__r__20280] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__20279) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__20280)
=> Vvar__0__r__20279 = Vvar__0__r__20280 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__20281,Vvar__0__r__20282] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__20281) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__20282)
=> Vvar__0__r__20281 = Vvar__0__r__20282 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__21206,Vvar__0__T__21207,Vvar__1__Flhs__21208,Vvar__1__Flhs__21209,Vvar__2__Fop__21210,Vvar__2__Fop__21211,Vvar__3__Frhs__21212,Vvar__3__Frhs__21213] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__21206,Vvar__1__Flhs__21208,Vvar__2__Fop__21210,Vvar__3__Frhs__21212) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__21207,Vvar__1__Flhs__21209,Vvar__2__Fop__21211,Vvar__3__Frhs__21213)
=> ( Vvar__3__Frhs__21212 = Vvar__3__Frhs__21213
& Vvar__2__Fop__21210 = Vvar__2__Fop__21211
& Vvar__1__Flhs__21208 = Vvar__1__Flhs__21209
& Vvar__0__T__21206 = Vvar__0__T__21207 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__21173,Vvar__0__C__21174,Vvar__1___24Anonymous__21175,Vvar__1___24Anonymous__21176,Vvar__2___24Anonymous__21177,Vvar__2___24Anonymous__21178] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__21173,Vvar__1___24Anonymous__21175,Vvar__2___24Anonymous__21177) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__21174,Vvar__1___24Anonymous__21176,Vvar__2___24Anonymous__21178)
=> ( Vvar__2___24Anonymous__21177 = Vvar__2___24Anonymous__21178
& Vvar__1___24Anonymous__21175 = Vvar__1___24Anonymous__21176
& Vvar__0__C__21173 = Vvar__0__C__21174 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__21179,Vvar__0__C__21180,Vvar__1___24Anonymous__21181,Vvar__1___24Anonymous__21182] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__21179,Vvar__1___24Anonymous__21181) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__21180,Vvar__1___24Anonymous__21182)
=> ( Vvar__1___24Anonymous__21181 = Vvar__1___24Anonymous__21182
& Vvar__0__C__21179 = Vvar__0__C__21180 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__21153,Vvar__0__C__21154,Vvar__1___24Anonymous__21155,Vvar__1___24Anonymous__21156] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21153,Vvar__1___24Anonymous__21155) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21154,Vvar__1___24Anonymous__21156)
=> ( Vvar__1___24Anonymous__21155 = Vvar__1___24Anonymous__21156
& Vvar__0__C__21153 = Vvar__0__C__21154 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__21161,Vvar__0__C__21162,Vvar__1___24Anonymous__21163,Vvar__1___24Anonymous__21164,Vvar__2___24Anonymous__21165,Vvar__2___24Anonymous__21166] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__21161,Vvar__1___24Anonymous__21163,Vvar__2___24Anonymous__21165) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__21162,Vvar__1___24Anonymous__21164,Vvar__2___24Anonymous__21166)
=> ( Vvar__2___24Anonymous__21165 = Vvar__2___24Anonymous__21166
& Vvar__1___24Anonymous__21163 = Vvar__1___24Anonymous__21164
& Vvar__0__C__21161 = Vvar__0__C__21162 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__21167,Vvar__0__C__21168,Vvar__1___24Anonymous__21169,Vvar__1___24Anonymous__21170,Vvar__2___24Anonymous__21171,Vvar__2___24Anonymous__21172] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__21167,Vvar__1___24Anonymous__21169,Vvar__2___24Anonymous__21171) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__21168,Vvar__1___24Anonymous__21170,Vvar__2___24Anonymous__21172)
=> ( Vvar__2___24Anonymous__21171 = Vvar__2___24Anonymous__21172
& Vvar__1___24Anonymous__21169 = Vvar__1___24Anonymous__21170
& Vvar__0__C__21167 = Vvar__0__C__21168 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__21157,Vvar__0__C__21158,Vvar__1___24Anonymous__21159,Vvar__1___24Anonymous__21160] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21157,Vvar__1___24Anonymous__21159) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21158,Vvar__1___24Anonymous__21160)
=> ( Vvar__1___24Anonymous__21159 = Vvar__1___24Anonymous__21160
& Vvar__0__C__21157 = Vvar__0__C__21158 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__21183,Vvar__0__C__21184] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__21183) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__21184)
=> Vvar__0__C__21183 = Vvar__0__C__21184 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__26479,Vvar__0__TA__26480,Vvar__1__TX__26481,Vvar__1__TX__26482,Vvar__2__AA__26483,Vvar__2__AA__26484,Vvar__3__AF__26485,Vvar__3__AF__26486,Vvar__4___24Anonymous__26487,Vvar__4___24Anonymous__26488,Vvar__5___24Anonymous__26489,Vvar__5___24Anonymous__26490] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__26479,Vvar__1__TX__26481,Vvar__2__AA__26483,Vvar__3__AF__26485,Vvar__4___24Anonymous__26487,Vvar__5___24Anonymous__26489) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__26480,Vvar__1__TX__26482,Vvar__2__AA__26484,Vvar__3__AF__26486,Vvar__4___24Anonymous__26488,Vvar__5___24Anonymous__26490)
=> ( Vvar__5___24Anonymous__26489 = Vvar__5___24Anonymous__26490
& Vvar__4___24Anonymous__26487 = Vvar__4___24Anonymous__26488
& Vvar__3__AF__26485 = Vvar__3__AF__26486
& Vvar__2__AA__26483 = Vvar__2__AA__26484
& Vvar__1__TX__26481 = Vvar__1__TX__26482
& Vvar__0__TA__26479 = Vvar__0__TA__26480 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__26491,Vvar__0__TA__26492,Vvar__1__TX__26493,Vvar__1__TX__26494,Vvar__2__AA__26495,Vvar__2__AA__26496,Vvar__3__AF__26497,Vvar__3__AF__26498,Vvar__4___24Anonymous__26499,Vvar__4___24Anonymous__26500,Vvar__5___24Anonymous__26501,Vvar__5___24Anonymous__26502] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__26491,Vvar__1__TX__26493,Vvar__2__AA__26495,Vvar__3__AF__26497,Vvar__4___24Anonymous__26499,Vvar__5___24Anonymous__26501) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__26492,Vvar__1__TX__26494,Vvar__2__AA__26496,Vvar__3__AF__26498,Vvar__4___24Anonymous__26500,Vvar__5___24Anonymous__26502)
=> ( Vvar__5___24Anonymous__26501 = Vvar__5___24Anonymous__26502
& Vvar__4___24Anonymous__26499 = Vvar__4___24Anonymous__26500
& Vvar__3__AF__26497 = Vvar__3__AF__26498
& Vvar__2__AA__26495 = Vvar__2__AA__26496
& Vvar__1__TX__26493 = Vvar__1__TX__26494
& Vvar__0__TA__26491 = Vvar__0__TA__26492 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__26503,Vvar__0__TA__26504,Vvar__1__TX__26505,Vvar__1__TX__26506,Vvar__2__AA__26507,Vvar__2__AA__26508,Vvar__3__AF__26509,Vvar__3__AF__26510,Vvar__4___24Anonymous__26511,Vvar__4___24Anonymous__26512,Vvar__5___24Anonymous__26513,Vvar__5___24Anonymous__26514] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__26503,Vvar__1__TX__26505,Vvar__2__AA__26507,Vvar__3__AF__26509,Vvar__4___24Anonymous__26511,Vvar__5___24Anonymous__26513) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__26504,Vvar__1__TX__26506,Vvar__2__AA__26508,Vvar__3__AF__26510,Vvar__4___24Anonymous__26512,Vvar__5___24Anonymous__26514)
=> ( Vvar__5___24Anonymous__26513 = Vvar__5___24Anonymous__26514
& Vvar__4___24Anonymous__26511 = Vvar__4___24Anonymous__26512
& Vvar__3__AF__26509 = Vvar__3__AF__26510
& Vvar__2__AA__26507 = Vvar__2__AA__26508
& Vvar__1__TX__26505 = Vvar__1__TX__26506
& Vvar__0__TA__26503 = Vvar__0__TA__26504 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__26461,Vvar__0__TA__26462,Vvar__1__TX__26463,Vvar__1__TX__26464,Vvar__2__AA__26465,Vvar__2__AA__26466,Vvar__3__AF__26467,Vvar__3__AF__26468] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__26461,Vvar__1__TX__26463,Vvar__2__AA__26465,Vvar__3__AF__26467) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__26462,Vvar__1__TX__26464,Vvar__2__AA__26466,Vvar__3__AF__26468)
=> ( Vvar__3__AF__26467 = Vvar__3__AF__26468
& Vvar__2__AA__26465 = Vvar__2__AA__26466
& Vvar__1__TX__26463 = Vvar__1__TX__26464
& Vvar__0__TA__26461 = Vvar__0__TA__26462 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__26525,Vvar__0__TA__26526,Vvar__1__TX__26527,Vvar__1__TX__26528,Vvar__2__AA__26529,Vvar__2__AA__26530,Vvar__3__AF__26531,Vvar__3__AF__26532,Vvar__4___24Anonymous__26533,Vvar__4___24Anonymous__26534,Vvar__5___24Anonymous__26535,Vvar__5___24Anonymous__26536,Vvar__6___24Anonymous__26537,Vvar__6___24Anonymous__26538] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__26525,Vvar__1__TX__26527,Vvar__2__AA__26529,Vvar__3__AF__26531,Vvar__4___24Anonymous__26533,Vvar__5___24Anonymous__26535,Vvar__6___24Anonymous__26537) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__26526,Vvar__1__TX__26528,Vvar__2__AA__26530,Vvar__3__AF__26532,Vvar__4___24Anonymous__26534,Vvar__5___24Anonymous__26536,Vvar__6___24Anonymous__26538)
=> ( Vvar__6___24Anonymous__26537 = Vvar__6___24Anonymous__26538
& Vvar__5___24Anonymous__26535 = Vvar__5___24Anonymous__26536
& Vvar__4___24Anonymous__26533 = Vvar__4___24Anonymous__26534
& Vvar__3__AF__26531 = Vvar__3__AF__26532
& Vvar__2__AA__26529 = Vvar__2__AA__26530
& Vvar__1__TX__26527 = Vvar__1__TX__26528
& Vvar__0__TA__26525 = Vvar__0__TA__26526 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__26515,Vvar__0__TA__26516,Vvar__1__TX__26517,Vvar__1__TX__26518,Vvar__2__AA__26519,Vvar__2__AA__26520,Vvar__3__AF__26521,Vvar__3__AF__26522,Vvar__4___24Anonymous__26523,Vvar__4___24Anonymous__26524] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__26515,Vvar__1__TX__26517,Vvar__2__AA__26519,Vvar__3__AF__26521,Vvar__4___24Anonymous__26523) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__26516,Vvar__1__TX__26518,Vvar__2__AA__26520,Vvar__3__AF__26522,Vvar__4___24Anonymous__26524)
=> ( Vvar__4___24Anonymous__26523 = Vvar__4___24Anonymous__26524
& Vvar__3__AF__26521 = Vvar__3__AF__26522
& Vvar__2__AA__26519 = Vvar__2__AA__26520
& Vvar__1__TX__26517 = Vvar__1__TX__26518
& Vvar__0__TA__26515 = Vvar__0__TA__26516 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__26453,Vvar__0__TA__26454,Vvar__1__TX__26455,Vvar__1__TX__26456,Vvar__2__AA__26457,Vvar__2__AA__26458,Vvar__3__AF__26459,Vvar__3__AF__26460] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__26453,Vvar__1__TX__26455,Vvar__2__AA__26457,Vvar__3__AF__26459) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__26454,Vvar__1__TX__26456,Vvar__2__AA__26458,Vvar__3__AF__26460)
=> ( Vvar__3__AF__26459 = Vvar__3__AF__26460
& Vvar__2__AA__26457 = Vvar__2__AA__26458
& Vvar__1__TX__26455 = Vvar__1__TX__26456
& Vvar__0__TA__26453 = Vvar__0__TA__26454 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__26469,Vvar__0__TA__26470,Vvar__1__TX__26471,Vvar__1__TX__26472,Vvar__2__AA__26473,Vvar__2__AA__26474,Vvar__3__AF__26475,Vvar__3__AF__26476,Vvar__4___24Anonymous__26477,Vvar__4___24Anonymous__26478] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__26469,Vvar__1__TX__26471,Vvar__2__AA__26473,Vvar__3__AF__26475,Vvar__4___24Anonymous__26477) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__26470,Vvar__1__TX__26472,Vvar__2__AA__26474,Vvar__3__AF__26476,Vvar__4___24Anonymous__26478)
=> ( Vvar__4___24Anonymous__26477 = Vvar__4___24Anonymous__26478
& Vvar__3__AF__26475 = Vvar__3__AF__26476
& Vvar__2__AA__26473 = Vvar__2__AA__26474
& Vvar__1__TX__26471 = Vvar__1__TX__26472
& Vvar__0__TA__26469 = Vvar__0__TA__26470 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__26608,Vvar__0__A__26609,Vvar__1___24Anonymous__26610,Vvar__1___24Anonymous__26611,Vvar__2___24Anonymous__26612,Vvar__2___24Anonymous__26613,Vvar__3___24Anonymous__26614,Vvar__3___24Anonymous__26615] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__26608,Vvar__1___24Anonymous__26610,Vvar__2___24Anonymous__26612,Vvar__3___24Anonymous__26614) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__26609,Vvar__1___24Anonymous__26611,Vvar__2___24Anonymous__26613,Vvar__3___24Anonymous__26615)
=> ( Vvar__3___24Anonymous__26614 = Vvar__3___24Anonymous__26615
& Vvar__2___24Anonymous__26612 = Vvar__2___24Anonymous__26613
& Vvar__1___24Anonymous__26610 = Vvar__1___24Anonymous__26611
& Vvar__0__A__26608 = Vvar__0__A__26609 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__26604,Vvar__0__A__26605,Vvar__1___24Anonymous__26606,Vvar__1___24Anonymous__26607] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__26604,Vvar__1___24Anonymous__26606) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__26605,Vvar__1___24Anonymous__26607)
=> ( Vvar__1___24Anonymous__26606 = Vvar__1___24Anonymous__26607
& Vvar__0__A__26604 = Vvar__0__A__26605 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__26602,Vvar__0__A__26603] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__26602) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__26603)
=> Vvar__0__A__26602 = Vvar__0__A__26603 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__561,Vvar__0__C__562] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__561) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__562)
=> Vvar__0__C__561 = Vvar__0__C__562 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__559,Vvar__0__C__560] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__559) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__560)
=> Vvar__0__C__559 = Vvar__0__C__560 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__567,Vvar__0__C__568,Vvar__1___24Anonymous__569,Vvar__1___24Anonymous__570] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__567,Vvar__1___24Anonymous__569) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__568,Vvar__1___24Anonymous__570)
=> ( Vvar__1___24Anonymous__569 = Vvar__1___24Anonymous__570
& Vvar__0__C__567 = Vvar__0__C__568 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__571,Vvar__0__C__572,Vvar__1___24Anonymous__573,Vvar__1___24Anonymous__574,Vvar__2___24Anonymous__575,Vvar__2___24Anonymous__576] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__571,Vvar__1___24Anonymous__573,Vvar__2___24Anonymous__575) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__572,Vvar__1___24Anonymous__574,Vvar__2___24Anonymous__576)
=> ( Vvar__2___24Anonymous__575 = Vvar__2___24Anonymous__576
& Vvar__1___24Anonymous__573 = Vvar__1___24Anonymous__574
& Vvar__0__C__571 = Vvar__0__C__572 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__563,Vvar__0__C__564,Vvar__1___24Anonymous__565,Vvar__1___24Anonymous__566] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__563,Vvar__1___24Anonymous__565) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__564,Vvar__1___24Anonymous__566)
=> ( Vvar__1___24Anonymous__565 = Vvar__1___24Anonymous__566
& Vvar__0__C__563 = Vvar__0__C__564 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__597,Vvar__0__C__598,Vvar__1___24Anonymous__599,Vvar__1___24Anonymous__600,Vvar__2___24Anonymous__601,Vvar__2___24Anonymous__602] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__597,Vvar__1___24Anonymous__599,Vvar__2___24Anonymous__601) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__598,Vvar__1___24Anonymous__600,Vvar__2___24Anonymous__602)
=> ( Vvar__2___24Anonymous__601 = Vvar__2___24Anonymous__602
& Vvar__1___24Anonymous__599 = Vvar__1___24Anonymous__600
& Vvar__0__C__597 = Vvar__0__C__598 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__593,Vvar__0__C__594,Vvar__1___24Anonymous__595,Vvar__1___24Anonymous__596] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__593,Vvar__1___24Anonymous__595) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__594,Vvar__1___24Anonymous__596)
=> ( Vvar__1___24Anonymous__595 = Vvar__1___24Anonymous__596
& Vvar__0__C__593 = Vvar__0__C__594 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__583,Vvar__0__C__584,Vvar__1___24Anonymous__585,Vvar__1___24Anonymous__586,Vvar__2___24Anonymous__587,Vvar__2___24Anonymous__588] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__583,Vvar__1___24Anonymous__585,Vvar__2___24Anonymous__587) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__584,Vvar__1___24Anonymous__586,Vvar__2___24Anonymous__588)
=> ( Vvar__2___24Anonymous__587 = Vvar__2___24Anonymous__588
& Vvar__1___24Anonymous__585 = Vvar__1___24Anonymous__586
& Vvar__0__C__583 = Vvar__0__C__584 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__589,Vvar__0__C__590,Vvar__1___24Anonymous__591,Vvar__1___24Anonymous__592] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__589,Vvar__1___24Anonymous__591) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__590,Vvar__1___24Anonymous__592)
=> ( Vvar__1___24Anonymous__591 = Vvar__1___24Anonymous__592
& Vvar__0__C__589 = Vvar__0__C__590 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__603,Vvar__0__C__604,Vvar__1___24Anonymous__605,Vvar__1___24Anonymous__606,Vvar__2___24Anonymous__607,Vvar__2___24Anonymous__608] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__603,Vvar__1___24Anonymous__605,Vvar__2___24Anonymous__607) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__604,Vvar__1___24Anonymous__606,Vvar__2___24Anonymous__608)
=> ( Vvar__2___24Anonymous__607 = Vvar__2___24Anonymous__608
& Vvar__1___24Anonymous__605 = Vvar__1___24Anonymous__606
& Vvar__0__C__603 = Vvar__0__C__604 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__577,Vvar__0__C__578,Vvar__1___24Anonymous__579,Vvar__1___24Anonymous__580,Vvar__2___24Anonymous__581,Vvar__2___24Anonymous__582] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__577,Vvar__1___24Anonymous__579,Vvar__2___24Anonymous__581) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__578,Vvar__1___24Anonymous__580,Vvar__2___24Anonymous__582)
=> ( Vvar__2___24Anonymous__581 = Vvar__2___24Anonymous__582
& Vvar__1___24Anonymous__579 = Vvar__1___24Anonymous__580
& Vvar__0__C__577 = Vvar__0__C__578 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__921,Vvar__0__C__922,Vvar__1__num__923,Vvar__1__num__924,Vvar__2__denum__925,Vvar__2__denum__926,Vvar__3__condition__927,Vvar__3__condition__928] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__921,Vvar__1__num__923,Vvar__2__denum__925,Vvar__3__condition__927) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__922,Vvar__1__num__924,Vvar__2__denum__926,Vvar__3__condition__928)
=> ( Vvar__3__condition__927 = Vvar__3__condition__928
& Vvar__2__denum__925 = Vvar__2__denum__926
& Vvar__1__num__923 = Vvar__1__num__924
& Vvar__0__C__921 = Vvar__0__C__922 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__30681,Vvar__0__C__30682,Vvar__1__rsplit__left__30683,Vvar__1__rsplit__left__30684,Vvar__2__rsplit__common__30685,Vvar__2__rsplit__common__30686,Vvar__3__rsplit__right__30687,Vvar__3__rsplit__right__30688] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__30681,Vvar__1__rsplit__left__30683,Vvar__2__rsplit__common__30685,Vvar__3__rsplit__right__30687) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__30682,Vvar__1__rsplit__left__30684,Vvar__2__rsplit__common__30686,Vvar__3__rsplit__right__30688)
=> ( Vvar__3__rsplit__right__30687 = Vvar__3__rsplit__right__30688
& Vvar__2__rsplit__common__30685 = Vvar__2__rsplit__common__30686
& Vvar__1__rsplit__left__30683 = Vvar__1__rsplit__left__30684
& Vvar__0__C__30681 = Vvar__0__C__30682 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__1990,Vvar__0__C__1991] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1990) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1991)
=> Vvar__0__C__1990 = Vvar__0__C__1991 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__1988,Vvar__0__C__1989] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1988) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1989)
=> Vvar__0__C__1988 = Vvar__0__C__1989 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__1996,Vvar__0__C__1997,Vvar__1___24Anonymous__1998,Vvar__1___24Anonymous__1999] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1996,Vvar__1___24Anonymous__1998) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1997,Vvar__1___24Anonymous__1999)
=> ( Vvar__1___24Anonymous__1998 = Vvar__1___24Anonymous__1999
& Vvar__0__C__1996 = Vvar__0__C__1997 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__2000,Vvar__0__C__2001,Vvar__1___24Anonymous__2002,Vvar__1___24Anonymous__2003,Vvar__2___24Anonymous__2004,Vvar__2___24Anonymous__2005] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2000,Vvar__1___24Anonymous__2002,Vvar__2___24Anonymous__2004) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2001,Vvar__1___24Anonymous__2003,Vvar__2___24Anonymous__2005)
=> ( Vvar__2___24Anonymous__2004 = Vvar__2___24Anonymous__2005
& Vvar__1___24Anonymous__2002 = Vvar__1___24Anonymous__2003
& Vvar__0__C__2000 = Vvar__0__C__2001 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__1992,Vvar__0__C__1993,Vvar__1___24Anonymous__1994,Vvar__1___24Anonymous__1995] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1992,Vvar__1___24Anonymous__1994) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1993,Vvar__1___24Anonymous__1995)
=> ( Vvar__1___24Anonymous__1994 = Vvar__1___24Anonymous__1995
& Vvar__0__C__1992 = Vvar__0__C__1993 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__2012,Vvar__0__C__2013,Vvar__1___24Anonymous__2014,Vvar__1___24Anonymous__2015,Vvar__2___24Anonymous__2016,Vvar__2___24Anonymous__2017] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2012,Vvar__1___24Anonymous__2014,Vvar__2___24Anonymous__2016) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2013,Vvar__1___24Anonymous__2015,Vvar__2___24Anonymous__2017)
=> ( Vvar__2___24Anonymous__2016 = Vvar__2___24Anonymous__2017
& Vvar__1___24Anonymous__2014 = Vvar__1___24Anonymous__2015
& Vvar__0__C__2012 = Vvar__0__C__2013 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__2018,Vvar__0__C__2019,Vvar__1___24Anonymous__2020,Vvar__1___24Anonymous__2021] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2018,Vvar__1___24Anonymous__2020) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2019,Vvar__1___24Anonymous__2021)
=> ( Vvar__1___24Anonymous__2020 = Vvar__1___24Anonymous__2021
& Vvar__0__C__2018 = Vvar__0__C__2019 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__2022,Vvar__0__C__2023,Vvar__1___24Anonymous__2024,Vvar__1___24Anonymous__2025,Vvar__2___24Anonymous__2026,Vvar__2___24Anonymous__2027] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2022,Vvar__1___24Anonymous__2024,Vvar__2___24Anonymous__2026) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2023,Vvar__1___24Anonymous__2025,Vvar__2___24Anonymous__2027)
=> ( Vvar__2___24Anonymous__2026 = Vvar__2___24Anonymous__2027
& Vvar__1___24Anonymous__2024 = Vvar__1___24Anonymous__2025
& Vvar__0__C__2022 = Vvar__0__C__2023 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__2006,Vvar__0__C__2007,Vvar__1___24Anonymous__2008,Vvar__1___24Anonymous__2009,Vvar__2___24Anonymous__2010,Vvar__2___24Anonymous__2011] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2006,Vvar__1___24Anonymous__2008,Vvar__2___24Anonymous__2010) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2007,Vvar__1___24Anonymous__2009,Vvar__2___24Anonymous__2011)
=> ( Vvar__2___24Anonymous__2010 = Vvar__2___24Anonymous__2011
& Vvar__1___24Anonymous__2008 = Vvar__1___24Anonymous__2009
& Vvar__0__C__2006 = Vvar__0__C__2007 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__1645,Vvar__0__C__1646,Vvar__1___24Anonymous__1647,Vvar__1___24Anonymous__1648,Vvar__2___24Anonymous__1649,Vvar__2___24Anonymous__1650,Vvar__3___24Anonymous__1651,Vvar__3___24Anonymous__1652] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1645,Vvar__1___24Anonymous__1647,Vvar__2___24Anonymous__1649,Vvar__3___24Anonymous__1651) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1646,Vvar__1___24Anonymous__1648,Vvar__2___24Anonymous__1650,Vvar__3___24Anonymous__1652)
=> ( Vvar__3___24Anonymous__1651 = Vvar__3___24Anonymous__1652
& Vvar__2___24Anonymous__1649 = Vvar__2___24Anonymous__1650
& Vvar__1___24Anonymous__1647 = Vvar__1___24Anonymous__1648
& Vvar__0__C__1645 = Vvar__0__C__1646 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__1635,Vvar__0__C__1636,Vvar__1___24Anonymous__1637,Vvar__1___24Anonymous__1638] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1635,Vvar__1___24Anonymous__1637) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1636,Vvar__1___24Anonymous__1638)
=> ( Vvar__1___24Anonymous__1637 = Vvar__1___24Anonymous__1638
& Vvar__0__C__1635 = Vvar__0__C__1636 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1639,Vvar__0__C__1640,Vvar__1___24Anonymous__1641,Vvar__1___24Anonymous__1642,Vvar__2___24Anonymous__1643,Vvar__2___24Anonymous__1644] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1639,Vvar__1___24Anonymous__1641,Vvar__2___24Anonymous__1643) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1640,Vvar__1___24Anonymous__1642,Vvar__2___24Anonymous__1644)
=> ( Vvar__2___24Anonymous__1643 = Vvar__2___24Anonymous__1644
& Vvar__1___24Anonymous__1641 = Vvar__1___24Anonymous__1642
& Vvar__0__C__1639 = Vvar__0__C__1640 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__1802,Vvar__0___24Anonymous__1803,Vvar__1___24Anonymous__1804,Vvar__1___24Anonymous__1805] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1802,Vvar__1___24Anonymous__1804) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1803,Vvar__1___24Anonymous__1805)
=> ( Vvar__1___24Anonymous__1804 = Vvar__1___24Anonymous__1805
& Vvar__0___24Anonymous__1802 = Vvar__0___24Anonymous__1803 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__1798,Vvar__0___24Anonymous__1799,Vvar__1___24Anonymous__1800,Vvar__1___24Anonymous__1801] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1798,Vvar__1___24Anonymous__1800) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1799,Vvar__1___24Anonymous__1801)
=> ( Vvar__1___24Anonymous__1800 = Vvar__1___24Anonymous__1801
& Vvar__0___24Anonymous__1798 = Vvar__0___24Anonymous__1799 ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__15544,Vvar__1__Q__15545,Vvar__2___24Anonymous__15546] :
( cProp___24t(Vvar__0__P__15544)
=> ( cProp___24t(Vvar__1__Q__15545)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__15546)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__15544,Vvar__1__Q__15545,Vvar__2___24Anonymous__15546)
=> ( ( p(Vvar__0__P__15544)
& Vvar__2___24Anonymous__15546 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__15545)
& Vvar__2___24Anonymous__15546 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__15581,Vvar__1__Plt__15582,Vvar__2__Pgt__15583,Vvar__3___24Anonymous__15584] :
( cProp___24t(Vvar__0__Peq__15581)
=> ( cProp___24t(Vvar__1__Plt__15582)
=> ( cProp___24t(Vvar__2__Pgt__15583)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__15584)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__15581,Vvar__1__Plt__15582,Vvar__2__Pgt__15583,Vvar__3___24Anonymous__15584)
=> ( ( p(Vvar__0__Peq__15581)
& Vvar__3___24Anonymous__15584 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__15582)
& Vvar__3___24Anonymous__15584 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__15583)
& Vvar__3___24Anonymous__15584 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX237] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX237)
=> ( VX237 = cCoq_2eInit_2eDatatypes_2etrue
| VX237 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX96] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX96)
=> ( VX96 = cCoq_2eInit_2eDatatypes_2eEq
| VX96 = cCoq_2eInit_2eDatatypes_2eLt
| VX96 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__243,VX244] :
( cType___24t(Vvar__0__A__243)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__243,VX244)
=> ( VX244 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__243)
| ? [Vvar__1___24Anonymous__247] :
( t(Vvar__1___24Anonymous__247,Vvar__0__A__243)
& ? [Vvar__2___24Anonymous__248] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__243,Vvar__2___24Anonymous__248)
& VX244 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__243,Vvar__1___24Anonymous__247,Vvar__2___24Anonymous__248) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX238] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX238)
=> ( VX238 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__239] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__239)
& VX238 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__239) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__15560,VX15561] :
( cType___24t(Vvar__0__A__15560)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__15560,VX15561)
=> ( ? [Vvar__1___24Anonymous__15563] :
( t(Vvar__1___24Anonymous__15563,Vvar__0__A__15560)
& VX15561 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__15560,Vvar__1___24Anonymous__15563) )
| VX15561 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__15560) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__64,Vvar__1__B__65,VX66] :
( cType___24t(Vvar__0__A__64)
=> ( cType___24t(Vvar__1__B__65)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__64,Vvar__1__B__65,VX66)
=> ? [Vvar__2___24Anonymous__69] :
( t(Vvar__2___24Anonymous__69,Vvar__0__A__64)
& ? [Vvar__3___24Anonymous__70] :
( t(Vvar__3___24Anonymous__70,Vvar__1__B__65)
& VX66 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__64,Vvar__1__B__65,Vvar__2___24Anonymous__69,Vvar__3___24Anonymous__70) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__30535,Vvar__1__B__30536,VX30537] :
( cType___24t(Vvar__0__A__30535)
=> ( cType___24t(Vvar__1__B__30536)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__30535,Vvar__1__B__30536,VX30537)
=> ( ? [Vvar__2___24Anonymous__30540] :
( t(Vvar__2___24Anonymous__30540,Vvar__0__A__30535)
& VX30537 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__30535,Vvar__1__B__30536,Vvar__2___24Anonymous__30540) )
| ? [Vvar__2___24Anonymous__30543] :
( t(Vvar__2___24Anonymous__30543,Vvar__1__B__30536)
& VX30537 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__30535,Vvar__1__B__30536,Vvar__2___24Anonymous__30543) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX2589] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX2589)
=> VX2589 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__20085,Vvar__1___24Anonymous__20086] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__20085)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__20086)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__20085,Vvar__1___24Anonymous__20086))
=> ( Vvar__1___24Anonymous__20086 = Vvar__0__n__20085
| ? [Vvar__1__m__20090] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__20090)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__20085,Vvar__1__m__20090))
& Vvar__1___24Anonymous__20086 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__20090) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__25904,Vvar__1__P__25905,VX25908] :
( cType___24t(Vvar__0__A__25904)
=> ( c_24__type__25918___24t(Vvar__0__A__25904,Vvar__1__P__25905,Vvar__1__P__25905)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__25904,Vvar__1__P__25905,VX25908)
=> ? [Vvar__2__x__25913] :
( t(Vvar__2__x__25913,Vvar__0__A__25904)
& p(happ(Vvar__1__P__25905,Vvar__2__x__25913))
& VX25908 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__25904,Vvar__1__P__25905,Vvar__2__x__25913) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__32367,Vvar__1__P__32368,VX32371] :
( cType___24t(Vvar__0__A__32367)
=> ( c_24__type__32381___24t(Vvar__0__A__32367,Vvar__1__P__32368,Vvar__1__P__32368)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__32367,Vvar__1__P__32368,VX32371)
=> ? [Vvar__2__x__32376] :
( t(Vvar__2__x__32376,Vvar__0__A__32367)
& ? [Vvar__3___24Anonymous__32377] :
( t(Vvar__3___24Anonymous__32377,happ(Vvar__1__P__32368,Vvar__2__x__32376))
& VX32371 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__32367,Vvar__1__P__32368,Vvar__2__x__32376,Vvar__3___24Anonymous__32377) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__114,Vvar__1__B__115,VX116] :
( cProp___24t(Vvar__0__A__114)
=> ( cProp___24t(Vvar__1__B__115)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__114,Vvar__1__B__115,VX116)
=> ( ( p(Vvar__0__A__114)
& VX116 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__114,Vvar__1__B__115) )
| ( p(Vvar__1__B__115)
& VX116 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__114,Vvar__1__B__115) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__2447,Vvar__1__B__2448,VX2449] :
( cType___24t(Vvar__0__A__2447)
=> ( cProp___24t(Vvar__1__B__2448)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__2447,Vvar__1__B__2448,VX2449)
=> ( ? [Vvar__2___24Anonymous__2452] :
( t(Vvar__2___24Anonymous__2452,Vvar__0__A__2447)
& VX2449 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2447,Vvar__1__B__2448,Vvar__2___24Anonymous__2452) )
| ( p(Vvar__1__B__2448)
& VX2449 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2447,Vvar__1__B__2448) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__37110,Vvar__1__eqA__37111,Vvar__2__x__37116,Vvar__3___24Anonymous__37117] :
( cType___24t(Vvar__0__A__37110)
=> ( c_24__type__37150___24t(Vvar__0__A__37110,Vvar__1__eqA__37111,Vvar__2__x__37116,Vvar__3___24Anonymous__37117,Vvar__1__eqA__37111)
=> ( t(Vvar__2__x__37116,Vvar__0__A__37110)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__37110,Vvar__3___24Anonymous__37117)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__37110,Vvar__1__eqA__37111,Vvar__2__x__37116,Vvar__3___24Anonymous__37117)
=> ( ? [Vvar__3__y__37126] :
( t(Vvar__3__y__37126,Vvar__0__A__37110)
& ? [Vvar__4__l__37127] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__37110,Vvar__4__l__37127)
& p(happ(happ(Vvar__1__eqA__37111,Vvar__2__x__37116),Vvar__3__y__37126))
& Vvar__3___24Anonymous__37117 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__37110,Vvar__3__y__37126,Vvar__4__l__37127) ) )
| ? [Vvar__3__y__37136] :
( t(Vvar__3__y__37136,Vvar__0__A__37110)
& ? [Vvar__4__l__37137] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__37110,Vvar__4__l__37137)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__37110,Vvar__1__eqA__37111,Vvar__2__x__37116,Vvar__4__l__37137)
& Vvar__3___24Anonymous__37117 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__37110,Vvar__3__y__37136,Vvar__4__l__37137) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__37158,Vvar__1__eqA__37159,Vvar__2___24Anonymous__37164] :
( cType___24t(Vvar__0__A__37158)
=> ( c_24__type__37191___24t(Vvar__0__A__37158,Vvar__1__eqA__37159,Vvar__2___24Anonymous__37164,Vvar__1__eqA__37159)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__37158,Vvar__2___24Anonymous__37164)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__37158,Vvar__1__eqA__37159,Vvar__2___24Anonymous__37164)
=> ( Vvar__2___24Anonymous__37164 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__37158)
| ? [Vvar__2__x__37178] :
( t(Vvar__2__x__37178,Vvar__0__A__37158)
& ? [Vvar__3__l__37179] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__37158,Vvar__3__l__37179)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__37158,Vvar__1__eqA__37159,Vvar__2__x__37178,Vvar__3__l__37179)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__37158,Vvar__1__eqA__37159,Vvar__3__l__37179)
& Vvar__2___24Anonymous__37164 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__37158,Vvar__2__x__37178,Vvar__3__l__37179) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX15501] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX15501)
=> ( VX15501 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__15502] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15502)
& VX15501 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__15502) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX51] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX51)
=> ( VX51 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__52] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__52)
& VX51 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__52) )
| ? [Vvar__0___24Anonymous__53] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__53)
& VX51 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__53) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX40] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX40)
=> ( ? [Vvar__0___24Anonymous__41] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41)
& VX40 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__41) )
| ? [Vvar__0___24Anonymous__42] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42)
& VX40 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__42) )
| VX40 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX32759] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX32759)
=> ( VX32759 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__32760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32760)
& VX32759 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__32760) )
| VX32759 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX20097] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX20097)
=> ? [Vvar__0__Qnum__20098] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__20098)
& ? [Vvar__1__Qden__20099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__20099)
& VX20097 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__20098,Vvar__1__Qden__20099) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX31532] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX31532)
=> ? [Vvar__0__nonneg__31533] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__31533)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__31533))
& VX31532 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__31533) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX31562] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX31562)
=> ? [Vvar__0__nonzero__31563] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__31563)
& Vvar__0__nonzero__31563 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX31562 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__31563) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX20143] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX20143)
=> ? [Vvar__0__pos__20144] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__20144)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__20144))
& VX20143 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__20144) ) ) ).
fof('$_inversion_Coq.Reals.RList.Rlist',axiom,
! [VX31572] :
( cCoq_2eReals_2eRList_2eRlist___24t(VX31572)
=> ( VX31572 = cCoq_2eReals_2eRList_2enil
| ? [Vvar__0___24Anonymous__31573] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__31573)
& ? [Vvar__1___24Anonymous__31574] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__31574)
& VX31572 = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__31573,Vvar__1___24Anonymous__31574) ) ) ) ) ).
fof('$_inversion_Coq.Reals.Rlimit.Metric_Space',axiom,
! [VX32300] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(VX32300)
=> ? [Vvar__0__Base__32301] :
( cType___24t(Vvar__0__Base__32301)
& ? [Vvar__1__dist__32302] :
( c_24__type__25665___24t(Vvar__0__Base__32301,Vvar__1__dist__32302)
& ! [Vvar__var__2__x__32308__32310] :
( t(Vvar__var__2__x__32308__32310,Vvar__0__Base__32301)
=> ! [Vvar__var__3__y__32309__32311] :
( t(Vvar__var__3__y__32309__32311,Vvar__0__Base__32301)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__dist__32302,Vvar__var__2__x__32308__32310),Vvar__var__3__y__32309__32311),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__3__x__32313__32315] :
( t(Vvar__var__3__x__32313__32315,Vvar__0__Base__32301)
=> ! [Vvar__var__4__y__32314__32316] :
( t(Vvar__var__4__y__32314__32316,Vvar__0__Base__32301)
=> happ(happ(Vvar__1__dist__32302,Vvar__var__3__x__32313__32315),Vvar__var__4__y__32314__32316) = happ(happ(Vvar__1__dist__32302,Vvar__var__4__y__32314__32316),Vvar__var__3__x__32313__32315) ) )
& ! [Vvar__var__4__x__32318__32320] :
( t(Vvar__var__4__x__32318__32320,Vvar__0__Base__32301)
=> ! [Vvar__var__5__y__32319__32321] :
( t(Vvar__var__5__y__32319__32321,Vvar__0__Base__32301)
=> ( happ(happ(Vvar__1__dist__32302,Vvar__var__4__x__32318__32320),Vvar__var__5__y__32319__32321) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vvar__var__4__x__32318__32320 = Vvar__var__5__y__32319__32321 ) ) )
& ! [Vvar__var__5__x__32323__32326] :
( t(Vvar__var__5__x__32323__32326,Vvar__0__Base__32301)
=> ! [Vvar__var__6__y__32324__32327] :
( t(Vvar__var__6__y__32324__32327,Vvar__0__Base__32301)
=> ! [Vvar__var__7__z__32325__32328] :
( t(Vvar__var__7__z__32325__32328,Vvar__0__Base__32301)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__dist__32302,Vvar__var__5__x__32323__32326),Vvar__var__6__y__32324__32327),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__dist__32302,Vvar__var__5__x__32323__32326),Vvar__var__7__z__32325__32328),happ(happ(Vvar__1__dist__32302,Vvar__var__7__z__32325__32328),Vvar__var__6__y__32324__32327)))) ) ) )
& VX32300 = cCoq_2eReals_2eRlimit_2eBuild__Metric__Space___24a2(Vvar__0__Base__32301,Vvar__1__dist__32302) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__150,Vvar__1__b__151,Vvar__2__g__152] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__150)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__151)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__152)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__150,Vvar__1__b__151,Vvar__2__g__152)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__152,Vvar__0__a__150)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__152,Vvar__1__b__151)
& ! [Vvar__var__var__var__var__5__x__160__163__166__169__172] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__160__163__166__169__172)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__160__163__166__169__172,Vvar__0__a__150)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__160__163__166__169__172,Vvar__1__b__151)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__160__163__166__169__172,Vvar__2__g__152) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__15600,VX15601] :
( cType___24t(Vvar__0__C__15600)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,VX15601)
=> ( ? [Vvar__1___24Anonymous__15603] :
( t(Vvar__1___24Anonymous__15603,Vvar__0__C__15600)
& VX15601 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__15600,Vvar__1___24Anonymous__15603) )
| ? [Vvar__1___24Anonymous__15605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15605)
& VX15601 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__15600,Vvar__1___24Anonymous__15605) )
| ? [Vvar__1___24Anonymous__15607] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__1___24Anonymous__15607)
& ? [Vvar__2___24Anonymous__15608] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__2___24Anonymous__15608)
& VX15601 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__15600,Vvar__1___24Anonymous__15607,Vvar__2___24Anonymous__15608) ) )
| ? [Vvar__1___24Anonymous__15610] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__1___24Anonymous__15610)
& ? [Vvar__2___24Anonymous__15611] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__2___24Anonymous__15611)
& VX15601 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__15600,Vvar__1___24Anonymous__15610,Vvar__2___24Anonymous__15611) ) )
| ? [Vvar__1___24Anonymous__15613] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__1___24Anonymous__15613)
& ? [Vvar__2___24Anonymous__15614] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__2___24Anonymous__15614)
& VX15601 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__15600,Vvar__1___24Anonymous__15613,Vvar__2___24Anonymous__15614) ) )
| ? [Vvar__1___24Anonymous__15616] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__1___24Anonymous__15616)
& VX15601 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__15600,Vvar__1___24Anonymous__15616) )
| ? [Vvar__1___24Anonymous__15618] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__15600,Vvar__1___24Anonymous__15618)
& ? [Vvar__2___24Anonymous__15619] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__15619)
& VX15601 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__15600,Vvar__1___24Anonymous__15618,Vvar__2___24Anonymous__15619) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__30602,VX30603] :
( cType___24t(Vvar__0__C__30602)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30602,VX30603)
=> ( ? [Vvar__1___24Anonymous__30605] :
( t(Vvar__1___24Anonymous__30605,Vvar__0__C__30602)
& VX30603 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30602,Vvar__1___24Anonymous__30605) )
| ? [Vvar__1___24Anonymous__30607] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__30607)
& ? [Vvar__2___24Anonymous__30608] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30602,Vvar__2___24Anonymous__30608)
& VX30603 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30602,Vvar__1___24Anonymous__30607,Vvar__2___24Anonymous__30608) ) )
| ? [Vvar__1___24Anonymous__30610] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30602,Vvar__1___24Anonymous__30610)
& ? [Vvar__2___24Anonymous__30611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__30611)
& ? [Vvar__3___24Anonymous__30612] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30602,Vvar__3___24Anonymous__30612)
& VX30603 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__30602,Vvar__1___24Anonymous__30610,Vvar__2___24Anonymous__30611,Vvar__3___24Anonymous__30612) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014] :
( cType___24t(Vvar__0__R__18983)
=> ( t(Vvar__1__rO__18984,Vvar__0__R__18983)
=> ( t(Vvar__2__rI__18985,Vvar__0__R__18983)
=> ( c_24__type__19415___24t(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014,Vvar__3__rplus__18986)
=> ( c_24__type__19516___24t(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014,Vvar__4__rtimes__18991)
=> ( c_24__type__19617___24t(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014,Vvar__5__rminus__18996)
=> ( c_24__type__19707___24t(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014,Vvar__6__ropp__19001)
=> ( c_24__type__19808___24t(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014,Vvar__7__req__19004)
=> ( c_24__type__19909___24t(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014,Vvar__8__rle__19009)
=> ( c_24__type__20010___24t(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014,Vvar__9__rlt__19014)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004,Vvar__8__rle__19009,Vvar__9__rlt__19014)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__18983,Vvar__7__req__19004)
& ! [Vvar__var__var__var__var__11__x1__19058__19064__19169__19175__19181] :
( t(Vvar__var__var__var__var__11__x1__19058__19064__19169__19175__19181,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__12__x2__19059__19065__19170__19176__19182] :
( t(Vvar__var__var__var__var__12__x2__19059__19065__19170__19176__19182,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__11__x1__19058__19064__19169__19175__19181),Vvar__var__var__var__var__12__x2__19059__19065__19170__19176__19182))
=> ! [Vvar__var__var__var__var__14__y1__19060__19066__19171__19177__19183] :
( t(Vvar__var__var__var__var__14__y1__19060__19066__19171__19177__19183,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__15__y2__19061__19067__19172__19178__19184] :
( t(Vvar__var__var__var__var__15__y2__19061__19067__19172__19178__19184,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__14__y1__19060__19066__19171__19177__19183),Vvar__var__var__var__var__15__y2__19061__19067__19172__19178__19184))
=> p(happ(happ(Vvar__7__req__19004,happ(happ(Vvar__3__rplus__18986,Vvar__var__var__var__var__11__x1__19058__19064__19169__19175__19181),Vvar__var__var__var__var__14__y1__19060__19066__19171__19177__19183)),happ(happ(Vvar__3__rplus__18986,Vvar__var__var__var__var__12__x2__19059__19065__19170__19176__19182),Vvar__var__var__var__var__15__y2__19061__19067__19172__19178__19184))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__19071__19077__19187__19193__19199] :
( t(Vvar__var__var__var__var__12__x1__19071__19077__19187__19193__19199,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__13__x2__19072__19078__19188__19194__19200] :
( t(Vvar__var__var__var__var__13__x2__19072__19078__19188__19194__19200,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__12__x1__19071__19077__19187__19193__19199),Vvar__var__var__var__var__13__x2__19072__19078__19188__19194__19200))
=> ! [Vvar__var__var__var__var__15__y1__19073__19079__19189__19195__19201] :
( t(Vvar__var__var__var__var__15__y1__19073__19079__19189__19195__19201,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__16__y2__19074__19080__19190__19196__19202] :
( t(Vvar__var__var__var__var__16__y2__19074__19080__19190__19196__19202,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__15__y1__19073__19079__19189__19195__19201),Vvar__var__var__var__var__16__y2__19074__19080__19190__19196__19202))
=> p(happ(happ(Vvar__7__req__19004,happ(happ(Vvar__4__rtimes__18991,Vvar__var__var__var__var__12__x1__19071__19077__19187__19193__19199),Vvar__var__var__var__var__15__y1__19073__19079__19189__19195__19201)),happ(happ(Vvar__4__rtimes__18991,Vvar__var__var__var__var__13__x2__19072__19078__19188__19194__19200),Vvar__var__var__var__var__16__y2__19074__19080__19190__19196__19202))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__19084__19087__19205__19208__19211] :
( t(Vvar__var__var__var__var__13__x1__19084__19087__19205__19208__19211,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__14__x2__19085__19088__19206__19209__19212] :
( t(Vvar__var__var__var__var__14__x2__19085__19088__19206__19209__19212,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__13__x1__19084__19087__19205__19208__19211),Vvar__var__var__var__var__14__x2__19085__19088__19206__19209__19212))
=> p(happ(happ(Vvar__7__req__19004,happ(Vvar__6__ropp__19001,Vvar__var__var__var__var__13__x1__19084__19087__19205__19208__19211)),happ(Vvar__6__ropp__19001,Vvar__var__var__var__var__14__x2__19085__19088__19206__19209__19212))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__19091__19097__19214__19220__19226] :
( t(Vvar__var__var__var__var__14__x1__19091__19097__19214__19220__19226,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__15__x2__19092__19098__19215__19221__19227] :
( t(Vvar__var__var__var__var__15__x2__19092__19098__19215__19221__19227,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__14__x1__19091__19097__19214__19220__19226),Vvar__var__var__var__var__15__x2__19092__19098__19215__19221__19227))
=> ! [Vvar__var__var__var__var__17__y1__19093__19099__19216__19222__19228] :
( t(Vvar__var__var__var__var__17__y1__19093__19099__19216__19222__19228,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__18__y2__19094__19100__19217__19223__19229] :
( t(Vvar__var__var__var__var__18__y2__19094__19100__19217__19223__19229,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__17__y1__19093__19099__19216__19222__19228),Vvar__var__var__var__var__18__y2__19094__19100__19217__19223__19229))
=> ( p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__var__14__x1__19091__19097__19214__19220__19226),Vvar__var__var__var__var__17__y1__19093__19099__19216__19222__19228))
<=> p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__var__15__x2__19092__19098__19215__19221__19227),Vvar__var__var__var__var__18__y2__19094__19100__19217__19223__19229)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__19104__19110__19232__19238__19244] :
( t(Vvar__var__var__var__var__15__x1__19104__19110__19232__19238__19244,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__16__x2__19105__19111__19233__19239__19245] :
( t(Vvar__var__var__var__var__16__x2__19105__19111__19233__19239__19245,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__15__x1__19104__19110__19232__19238__19244),Vvar__var__var__var__var__16__x2__19105__19111__19233__19239__19245))
=> ! [Vvar__var__var__var__var__18__y1__19106__19112__19234__19240__19246] :
( t(Vvar__var__var__var__var__18__y1__19106__19112__19234__19240__19246,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__19__y2__19107__19113__19235__19241__19247] :
( t(Vvar__var__var__var__var__19__y2__19107__19113__19235__19241__19247,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__18__y1__19106__19112__19234__19240__19246),Vvar__var__var__var__var__19__y2__19107__19113__19235__19241__19247))
=> ( p(happ(happ(Vvar__9__rlt__19014,Vvar__var__var__var__var__15__x1__19104__19110__19232__19238__19244),Vvar__var__var__var__var__18__y1__19106__19112__19234__19240__19246))
<=> p(happ(happ(Vvar__9__rlt__19014,Vvar__var__var__var__var__16__x2__19105__19111__19233__19239__19245),Vvar__var__var__var__var__19__y2__19107__19113__19235__19241__19247)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__18983,Vvar__1__rO__18984,Vvar__2__rI__18985,Vvar__3__rplus__18986,Vvar__4__rtimes__18991,Vvar__5__rminus__18996,Vvar__6__ropp__19001,Vvar__7__req__19004)
& ! [Vvar__var__var__var__17__n__19118__19119__19250__19251] :
( t(Vvar__var__var__var__17__n__19118__19119__19250__19251,Vvar__0__R__18983)
=> p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__17__n__19118__19119__19250__19251),Vvar__var__var__var__17__n__19118__19119__19250__19251)) )
& ! [Vvar__var__var__var__var__18__n__19121__19125__19252__19256__19260] :
( t(Vvar__var__var__var__var__18__n__19121__19125__19252__19256__19260,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__19__m__19122__19126__19253__19257__19261] :
( t(Vvar__var__var__var__var__19__m__19122__19126__19253__19257__19261,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__var__18__n__19121__19125__19252__19256__19260),Vvar__var__var__var__var__19__m__19122__19126__19253__19257__19261))
=> ( p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__var__19__m__19122__19126__19253__19257__19261),Vvar__var__var__var__var__18__n__19121__19125__19252__19256__19260))
=> p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__18__n__19121__19125__19252__19256__19260),Vvar__var__var__var__var__19__m__19122__19126__19253__19257__19261)) ) ) ) )
& ! [Vvar__var__var__var__19__n__19130__19135__19264__19269] :
( t(Vvar__var__var__var__19__n__19130__19135__19264__19269,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__20__m__19131__19136__19265__19270] :
( t(Vvar__var__var__var__20__m__19131__19136__19265__19270,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__21__p__19132__19137__19266__19271] :
( t(Vvar__var__var__var__21__p__19132__19137__19266__19271,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__19__n__19130__19135__19264__19269),Vvar__var__var__var__20__m__19131__19136__19265__19270))
=> ( p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__20__m__19131__19136__19265__19270),Vvar__var__var__var__21__p__19132__19137__19266__19271))
=> p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__19__n__19130__19135__19264__19269),Vvar__var__var__var__21__p__19132__19137__19266__19271)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__19141__19143__19274__19276__19278__19280] :
( t(Vvar__var__var__var__var__var__20__n__19141__19143__19274__19276__19278__19280,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__var__21__m__19142__19144__19275__19277__19279__19281] :
( t(Vvar__var__var__var__var__var__21__m__19142__19144__19275__19277__19279__19281,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__9__rlt__19014,Vvar__var__var__var__var__var__20__n__19141__19143__19274__19276__19278__19280),Vvar__var__var__var__var__var__21__m__19142__19144__19275__19277__19279__19281))
<=> ( p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__var__var__20__n__19141__19143__19274__19276__19278__19280),Vvar__var__var__var__var__var__21__m__19142__19144__19275__19277__19279__19281))
& ~ p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__var__20__n__19141__19143__19274__19276__19278__19280),Vvar__var__var__var__var__var__21__m__19142__19144__19275__19277__19279__19281)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__19146__19148__19282__19284__19286] :
( t(Vvar__var__var__var__var__21__n__19146__19148__19282__19284__19286,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__22__m__19147__19149__19283__19285__19287] :
( t(Vvar__var__var__var__var__22__m__19147__19149__19283__19285__19287,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__9__rlt__19014,Vvar__var__var__var__var__21__n__19146__19148__19282__19284__19286),Vvar__var__var__var__var__22__m__19147__19149__19283__19285__19287))
| p(happ(happ(Vvar__7__req__19004,Vvar__var__var__var__var__21__n__19146__19148__19282__19284__19286),Vvar__var__var__var__var__22__m__19147__19149__19283__19285__19287))
| p(happ(happ(Vvar__9__rlt__19014,Vvar__var__var__var__var__22__m__19147__19149__19283__19285__19287),Vvar__var__var__var__var__21__n__19146__19148__19282__19284__19286)) ) ) )
& ! [Vvar__var__var__var__var__22__n__19151__19155__19288__19292__19296] :
( t(Vvar__var__var__var__var__22__n__19151__19155__19288__19292__19296,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__23__m__19152__19156__19289__19293__19297] :
( t(Vvar__var__var__var__var__23__m__19152__19156__19289__19293__19297,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__24__p__19153__19157__19290__19294__19298] :
( t(Vvar__var__var__var__var__24__p__19153__19157__19290__19294__19298,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__8__rle__19009,Vvar__var__var__var__var__22__n__19151__19155__19288__19292__19296),Vvar__var__var__var__var__23__m__19152__19156__19289__19293__19297))
=> p(happ(happ(Vvar__8__rle__19009,happ(happ(Vvar__3__rplus__18986,Vvar__var__var__var__var__24__p__19153__19157__19290__19294__19298),Vvar__var__var__var__var__22__n__19151__19155__19288__19292__19296)),happ(happ(Vvar__3__rplus__18986,Vvar__var__var__var__var__24__p__19153__19157__19290__19294__19298),Vvar__var__var__var__var__23__m__19152__19156__19289__19293__19297))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__19160__19164__19300__19304__19308__19312] :
( t(Vvar__var__var__var__var__var__23__n__19160__19164__19300__19304__19308__19312,Vvar__0__R__18983)
=> ! [Vvar__var__var__var__var__var__24__m__19161__19165__19301__19305__19309__19313] :
( t(Vvar__var__var__var__var__var__24__m__19161__19165__19301__19305__19309__19313,Vvar__0__R__18983)
=> ( p(happ(happ(Vvar__9__rlt__19014,Vvar__1__rO__18984),Vvar__var__var__var__var__var__23__n__19160__19164__19300__19304__19308__19312))
=> ( p(happ(happ(Vvar__9__rlt__19014,Vvar__1__rO__18984),Vvar__var__var__var__var__var__24__m__19161__19165__19301__19305__19309__19313))
=> p(happ(happ(Vvar__9__rlt__19014,Vvar__1__rO__18984),happ(happ(Vvar__4__rtimes__18991,Vvar__var__var__var__var__var__23__n__19160__19164__19300__19304__19308__19312),Vvar__var__var__var__var__var__24__m__19161__19165__19301__19305__19309__19313))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__19004,Vvar__1__rO__18984),Vvar__2__rI__18985))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX20158] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX20158)
=> ( VX20158 = cCoq_2emicromega_2eRMicromega_2eC0
| VX20158 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__20159] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__20159)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__20159) )
| ? [Vvar__0__r__20160] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__20160)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__20160) )
| ? [Vvar__0__r1__20161] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__20161)
& ? [Vvar__1__r2__20162] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__20162)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__20161,Vvar__1__r2__20162) ) )
| ? [Vvar__0__r1__20163] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__20163)
& ? [Vvar__1__r2__20164] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__20164)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__20163,Vvar__1__r2__20164) ) )
| ? [Vvar__0__r1__20165] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__20165)
& ? [Vvar__1__r2__20166] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__20166)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__20165,Vvar__1__r2__20166) ) )
| ? [Vvar__0__r1__20167] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__20167)
& ? [Vvar__1__z__20168] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__20168)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__20167,Vvar__1__z__20168) ) )
| ? [Vvar__0__r__20169] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__20169)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__20169) )
| ? [Vvar__0__r__20170] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__20170)
& VX20158 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__20170) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__21200,VX21201] :
( cType___24t(Vvar__0__T__21200)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__21200,VX21201)
=> ? [Vvar__1__Flhs__21203] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__21200,Vvar__1__Flhs__21203)
& ? [Vvar__2__Fop__21204] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__21204)
& ? [Vvar__3__Frhs__21205] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__21200,Vvar__3__Frhs__21205)
& VX21201 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__21200,Vvar__1__Flhs__21203,Vvar__2__Fop__21204,Vvar__3__Frhs__21205) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX31761] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX31761)
=> ( VX31761 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX31761 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX31761 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX31761 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX21199] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX21199)
=> ( VX21199 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX21199 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX21199 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX21199 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX21199 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX21199 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__21039,VX21040] :
( cType___24t(Vvar__0__C__21039)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21039,VX21040)
=> ( ? [Vvar__1___24Anonymous__21042] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__21042)
& VX21040 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__21039,Vvar__1___24Anonymous__21042) )
| ? [Vvar__1___24Anonymous__21044] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__21039,Vvar__1___24Anonymous__21044)
& VX21040 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__21039,Vvar__1___24Anonymous__21044) )
| ? [Vvar__1___24Anonymous__21046] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__21039,Vvar__1___24Anonymous__21046)
& ? [Vvar__2___24Anonymous__21047] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21039,Vvar__2___24Anonymous__21047)
& VX21040 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__21039,Vvar__1___24Anonymous__21046,Vvar__2___24Anonymous__21047) ) )
| ? [Vvar__1___24Anonymous__21049] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21039,Vvar__1___24Anonymous__21049)
& ? [Vvar__2___24Anonymous__21050] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21039,Vvar__2___24Anonymous__21050)
& VX21040 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__21039,Vvar__1___24Anonymous__21049,Vvar__2___24Anonymous__21050) ) )
| ? [Vvar__1___24Anonymous__21052] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21039,Vvar__1___24Anonymous__21052)
& ? [Vvar__2___24Anonymous__21053] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__21039,Vvar__2___24Anonymous__21053)
& VX21040 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__21039,Vvar__1___24Anonymous__21052,Vvar__2___24Anonymous__21053) ) )
| ? [Vvar__1___24Anonymous__21055] :
( t(Vvar__1___24Anonymous__21055,Vvar__0__C__21039)
& VX21040 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__21039,Vvar__1___24Anonymous__21055) )
| VX21040 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__21039) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096] :
( cType___24t(Vvar__0__R__62027)
=> ( t(Vvar__1__rO__62028,Vvar__0__R__62027)
=> ( t(Vvar__2__rI__62029,Vvar__0__R__62027)
=> ( c_24__type__62560___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__3__rplus__62030)
=> ( c_24__type__62906___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__4__rtimes__62035)
=> ( c_24__type__63252___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__5__rminus__62040)
=> ( c_24__type__63575___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__6__ropp__62045)
=> ( c_24__type__63921___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__7__req__62048)
=> ( c_24__type__64267___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__8__rle__62053)
=> ( cType___24t(Vvar__9__C__62058)
=> ( t(Vvar__10__cO__62059,Vvar__9__C__62058)
=> ( t(Vvar__11__cI__62060,Vvar__9__C__62058)
=> ( c_24__type__64613___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__12__cplus__62061)
=> ( c_24__type__64959___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__13__ctimes__62066)
=> ( c_24__type__65305___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__14__cminus__62071)
=> ( c_24__type__65628___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__15__copp__62076)
=> ( c_24__type__65974___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__16__ceqb__62079)
=> ( c_24__type__66320___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__17__cleb__62084)
=> ( c_24__type__66643___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__18__phi__62089)
=> ( cType___24t(Vvar__19__E__62092)
=> ( c_24__type__66966___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__20__pow__phi__62093)
=> ( c_24__type__67312___24t(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096,Vvar__21__rpow__62096)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__8__rle__62053,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__17__cleb__62084,Vvar__18__phi__62089,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__62027,Vvar__1__rO__62028,Vvar__2__rI__62029,Vvar__3__rplus__62030,Vvar__4__rtimes__62035,Vvar__5__rminus__62040,Vvar__6__ropp__62045,Vvar__7__req__62048,Vvar__9__C__62058,Vvar__10__cO__62059,Vvar__11__cI__62060,Vvar__12__cplus__62061,Vvar__13__ctimes__62066,Vvar__14__cminus__62071,Vvar__15__copp__62076,Vvar__16__ceqb__62079,Vvar__18__phi__62089)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__62027,Vvar__2__rI__62029,Vvar__4__rtimes__62035,Vvar__7__req__62048,Vvar__19__E__62092,Vvar__20__pow__phi__62093,Vvar__21__rpow__62096)
& ! [Vvar__var__var__var__var__var__24__x__62179__62182__62192__62195__62198__62201] :
( t(Vvar__var__var__var__var__var__24__x__62179__62182__62192__62195__62198__62201,Vvar__9__C__62058)
=> ! [Vvar__var__var__var__var__var__25__y__62180__62183__62193__62196__62199__62202] :
( t(Vvar__var__var__var__var__var__25__y__62180__62183__62193__62196__62199__62202,Vvar__9__C__62058)
=> ( happ(happ(Vvar__16__ceqb__62079,Vvar__var__var__var__var__var__24__x__62179__62182__62192__62195__62198__62201),Vvar__var__var__var__var__var__25__y__62180__62183__62193__62196__62199__62202) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__62048,happ(Vvar__18__phi__62089,Vvar__var__var__var__var__var__24__x__62179__62182__62192__62195__62198__62201)),happ(Vvar__18__phi__62089,Vvar__var__var__var__var__var__25__y__62180__62183__62193__62196__62199__62202))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__62186__62189__62204__62207__62210__62213] :
( t(Vvar__var__var__var__var__var__25__x__62186__62189__62204__62207__62210__62213,Vvar__9__C__62058)
=> ! [Vvar__var__var__var__var__var__26__y__62187__62190__62205__62208__62211__62214] :
( t(Vvar__var__var__var__var__var__26__y__62187__62190__62205__62208__62211__62214,Vvar__9__C__62058)
=> ( happ(happ(Vvar__17__cleb__62084,Vvar__var__var__var__var__var__25__x__62186__62189__62204__62207__62210__62213),Vvar__var__var__var__var__var__26__y__62187__62190__62205__62208__62211__62214) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__62053,happ(Vvar__18__phi__62089,Vvar__var__var__var__var__var__25__x__62186__62189__62204__62207__62210__62213)),happ(Vvar__18__phi__62089,Vvar__var__var__var__var__var__26__y__62187__62190__62205__62208__62211__62214))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,VX26100] :
( cType___24t(Vvar__0__TA__26096)
=> ( cType___24t(Vvar__1__TX__26097)
=> ( cType___24t(Vvar__2__AA__26098)
=> ( cType___24t(Vvar__3__AF__26099)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,VX26100)
=> ( VX26100 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099)
| VX26100 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099)
| ? [Vvar__4___24Anonymous__26113] :
( t(Vvar__4___24Anonymous__26113,Vvar__1__TX__26097)
& VX26100 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26113) )
| ? [Vvar__4___24Anonymous__26118] :
( t(Vvar__4___24Anonymous__26118,Vvar__0__TA__26096)
& ? [Vvar__5___24Anonymous__26119] :
( t(Vvar__5___24Anonymous__26119,Vvar__2__AA__26098)
& VX26100 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26118,Vvar__5___24Anonymous__26119) ) )
| ? [Vvar__4___24Anonymous__26124] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26124)
& ? [Vvar__5___24Anonymous__26125] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__5___24Anonymous__26125)
& VX26100 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26124,Vvar__5___24Anonymous__26125) ) )
| ? [Vvar__4___24Anonymous__26130] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26130)
& ? [Vvar__5___24Anonymous__26131] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__5___24Anonymous__26131)
& VX26100 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26130,Vvar__5___24Anonymous__26131) ) )
| ? [Vvar__4___24Anonymous__26136] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26136)
& VX26100 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26136) )
| ? [Vvar__4___24Anonymous__26141] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26141)
& ? [Vvar__5___24Anonymous__26142] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__26099,Vvar__5___24Anonymous__26142)
& ? [Vvar__6___24Anonymous__26143] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__6___24Anonymous__26143)
& VX26100 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__26096,Vvar__1__TX__26097,Vvar__2__AA__26098,Vvar__3__AF__26099,Vvar__4___24Anonymous__26141,Vvar__5___24Anonymous__26142,Vvar__6___24Anonymous__26143) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__26579,VX26580] :
( cType___24t(Vvar__0__A__26579)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__26579,VX26580)
=> ( VX26580 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__26579)
| ? [Vvar__1___24Anonymous__26583] :
( t(Vvar__1___24Anonymous__26583,Vvar__0__A__26579)
& VX26580 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__26579,Vvar__1___24Anonymous__26583) )
| ? [Vvar__1___24Anonymous__26585] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__26579,Vvar__1___24Anonymous__26585)
& ? [Vvar__2___24Anonymous__26586] :
( t(Vvar__2___24Anonymous__26586,Vvar__0__A__26579)
& ? [Vvar__3___24Anonymous__26587] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__26579,Vvar__3___24Anonymous__26587)
& VX26580 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__26579,Vvar__1___24Anonymous__26585,Vvar__2___24Anonymous__26586,Vvar__3___24Anonymous__26587) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__282,VX283] :
( cType___24t(Vvar__0__C__282)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,VX283)
=> ( VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__282)
| VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__282)
| ? [Vvar__1___24Anonymous__287] :
( t(Vvar__1___24Anonymous__287,Vvar__0__C__282)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__282,Vvar__1___24Anonymous__287) )
| ? [Vvar__1___24Anonymous__289] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__289)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__282,Vvar__1___24Anonymous__289) )
| ? [Vvar__1___24Anonymous__291] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__1___24Anonymous__291)
& ? [Vvar__2___24Anonymous__292] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__2___24Anonymous__292)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__282,Vvar__1___24Anonymous__291,Vvar__2___24Anonymous__292) ) )
| ? [Vvar__1___24Anonymous__294] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__1___24Anonymous__294)
& ? [Vvar__2___24Anonymous__295] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__2___24Anonymous__295)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__282,Vvar__1___24Anonymous__294,Vvar__2___24Anonymous__295) ) )
| ? [Vvar__1___24Anonymous__297] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__1___24Anonymous__297)
& ? [Vvar__2___24Anonymous__298] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__2___24Anonymous__298)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__282,Vvar__1___24Anonymous__297,Vvar__2___24Anonymous__298) ) )
| ? [Vvar__1___24Anonymous__300] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__1___24Anonymous__300)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__282,Vvar__1___24Anonymous__300) )
| ? [Vvar__1___24Anonymous__302] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__1___24Anonymous__302)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__282,Vvar__1___24Anonymous__302) )
| ? [Vvar__1___24Anonymous__304] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__1___24Anonymous__304)
& ? [Vvar__2___24Anonymous__305] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__2___24Anonymous__305)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__282,Vvar__1___24Anonymous__304,Vvar__2___24Anonymous__305) ) )
| ? [Vvar__1___24Anonymous__307] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__282,Vvar__1___24Anonymous__307)
& ? [Vvar__2___24Anonymous__308] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__308)
& VX283 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__282,Vvar__1___24Anonymous__307,Vvar__2___24Anonymous__308) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718] :
( cType___24t(Vvar__0__R__30689)
=> ( t(Vvar__1__rO__30690,Vvar__0__R__30689)
=> ( t(Vvar__2__rI__30691,Vvar__0__R__30689)
=> ( c_24__type__30883___24t(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718,Vvar__3__radd__30692)
=> ( c_24__type__30976___24t(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718,Vvar__4__rmul__30697)
=> ( c_24__type__31069___24t(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718,Vvar__5__rsub__30702)
=> ( c_24__type__31151___24t(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718,Vvar__6__ropp__30707)
=> ( c_24__type__31244___24t(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718,Vvar__7__rdiv__30710)
=> ( c_24__type__31326___24t(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718,Vvar__8__rinv__30715)
=> ( c_24__type__31419___24t(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718,Vvar__9__req__30718)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__7__rdiv__30710,Vvar__8__rinv__30715,Vvar__9__req__30718)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__30689,Vvar__1__rO__30690,Vvar__2__rI__30691,Vvar__3__radd__30692,Vvar__4__rmul__30697,Vvar__5__rsub__30702,Vvar__6__ropp__30707,Vvar__9__req__30718)
& ~ p(happ(happ(Vvar__9__req__30718,Vvar__2__rI__30691),Vvar__1__rO__30690))
& ! [Vvar__var__var__var__var__var__var__12__p__30761__30763__30770__30772__30774__30776__30778] :
( t(Vvar__var__var__var__var__var__var__12__p__30761__30763__30770__30772__30774__30776__30778,Vvar__0__R__30689)
=> ! [Vvar__var__var__var__var__var__var__13__q__30762__30764__30771__30773__30775__30777__30779] :
( t(Vvar__var__var__var__var__var__var__13__q__30762__30764__30771__30773__30775__30777__30779,Vvar__0__R__30689)
=> p(happ(happ(Vvar__9__req__30718,happ(happ(Vvar__7__rdiv__30710,Vvar__var__var__var__var__var__var__12__p__30761__30763__30770__30772__30774__30776__30778),Vvar__var__var__var__var__var__var__13__q__30762__30764__30771__30773__30775__30777__30779)),happ(happ(Vvar__4__rmul__30697,Vvar__var__var__var__var__var__var__12__p__30761__30763__30770__30772__30774__30776__30778),happ(Vvar__8__rinv__30715,Vvar__var__var__var__var__var__var__13__q__30762__30764__30771__30773__30775__30777__30779)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__30766__30768__30780__30782__30784__30786__30788__30790] :
( t(Vvar__var__var__var__var__var__var__var__13__p__30766__30768__30780__30782__30784__30786__30788__30790,Vvar__0__R__30689)
=> ( ~ p(happ(happ(Vvar__9__req__30718,Vvar__var__var__var__var__var__var__var__13__p__30766__30768__30780__30782__30784__30786__30788__30790),Vvar__1__rO__30690))
=> p(happ(happ(Vvar__9__req__30718,happ(happ(Vvar__4__rmul__30697,happ(Vvar__8__rinv__30715,Vvar__var__var__var__var__var__var__var__13__p__30766__30768__30780__30782__30784__30786__30788__30790)),Vvar__var__var__var__var__var__var__var__13__p__30766__30768__30780__30782__30784__30786__30788__30790)),Vvar__2__rI__30691)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__915,VX916] :
( cType___24t(Vvar__0__C__915)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__915,VX916)
=> ? [Vvar__1__num__918] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__915,Vvar__1__num__918)
& ? [Vvar__2__denum__919] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__915,Vvar__2__denum__919)
& ? [Vvar__3__condition__920] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__915),Vvar__3__condition__920)
& VX916 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__915,Vvar__1__num__918,Vvar__2__denum__919,Vvar__3__condition__920) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__30675,VX30676] :
( cType___24t(Vvar__0__C__30675)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__30675,VX30676)
=> ? [Vvar__1__rsplit__left__30678] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__30675,Vvar__1__rsplit__left__30678)
& ? [Vvar__2__rsplit__common__30679] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__30675,Vvar__2__rsplit__common__30679)
& ? [Vvar__3__rsplit__right__30680] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__30675,Vvar__3__rsplit__right__30680)
& VX30676 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__30675,Vvar__1__rsplit__left__30678,Vvar__2__rsplit__common__30679,Vvar__3__rsplit__right__30680) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX1785] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX1785)
=> ( VX1785 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__1786] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1786)
& ? [Vvar__1___24Anonymous__1787] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1787)
& VX1785 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1786,Vvar__1___24Anonymous__1787) ) )
| ? [Vvar__0___24Anonymous__1788] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1788)
& ? [Vvar__1___24Anonymous__1789] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1789)
& VX1785 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1788,Vvar__1___24Anonymous__1789) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__1806,VX1807] :
( cType___24t(Vvar__0__C__1806)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,VX1807)
=> ( VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1806)
| VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1806)
| ? [Vvar__1___24Anonymous__1811] :
( t(Vvar__1___24Anonymous__1811,Vvar__0__C__1806)
& VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1806,Vvar__1___24Anonymous__1811) )
| ? [Vvar__1___24Anonymous__1813] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1813)
& VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1806,Vvar__1___24Anonymous__1813) )
| ? [Vvar__1___24Anonymous__1815] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__1___24Anonymous__1815)
& ? [Vvar__2___24Anonymous__1816] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__2___24Anonymous__1816)
& VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1806,Vvar__1___24Anonymous__1815,Vvar__2___24Anonymous__1816) ) )
| ? [Vvar__1___24Anonymous__1818] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__1___24Anonymous__1818)
& ? [Vvar__2___24Anonymous__1819] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__2___24Anonymous__1819)
& VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1806,Vvar__1___24Anonymous__1818,Vvar__2___24Anonymous__1819) ) )
| ? [Vvar__1___24Anonymous__1821] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__1___24Anonymous__1821)
& ? [Vvar__2___24Anonymous__1822] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__2___24Anonymous__1822)
& VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1806,Vvar__1___24Anonymous__1821,Vvar__2___24Anonymous__1822) ) )
| ? [Vvar__1___24Anonymous__1824] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__1___24Anonymous__1824)
& VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1806,Vvar__1___24Anonymous__1824) )
| ? [Vvar__1___24Anonymous__1826] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1806,Vvar__1___24Anonymous__1826)
& ? [Vvar__2___24Anonymous__1827] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__1827)
& VX1807 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1806,Vvar__1___24Anonymous__1826,Vvar__2___24Anonymous__1827) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__1606,VX1607] :
( cType___24t(Vvar__0__C__1606)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1606,VX1607)
=> ( ? [Vvar__1___24Anonymous__1609] :
( t(Vvar__1___24Anonymous__1609,Vvar__0__C__1606)
& VX1607 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1606,Vvar__1___24Anonymous__1609) )
| ? [Vvar__1___24Anonymous__1611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1611)
& ? [Vvar__2___24Anonymous__1612] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1606,Vvar__2___24Anonymous__1612)
& VX1607 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1606,Vvar__1___24Anonymous__1611,Vvar__2___24Anonymous__1612) ) )
| ? [Vvar__1___24Anonymous__1614] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1606,Vvar__1___24Anonymous__1614)
& ? [Vvar__2___24Anonymous__1615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1615)
& ? [Vvar__3___24Anonymous__1616] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1606,Vvar__3___24Anonymous__1616)
& VX1607 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1606,Vvar__1___24Anonymous__1614,Vvar__2___24Anonymous__1615,Vvar__3___24Anonymous__1616) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__21835,Vvar__1__rO__21836,Vvar__2__rI__21837,Vvar__3__radd__21838,Vvar__4__rmul__21843,Vvar__5__rsub__21848,Vvar__6__ropp__21853,Vvar__7__req__21856] :
( cType___24t(Vvar__0__R__21835)
=> ( t(Vvar__1__rO__21836,Vvar__0__R__21835)
=> ( t(Vvar__2__rI__21837,Vvar__0__R__21835)
=> ( c_24__type__22084___24t(Vvar__0__R__21835,Vvar__1__rO__21836,Vvar__2__rI__21837,Vvar__3__radd__21838,Vvar__4__rmul__21843,Vvar__5__rsub__21848,Vvar__6__ropp__21853,Vvar__7__req__21856,Vvar__3__radd__21838)
=> ( c_24__type__22147___24t(Vvar__0__R__21835,Vvar__1__rO__21836,Vvar__2__rI__21837,Vvar__3__radd__21838,Vvar__4__rmul__21843,Vvar__5__rsub__21848,Vvar__6__ropp__21853,Vvar__7__req__21856,Vvar__4__rmul__21843)
=> ( c_24__type__22210___24t(Vvar__0__R__21835,Vvar__1__rO__21836,Vvar__2__rI__21837,Vvar__3__radd__21838,Vvar__4__rmul__21843,Vvar__5__rsub__21848,Vvar__6__ropp__21853,Vvar__7__req__21856,Vvar__5__rsub__21848)
=> ( c_24__type__22264___24t(Vvar__0__R__21835,Vvar__1__rO__21836,Vvar__2__rI__21837,Vvar__3__radd__21838,Vvar__4__rmul__21843,Vvar__5__rsub__21848,Vvar__6__ropp__21853,Vvar__7__req__21856,Vvar__6__ropp__21853)
=> ( c_24__type__22327___24t(Vvar__0__R__21835,Vvar__1__rO__21836,Vvar__2__rI__21837,Vvar__3__radd__21838,Vvar__4__rmul__21843,Vvar__5__rsub__21848,Vvar__6__ropp__21853,Vvar__7__req__21856,Vvar__7__req__21856)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__21835,Vvar__1__rO__21836,Vvar__2__rI__21837,Vvar__3__radd__21838,Vvar__4__rmul__21843,Vvar__5__rsub__21848,Vvar__6__ropp__21853,Vvar__7__req__21856)
=> ( ! [Vvar__var__var__var__var__var__8__x__21889__21890__21943__21944__21945__21946] :
( t(Vvar__var__var__var__var__var__8__x__21889__21890__21943__21944__21945__21946,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__3__radd__21838,Vvar__1__rO__21836),Vvar__var__var__var__var__var__8__x__21889__21890__21943__21944__21945__21946)),Vvar__var__var__var__var__var__8__x__21889__21890__21943__21944__21945__21946)) )
& ! [Vvar__var__var__var__var__9__x__21892__21894__21947__21949__21951] :
( t(Vvar__var__var__var__var__9__x__21892__21894__21947__21949__21951,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__10__y__21893__21895__21948__21950__21952] :
( t(Vvar__var__var__var__var__10__y__21893__21895__21948__21950__21952,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__9__x__21892__21894__21947__21949__21951),Vvar__var__var__var__var__10__y__21893__21895__21948__21950__21952)),happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__10__y__21893__21895__21948__21950__21952),Vvar__var__var__var__var__9__x__21892__21894__21947__21949__21951))) ) )
& ! [Vvar__var__var__var__var__10__x__21897__21900__21953__21956__21959] :
( t(Vvar__var__var__var__var__10__x__21897__21900__21953__21956__21959,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__11__y__21898__21901__21954__21957__21960] :
( t(Vvar__var__var__var__var__11__y__21898__21901__21954__21957__21960,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__12__z__21899__21902__21955__21958__21961] :
( t(Vvar__var__var__var__var__12__z__21899__21902__21955__21958__21961,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__10__x__21897__21900__21953__21956__21959),happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__11__y__21898__21901__21954__21957__21960),Vvar__var__var__var__var__12__z__21899__21902__21955__21958__21961))),happ(happ(Vvar__3__radd__21838,happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__10__x__21897__21900__21953__21956__21959),Vvar__var__var__var__var__11__y__21898__21901__21954__21957__21960)),Vvar__var__var__var__var__12__z__21899__21902__21955__21958__21961))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__21904__21905__21962__21963__21964__21965] :
( t(Vvar__var__var__var__var__var__11__x__21904__21905__21962__21963__21964__21965,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__4__rmul__21843,Vvar__2__rI__21837),Vvar__var__var__var__var__var__11__x__21904__21905__21962__21963__21964__21965)),Vvar__var__var__var__var__var__11__x__21904__21905__21962__21963__21964__21965)) )
& ! [Vvar__var__var__var__var__var__12__x__21907__21908__21966__21967__21968__21969] :
( t(Vvar__var__var__var__var__var__12__x__21907__21908__21966__21967__21968__21969,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__4__rmul__21843,Vvar__1__rO__21836),Vvar__var__var__var__var__var__12__x__21907__21908__21966__21967__21968__21969)),Vvar__1__rO__21836)) )
& ! [Vvar__var__var__var__var__13__x__21910__21912__21970__21972__21974] :
( t(Vvar__var__var__var__var__13__x__21910__21912__21970__21972__21974,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__14__y__21911__21913__21971__21973__21975] :
( t(Vvar__var__var__var__var__14__y__21911__21913__21971__21973__21975,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__13__x__21910__21912__21970__21972__21974),Vvar__var__var__var__var__14__y__21911__21913__21971__21973__21975)),happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__14__y__21911__21913__21971__21973__21975),Vvar__var__var__var__var__13__x__21910__21912__21970__21972__21974))) ) )
& ! [Vvar__var__var__var__var__14__x__21915__21918__21976__21979__21982] :
( t(Vvar__var__var__var__var__14__x__21915__21918__21976__21979__21982,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__15__y__21916__21919__21977__21980__21983] :
( t(Vvar__var__var__var__var__15__y__21916__21919__21977__21980__21983,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__16__z__21917__21920__21978__21981__21984] :
( t(Vvar__var__var__var__var__16__z__21917__21920__21978__21981__21984,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__14__x__21915__21918__21976__21979__21982),happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__15__y__21916__21919__21977__21980__21983),Vvar__var__var__var__var__16__z__21917__21920__21978__21981__21984))),happ(happ(Vvar__4__rmul__21843,happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__14__x__21915__21918__21976__21979__21982),Vvar__var__var__var__var__15__y__21916__21919__21977__21980__21983)),Vvar__var__var__var__var__16__z__21917__21920__21978__21981__21984))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__21922__21925__21985__21988__21991__21994] :
( t(Vvar__var__var__var__var__var__15__x__21922__21925__21985__21988__21991__21994,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__var__16__y__21923__21926__21986__21989__21992__21995] :
( t(Vvar__var__var__var__var__var__16__y__21923__21926__21986__21989__21992__21995,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__var__17__z__21924__21927__21987__21990__21993__21996] :
( t(Vvar__var__var__var__var__var__17__z__21924__21927__21987__21990__21993__21996,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__4__rmul__21843,happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__var__15__x__21922__21925__21985__21988__21991__21994),Vvar__var__var__var__var__var__16__y__21923__21926__21986__21989__21992__21995)),Vvar__var__var__var__var__var__17__z__21924__21927__21987__21990__21993__21996)),happ(happ(Vvar__3__radd__21838,happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__var__15__x__21922__21925__21985__21988__21991__21994),Vvar__var__var__var__var__var__17__z__21924__21927__21987__21990__21993__21996)),happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__var__16__y__21923__21926__21986__21989__21992__21995),Vvar__var__var__var__var__var__17__z__21924__21927__21987__21990__21993__21996)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__21929__21931__21997__21999__22001__22003] :
( t(Vvar__var__var__var__var__var__16__x__21929__21931__21997__21999__22001__22003,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__var__17__y__21930__21932__21998__22000__22002__22004] :
( t(Vvar__var__var__var__var__var__17__y__21930__21932__21998__22000__22002__22004,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(Vvar__6__ropp__21853,happ(happ(Vvar__4__rmul__21843,Vvar__var__var__var__var__var__16__x__21929__21931__21997__21999__22001__22003),Vvar__var__var__var__var__var__17__y__21930__21932__21998__22000__22002__22004))),happ(happ(Vvar__4__rmul__21843,happ(Vvar__6__ropp__21853,Vvar__var__var__var__var__var__16__x__21929__21931__21997__21999__22001__22003)),Vvar__var__var__var__var__var__17__y__21930__21932__21998__22000__22002__22004))) ) )
& ! [Vvar__var__var__var__var__var__17__x__21934__21936__22005__22007__22009__22011] :
( t(Vvar__var__var__var__var__var__17__x__21934__21936__22005__22007__22009__22011,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__var__18__y__21935__21937__22006__22008__22010__22012] :
( t(Vvar__var__var__var__var__var__18__y__21935__21937__22006__22008__22010__22012,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(Vvar__6__ropp__21853,happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__var__17__x__21934__21936__22005__22007__22009__22011),Vvar__var__var__var__var__var__18__y__21935__21937__22006__22008__22010__22012))),happ(happ(Vvar__3__radd__21838,happ(Vvar__6__ropp__21853,Vvar__var__var__var__var__var__17__x__21934__21936__22005__22007__22009__22011)),happ(Vvar__6__ropp__21853,Vvar__var__var__var__var__var__18__y__21935__21937__22006__22008__22010__22012)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__21939__21941__22013__22015__22017__22019__22021] :
( t(Vvar__var__var__var__var__var__var__18__x__21939__21941__22013__22015__22017__22019__22021,Vvar__0__R__21835)
=> ! [Vvar__var__var__var__var__var__var__19__y__21940__21942__22014__22016__22018__22020__22022] :
( t(Vvar__var__var__var__var__var__var__19__y__21940__21942__22014__22016__22018__22020__22022,Vvar__0__R__21835)
=> p(happ(happ(Vvar__7__req__21856,happ(happ(Vvar__5__rsub__21848,Vvar__var__var__var__var__var__var__18__x__21939__21941__22013__22015__22017__22019__22021),Vvar__var__var__var__var__var__var__19__y__21940__21942__22014__22016__22018__22020__22022)),happ(happ(Vvar__3__radd__21838,Vvar__var__var__var__var__var__var__18__x__21939__21941__22013__22015__22017__22019__22021),happ(Vvar__6__ropp__21853,Vvar__var__var__var__var__var__var__19__y__21940__21942__22014__22016__22018__22020__22022)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__25304,Vvar__1__rI__25305,Vvar__2__rmul__25306,Vvar__3__req__25311,Vvar__4__Cpow__25316,Vvar__5__Cp__phi__25317,Vvar__6__rpow__25320] :
( cType___24t(Vvar__0__R__25304)
=> ( t(Vvar__1__rI__25305,Vvar__0__R__25304)
=> ( c_24__type__25406___24t(Vvar__0__R__25304,Vvar__1__rI__25305,Vvar__2__rmul__25306,Vvar__3__req__25311,Vvar__4__Cpow__25316,Vvar__5__Cp__phi__25317,Vvar__6__rpow__25320,Vvar__2__rmul__25306)
=> ( c_24__type__25450___24t(Vvar__0__R__25304,Vvar__1__rI__25305,Vvar__2__rmul__25306,Vvar__3__req__25311,Vvar__4__Cpow__25316,Vvar__5__Cp__phi__25317,Vvar__6__rpow__25320,Vvar__3__req__25311)
=> ( cType___24t(Vvar__4__Cpow__25316)
=> ( c_24__type__25486___24t(Vvar__0__R__25304,Vvar__1__rI__25305,Vvar__2__rmul__25306,Vvar__3__req__25311,Vvar__4__Cpow__25316,Vvar__5__Cp__phi__25317,Vvar__6__rpow__25320,Vvar__5__Cp__phi__25317)
=> ( c_24__type__25530___24t(Vvar__0__R__25304,Vvar__1__rI__25305,Vvar__2__rmul__25306,Vvar__3__req__25311,Vvar__4__Cpow__25316,Vvar__5__Cp__phi__25317,Vvar__6__rpow__25320,Vvar__6__rpow__25320)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__25304,Vvar__1__rI__25305,Vvar__2__rmul__25306,Vvar__3__req__25311,Vvar__4__Cpow__25316,Vvar__5__Cp__phi__25317,Vvar__6__rpow__25320)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__25348__25350__25352__25354__25356__25358__25360__25362] :
( t(Vvar__var__var__var__var__var__var__var__7__r__25348__25350__25352__25354__25356__25358__25360__25362,Vvar__0__R__25304)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__25349__25351__25353__25355__25357__25359__25361__25363] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__25349__25351__25353__25355__25357__25359__25361__25363)
=> p(happ(happ(Vvar__3__req__25311,happ(happ(Vvar__6__rpow__25320,Vvar__var__var__var__var__var__var__var__7__r__25348__25350__25352__25354__25356__25358__25360__25362),happ(Vvar__5__Cp__phi__25317,Vvar__var__var__var__var__var__var__var__8__n__25349__25351__25353__25355__25357__25359__25361__25363))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__25304,Vvar__1__rI__25305,Vvar__2__rmul__25306,Vvar__var__var__var__var__var__var__var__7__r__25348__25350__25352__25354__25356__25358__25360__25362,Vvar__var__var__var__var__var__var__var__8__n__25349__25351__25353__25355__25357__25359__25361__25363))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404] :
( cType___24t(Vvar__0__R__22390)
=> ( c_24__type__22495___24t(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404,Vvar__1__radd__22391)
=> ( c_24__type__22525___24t(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404,Vvar__2__rmul__22396)
=> ( c_24__type__22549___24t(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404,Vvar__3__ropp__22401)
=> ( c_24__type__22579___24t(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404,Vvar__4__req__22404)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22609___24a5(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__22390,c_24__type__22633___24a5(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404),Vvar__4__req__22404,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__22390,Vvar__0__R__22390,Vvar__4__req__22404,Vvar__4__req__22404)),Vvar__1__radd__22391)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22666___24a5(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__22390,c_24__type__22690___24a5(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404),Vvar__4__req__22404,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__22390,Vvar__0__R__22390,Vvar__4__req__22404,Vvar__4__req__22404)),Vvar__2__rmul__22396)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22717___24a5(Vvar__0__R__22390,Vvar__1__radd__22391,Vvar__2__rmul__22396,Vvar__3__ropp__22401,Vvar__4__req__22404),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__22390,Vvar__0__R__22390,Vvar__4__req__22404,Vvar__4__req__22404),Vvar__3__ropp__22401)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798] :
( cType___24t(Vvar__0__R__22746)
=> ( t(Vvar__1__rO__22747,Vvar__0__R__22746)
=> ( t(Vvar__2__rI__22748,Vvar__0__R__22746)
=> ( c_24__type__23142___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__3__radd__22749)
=> ( c_24__type__23355___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__4__rmul__22754)
=> ( c_24__type__23568___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__5__rsub__22759)
=> ( c_24__type__23763___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__6__ropp__22764)
=> ( c_24__type__23976___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__7__req__22767)
=> ( cType___24t(Vvar__8__C__22772)
=> ( t(Vvar__9__cO__22773,Vvar__8__C__22772)
=> ( t(Vvar__10__cI__22774,Vvar__8__C__22772)
=> ( c_24__type__24189___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__11__cadd__22775)
=> ( c_24__type__24402___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__12__cmul__22780)
=> ( c_24__type__24615___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__13__csub__22785)
=> ( c_24__type__24810___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__14__copp__22790)
=> ( c_24__type__25023___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__15__ceqb__22793)
=> ( c_24__type__25218___24t(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798,Vvar__16__phi__22798)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__22746,Vvar__1__rO__22747,Vvar__2__rI__22748,Vvar__3__radd__22749,Vvar__4__rmul__22754,Vvar__5__rsub__22759,Vvar__6__ropp__22764,Vvar__7__req__22767,Vvar__8__C__22772,Vvar__9__cO__22773,Vvar__10__cI__22774,Vvar__11__cadd__22775,Vvar__12__cmul__22780,Vvar__13__csub__22785,Vvar__14__copp__22790,Vvar__15__ceqb__22793,Vvar__16__phi__22798)
=> ( p(happ(happ(Vvar__7__req__22767,happ(Vvar__16__phi__22798,Vvar__9__cO__22773)),Vvar__1__rO__22747))
& p(happ(happ(Vvar__7__req__22767,happ(Vvar__16__phi__22798,Vvar__10__cI__22774)),Vvar__2__rI__22748))
& ! [Vvar__var__var__var__var__var__var__19__x__22860__22862__22884__22886__22888__22890__22892] :
( t(Vvar__var__var__var__var__var__var__19__x__22860__22862__22884__22886__22888__22890__22892,Vvar__8__C__22772)
=> ! [Vvar__var__var__var__var__var__var__20__y__22861__22863__22885__22887__22889__22891__22893] :
( t(Vvar__var__var__var__var__var__var__20__y__22861__22863__22885__22887__22889__22891__22893,Vvar__8__C__22772)
=> p(happ(happ(Vvar__7__req__22767,happ(Vvar__16__phi__22798,happ(happ(Vvar__11__cadd__22775,Vvar__var__var__var__var__var__var__19__x__22860__22862__22884__22886__22888__22890__22892),Vvar__var__var__var__var__var__var__20__y__22861__22863__22885__22887__22889__22891__22893))),happ(happ(Vvar__3__radd__22749,happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__var__19__x__22860__22862__22884__22886__22888__22890__22892)),happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__var__20__y__22861__22863__22885__22887__22889__22891__22893)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__22865__22867__22894__22896__22898__22900__22902] :
( t(Vvar__var__var__var__var__var__var__20__x__22865__22867__22894__22896__22898__22900__22902,Vvar__8__C__22772)
=> ! [Vvar__var__var__var__var__var__var__21__y__22866__22868__22895__22897__22899__22901__22903] :
( t(Vvar__var__var__var__var__var__var__21__y__22866__22868__22895__22897__22899__22901__22903,Vvar__8__C__22772)
=> p(happ(happ(Vvar__7__req__22767,happ(Vvar__16__phi__22798,happ(happ(Vvar__13__csub__22785,Vvar__var__var__var__var__var__var__20__x__22865__22867__22894__22896__22898__22900__22902),Vvar__var__var__var__var__var__var__21__y__22866__22868__22895__22897__22899__22901__22903))),happ(happ(Vvar__5__rsub__22759,happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__var__20__x__22865__22867__22894__22896__22898__22900__22902)),happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__var__21__y__22866__22868__22895__22897__22899__22901__22903)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__22870__22872__22904__22906__22908__22910__22912] :
( t(Vvar__var__var__var__var__var__var__21__x__22870__22872__22904__22906__22908__22910__22912,Vvar__8__C__22772)
=> ! [Vvar__var__var__var__var__var__var__22__y__22871__22873__22905__22907__22909__22911__22913] :
( t(Vvar__var__var__var__var__var__var__22__y__22871__22873__22905__22907__22909__22911__22913,Vvar__8__C__22772)
=> p(happ(happ(Vvar__7__req__22767,happ(Vvar__16__phi__22798,happ(happ(Vvar__12__cmul__22780,Vvar__var__var__var__var__var__var__21__x__22870__22872__22904__22906__22908__22910__22912),Vvar__var__var__var__var__var__var__22__y__22871__22873__22905__22907__22909__22911__22913))),happ(happ(Vvar__4__rmul__22754,happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__var__21__x__22870__22872__22904__22906__22908__22910__22912)),happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__var__22__y__22871__22873__22905__22907__22909__22911__22913)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__22875__22876__22914__22915__22916__22917__22918] :
( t(Vvar__var__var__var__var__var__var__22__x__22875__22876__22914__22915__22916__22917__22918,Vvar__8__C__22772)
=> p(happ(happ(Vvar__7__req__22767,happ(Vvar__16__phi__22798,happ(Vvar__14__copp__22790,Vvar__var__var__var__var__var__var__22__x__22875__22876__22914__22915__22916__22917__22918))),happ(Vvar__6__ropp__22764,happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__var__22__x__22875__22876__22914__22915__22916__22917__22918)))) )
& ! [Vvar__var__var__var__var__var__23__x__22878__22881__22919__22922__22925__22928] :
( t(Vvar__var__var__var__var__var__23__x__22878__22881__22919__22922__22925__22928,Vvar__8__C__22772)
=> ! [Vvar__var__var__var__var__var__24__y__22879__22882__22920__22923__22926__22929] :
( t(Vvar__var__var__var__var__var__24__y__22879__22882__22920__22923__22926__22929,Vvar__8__C__22772)
=> ( happ(happ(Vvar__15__ceqb__22793,Vvar__var__var__var__var__var__23__x__22878__22881__22919__22922__22925__22928),Vvar__var__var__var__var__var__24__y__22879__22882__22920__22923__22926__22929) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__22767,happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__23__x__22878__22881__22919__22922__22925__22928)),happ(Vvar__16__phi__22798,Vvar__var__var__var__var__var__24__y__22879__22882__22920__22923__22926__22929))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__31802,Vvar__1__rO__31803,Vvar__2__rI__31804,Vvar__3__radd__31805,Vvar__4__rmul__31810,Vvar__5__rsub__31815,Vvar__6__ropp__31820,Vvar__7__req__31823] :
( cType___24t(Vvar__0__R__31802)
=> ( t(Vvar__1__rO__31803,Vvar__0__R__31802)
=> ( t(Vvar__2__rI__31804,Vvar__0__R__31802)
=> ( c_24__type__32026___24t(Vvar__0__R__31802,Vvar__1__rO__31803,Vvar__2__rI__31804,Vvar__3__radd__31805,Vvar__4__rmul__31810,Vvar__5__rsub__31815,Vvar__6__ropp__31820,Vvar__7__req__31823,Vvar__3__radd__31805)
=> ( c_24__type__32089___24t(Vvar__0__R__31802,Vvar__1__rO__31803,Vvar__2__rI__31804,Vvar__3__radd__31805,Vvar__4__rmul__31810,Vvar__5__rsub__31815,Vvar__6__ropp__31820,Vvar__7__req__31823,Vvar__4__rmul__31810)
=> ( c_24__type__32152___24t(Vvar__0__R__31802,Vvar__1__rO__31803,Vvar__2__rI__31804,Vvar__3__radd__31805,Vvar__4__rmul__31810,Vvar__5__rsub__31815,Vvar__6__ropp__31820,Vvar__7__req__31823,Vvar__5__rsub__31815)
=> ( c_24__type__32206___24t(Vvar__0__R__31802,Vvar__1__rO__31803,Vvar__2__rI__31804,Vvar__3__radd__31805,Vvar__4__rmul__31810,Vvar__5__rsub__31815,Vvar__6__ropp__31820,Vvar__7__req__31823,Vvar__6__ropp__31820)
=> ( c_24__type__32269___24t(Vvar__0__R__31802,Vvar__1__rO__31803,Vvar__2__rI__31804,Vvar__3__radd__31805,Vvar__4__rmul__31810,Vvar__5__rsub__31815,Vvar__6__ropp__31820,Vvar__7__req__31823,Vvar__7__req__31823)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__31802,Vvar__1__rO__31803,Vvar__2__rI__31804,Vvar__3__radd__31805,Vvar__4__rmul__31810,Vvar__5__rsub__31815,Vvar__6__ropp__31820,Vvar__7__req__31823)
=> ( ! [Vvar__var__var__var__var__var__8__x__31856__31857__31900__31901__31902__31903] :
( t(Vvar__var__var__var__var__var__8__x__31856__31857__31900__31901__31902__31903,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__3__radd__31805,Vvar__1__rO__31803),Vvar__var__var__var__var__var__8__x__31856__31857__31900__31901__31902__31903)),Vvar__var__var__var__var__var__8__x__31856__31857__31900__31901__31902__31903)) )
& ! [Vvar__var__var__var__var__9__x__31859__31861__31904__31906__31908] :
( t(Vvar__var__var__var__var__9__x__31859__31861__31904__31906__31908,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__10__y__31860__31862__31905__31907__31909] :
( t(Vvar__var__var__var__var__10__y__31860__31862__31905__31907__31909,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__9__x__31859__31861__31904__31906__31908),Vvar__var__var__var__var__10__y__31860__31862__31905__31907__31909)),happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__10__y__31860__31862__31905__31907__31909),Vvar__var__var__var__var__9__x__31859__31861__31904__31906__31908))) ) )
& ! [Vvar__var__var__var__var__10__x__31864__31867__31910__31913__31916] :
( t(Vvar__var__var__var__var__10__x__31864__31867__31910__31913__31916,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__11__y__31865__31868__31911__31914__31917] :
( t(Vvar__var__var__var__var__11__y__31865__31868__31911__31914__31917,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__12__z__31866__31869__31912__31915__31918] :
( t(Vvar__var__var__var__var__12__z__31866__31869__31912__31915__31918,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__10__x__31864__31867__31910__31913__31916),happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__11__y__31865__31868__31911__31914__31917),Vvar__var__var__var__var__12__z__31866__31869__31912__31915__31918))),happ(happ(Vvar__3__radd__31805,happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__10__x__31864__31867__31910__31913__31916),Vvar__var__var__var__var__11__y__31865__31868__31911__31914__31917)),Vvar__var__var__var__var__12__z__31866__31869__31912__31915__31918))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__31871__31872__31919__31920__31921__31922] :
( t(Vvar__var__var__var__var__var__11__x__31871__31872__31919__31920__31921__31922,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__4__rmul__31810,Vvar__2__rI__31804),Vvar__var__var__var__var__var__11__x__31871__31872__31919__31920__31921__31922)),Vvar__var__var__var__var__var__11__x__31871__31872__31919__31920__31921__31922)) )
& ! [Vvar__var__var__var__var__12__x__31874__31876__31923__31925__31927] :
( t(Vvar__var__var__var__var__12__x__31874__31876__31923__31925__31927,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__13__y__31875__31877__31924__31926__31928] :
( t(Vvar__var__var__var__var__13__y__31875__31877__31924__31926__31928,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__4__rmul__31810,Vvar__var__var__var__var__12__x__31874__31876__31923__31925__31927),Vvar__var__var__var__var__13__y__31875__31877__31924__31926__31928)),happ(happ(Vvar__4__rmul__31810,Vvar__var__var__var__var__13__y__31875__31877__31924__31926__31928),Vvar__var__var__var__var__12__x__31874__31876__31923__31925__31927))) ) )
& ! [Vvar__var__var__var__var__13__x__31879__31882__31929__31932__31935] :
( t(Vvar__var__var__var__var__13__x__31879__31882__31929__31932__31935,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__14__y__31880__31883__31930__31933__31936] :
( t(Vvar__var__var__var__var__14__y__31880__31883__31930__31933__31936,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__15__z__31881__31884__31931__31934__31937] :
( t(Vvar__var__var__var__var__15__z__31881__31884__31931__31934__31937,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__4__rmul__31810,Vvar__var__var__var__var__13__x__31879__31882__31929__31932__31935),happ(happ(Vvar__4__rmul__31810,Vvar__var__var__var__var__14__y__31880__31883__31930__31933__31936),Vvar__var__var__var__var__15__z__31881__31884__31931__31934__31937))),happ(happ(Vvar__4__rmul__31810,happ(happ(Vvar__4__rmul__31810,Vvar__var__var__var__var__13__x__31879__31882__31929__31932__31935),Vvar__var__var__var__var__14__y__31880__31883__31930__31933__31936)),Vvar__var__var__var__var__15__z__31881__31884__31931__31934__31937))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__31886__31889__31938__31941__31944__31947] :
( t(Vvar__var__var__var__var__var__14__x__31886__31889__31938__31941__31944__31947,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__var__15__y__31887__31890__31939__31942__31945__31948] :
( t(Vvar__var__var__var__var__var__15__y__31887__31890__31939__31942__31945__31948,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__var__16__z__31888__31891__31940__31943__31946__31949] :
( t(Vvar__var__var__var__var__var__16__z__31888__31891__31940__31943__31946__31949,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__4__rmul__31810,happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__var__14__x__31886__31889__31938__31941__31944__31947),Vvar__var__var__var__var__var__15__y__31887__31890__31939__31942__31945__31948)),Vvar__var__var__var__var__var__16__z__31888__31891__31940__31943__31946__31949)),happ(happ(Vvar__3__radd__31805,happ(happ(Vvar__4__rmul__31810,Vvar__var__var__var__var__var__14__x__31886__31889__31938__31941__31944__31947),Vvar__var__var__var__var__var__16__z__31888__31891__31940__31943__31946__31949)),happ(happ(Vvar__4__rmul__31810,Vvar__var__var__var__var__var__15__y__31887__31890__31939__31942__31945__31948),Vvar__var__var__var__var__var__16__z__31888__31891__31940__31943__31946__31949)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__31893__31895__31950__31952__31954__31956__31958] :
( t(Vvar__var__var__var__var__var__var__15__x__31893__31895__31950__31952__31954__31956__31958,Vvar__0__R__31802)
=> ! [Vvar__var__var__var__var__var__var__16__y__31894__31896__31951__31953__31955__31957__31959] :
( t(Vvar__var__var__var__var__var__var__16__y__31894__31896__31951__31953__31955__31957__31959,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__5__rsub__31815,Vvar__var__var__var__var__var__var__15__x__31893__31895__31950__31952__31954__31956__31958),Vvar__var__var__var__var__var__var__16__y__31894__31896__31951__31953__31955__31957__31959)),happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__var__var__15__x__31893__31895__31950__31952__31954__31956__31958),happ(Vvar__6__ropp__31820,Vvar__var__var__var__var__var__var__16__y__31894__31896__31951__31953__31955__31957__31959)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__31898__31899__31960__31961__31962__31963__31964] :
( t(Vvar__var__var__var__var__var__var__16__x__31898__31899__31960__31961__31962__31963__31964,Vvar__0__R__31802)
=> p(happ(happ(Vvar__7__req__31823,happ(happ(Vvar__3__radd__31805,Vvar__var__var__var__var__var__var__16__x__31898__31899__31960__31961__31962__31963__31964),happ(Vvar__6__ropp__31820,Vvar__var__var__var__var__var__var__16__x__31898__31899__31960__31961__31962__31963__31964))),Vvar__1__rO__31803)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_15479',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__15479___24a1(Vv__CANONICAL__0)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__15480,Vv__CANONICAL__0) ) ).
fof('$_lam_15480',axiom,
! [Vv__CANONICAL__0] : c_24__lam__15480___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(cCoq_2eReals_2eAltSeries_2ePI__tg),Vv__CANONICAL__0) ).
fof('$_lam_20310',axiom,
! [Vv__CANONICAL__0] : c_24__lam__20310___24a1(Vv__CANONICAL__0) = cCoq_2emicromega_2eRMicromega_2eRWeakChecker___24a1(cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2efst___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit),Vv__CANONICAL__0)) ).
fof('$_lam_20377',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__20377___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__20379___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_20379',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__20379___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('$_lam_20388',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__20388___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(Vv__CANONICAL__1)),Vv__CANONICAL__0) ).
fof('$_lam_2116',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__2116___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__2044___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('$_lam_25789',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__25789___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = cCoq_2eReals_2eRtrigo__def_2eexp___24a1(Vv__CANONICAL__1) ) ).
fof('$_lam_25812',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__25812___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2eexp__in___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_25825',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__25825___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_31510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__31510___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2)
| cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__2,Vv__CANONICAL__1) ) ) ).
fof('$_lam_31516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__31516___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__1) ).
fof('$_lam_31626',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__31626___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('$_lam_31642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__31642___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) ).
fof('$_lam_34302',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__34302___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_34462',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__34462___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_34482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__34482___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__1))
& cCoq_2eReals_2eRIneq_2enonneg___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__1) ) ) ).
fof('$_lam_48897',axiom,
! [Vv__CANONICAL__0] : c_24__lam__48897___24a1(Vv__CANONICAL__0) = c_24__type__48899___24a1(Vv__CANONICAL__0) ).
fof('$_lam_48904',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__48904___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2einleft___24a3(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO),c_24__prop__48906),cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eSpecif_2eright___24a3(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO),c_24__prop__48907,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO))) )
| ? [Vvar__0___24Anonymous__48905] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__48905)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48905)
& c_24__lam__48904___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eSpecif_2einleft___24a3(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48905)),c_24__prop__48908___24a1(Vvar__0___24Anonymous__48905)),cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48905),cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48905)),c_24__prop__48909___24a1(Vvar__0___24Anonymous__48905))) ) ) ) ).
fof('$_lam_48949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__48949___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2einright___24a2(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2eO),c_24__prop__48952___24a1(Vv__CANONICAL__0)),cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0))) )
| ? [Vvar__0___24Anonymous__48950] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__48950)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48950)
& c_24__lam__48949___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumor___24a2(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__48950),c_24__prop__48955___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__48950)),cCoq_2eInit_2ePeano_2elt___24a2(Vvar__0___24Anonymous__48950,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_lam_52086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__52086___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('$_lam_52088',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__52088___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_52105',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__52105___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRaxioms_2eis__lub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_67809',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__67809___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2esin__in___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_70508',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__70508___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(Vv__CANONICAL__1))),cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_71916',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__71916___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo1_2ePI),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),Vv__CANONICAL__1))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))
& cCoq_2eReals_2eRtrigo1_2etan___24a1(Vv__CANONICAL__1) = Vv__CANONICAL__0 ) ) ).
fof('$_lam_71995',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__71995___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) ).
fof('$_lam_72010',axiom,
! [Vv__CANONICAL__0] : c_24__lam__72010___24a1(Vv__CANONICAL__0) = Vv__CANONICAL__0 ).
fof('$_lam_72011',axiom,
! [Vv__CANONICAL__0] : c_24__lam__72011___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_lam_74801',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__74801___24a1(Vv__CANONICAL__0)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0)) ) ).
fof('$_lam_74805',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__74805___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRpower_2eRpower___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0) ).
fof('$_lam_74807',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__74807___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRpower_2eRpower___24a2(Vv__CANONICAL__1,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('$_lam_75030',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__75030___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2ecos__n___24a1(Vv__CANONICAL__1),cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_75036',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__75036___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRtrigo__def_2ecos__in___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_75083',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__75083___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_76355',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__76355___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__1) ).
fof('$_lam_77001',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__77001___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__77031___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_77031',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__77031___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__77035___24a1(Vv__CANONICAL__2),Vv__CANONICAL__3)
& ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__5)
=> ( cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__1,Vv__CANONICAL__5)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__4),Vv__CANONICAL__5)),happ(Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ) ) ) ) ).
fof('$_lam_77035',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__77035___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__77037___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ).
fof('$_lam_77037',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__77037___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_77220',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__77220___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___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_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_2eRbasic__fun_2eRabs___24a1(Vv__CANONICAL__0),cCoq_2eReals_2eRtrigo1_2etan___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_lam_77251',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__77251___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2esin__n___24a1(Vv__CANONICAL__1),cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_78167',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__78167___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__78169___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ) ).
fof('$_lam_78169',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__78169___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ).
fof('$_lam_78171',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__78171___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ).
fof('$_lam_98347',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__98347___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2))
& happ(Vv__CANONICAL__0,Vv__CANONICAL__3) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('$_lam_98354',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__98354___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__1))
& Vv__CANONICAL__0 = cCoq_2eReals_2eRIneq_2eRsqr___24a1(Vv__CANONICAL__1) ) ) ).
fof('$_lam_98355',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__98355___24a1(Vv__CANONICAL__0)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),Vv__CANONICAL__0))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))))
& cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(Vv__CANONICAL__0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('$_lam_98365',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__98365___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(Vv__CANONICAL__1))) ).
fof('$_lam_98621',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__98621___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)) ).
fof('$_lam_98623',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__98623___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_98744',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__98753___24a1(Vv__CANONICAL__0),c_24__prop__98754___24a1(Vv__CANONICAL__0))
& c_24__lam__98744___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ( Vv__CANONICAL__0 != cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__98755___24a1(Vv__CANONICAL__0),c_24__prop__98756___24a1(Vv__CANONICAL__0))
& c_24__lam__98744___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRaxioms_2eINR___24a1(Vv__CANONICAL__0) ) ) ) ).
fof('$_lam_98792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__98792___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('$_lam_98796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__98796___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_prop_20142',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__20142___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_20372',axiom,
! [V0__x] :
( p(c_24__prop__20372___24a1(V0__x))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('$_prop_20373',axiom,
! [V0__x] :
( p(c_24__prop__20373___24a1(V0__x))
<=> ~ ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('$_prop_20385',axiom,
! [V0__x] :
( p(c_24__prop__20385___24a1(V0__x))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('$_prop_20386',axiom,
! [V0__x] :
( p(c_24__prop__20386___24a1(V0__x))
<=> ~ ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('$_prop_20406',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__20406___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_20407',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__20407___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_20417',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__20417___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_20418',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__20418___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_234',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__234___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_25804',axiom,
! [V0__x] :
( p(c_24__prop__25804___24a1(V0__x))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x)) ) ).
fof('$_prop_25805',axiom,
! [V0__x] :
( p(c_24__prop__25805___24a1(V0__x))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x)) ) ).
fof('$_prop_29921',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__29921___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_30585',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__30585___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_34403',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__34403___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_4',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__4___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_48901',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__48901___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_48906',axiom,
( p(c_24__prop__48906)
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_48907',axiom,
( p(c_24__prop__48907)
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_48908',axiom,
! [Vvar__0___24Anonymous__48905] :
( p(c_24__prop__48908___24a1(Vvar__0___24Anonymous__48905))
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48905) ) ).
fof('$_prop_48909',axiom,
! [Vvar__0___24Anonymous__48905] :
( p(c_24__prop__48909___24a1(Vvar__0___24Anonymous__48905))
<=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__48905) ) ).
fof('$_prop_48952',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__48952___24a1(Vv__CANONICAL__0))
<=> cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_48955',axiom,
! [Vv__CANONICAL__0,Vvar__0___24Anonymous__48950] :
( p(c_24__prop__48955___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__48950))
<=> Vv__CANONICAL__0 = Vvar__0___24Anonymous__48950 ) ).
fof('$_prop_48959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__48959___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_98214',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__98214___24a1(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)))) ) ) ).
fof('$_prop_98215',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__98215___24a1(Vv__CANONICAL__0))
<=> ~ ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),Vv__CANONICAL__0))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('$_prop_98319',axiom,
! [V0__x] :
( p(c_24__prop__98319___24a1(V0__x))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x)) ) ).
fof('$_prop_98320',axiom,
! [V0__x] :
( p(c_24__prop__98320___24a1(V0__x))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x)) ) ).
fof('$_prop_98626',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__98626___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_98753',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__98753___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_98754',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__98754___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_98755',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__98755___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_prop_98756',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__98756___24a1(Vv__CANONICAL__0))
<=> Vv__CANONICAL__0 != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('$_type_101',axiom,
! [Vvar__102] :
( c_24__type__101___24t(Vvar__102)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__102,Vv__CANONICAL__0)) ) ) ).
fof('$_type_107',axiom,
! [Vvar__108] :
( c_24__type__107___24t(Vvar__108)
<=> ! [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__108,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_112',axiom,
! [Vvar__113] :
( c_24__type__112___24t(Vvar__113)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__113,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1185',axiom,
! [Vvar__1186] :
( c_24__type__1185___24t(Vvar__1186)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1200___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__899___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__904___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__913___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__1186,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_1200',axiom,
! [Vv__CANONICAL__0,Vvar__1201] :
( c_24__type__1200___24t(Vv__CANONICAL__0,Vvar__1201)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1201,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_124',axiom,
! [Vvar__125] :
( c_24__type__124___24t(Vvar__125)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__125,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1415',axiom,
! [Vvar__1416] :
( c_24__type__1415___24t(Vvar__1416)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1430___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1416,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1430',axiom,
! [Vv__CANONICAL__0,Vvar__1431] :
( c_24__type__1430___24t(Vv__CANONICAL__0,Vvar__1431)
<=> ! [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__1431,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1448',axiom,
! [Vvar__1449] :
( c_24__type__1448___24t(Vvar__1449)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__1449,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1453',axiom,
! [Vv__CANONICAL__0,Vvar__1454] :
( c_24__type__1453___24t(Vv__CANONICAL__0,Vvar__1454)
<=> ! [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__1454,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_146',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__147] :
( c_24__type__146___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__147)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__147,Vv__CANONICAL__2)) ) ) ).
fof('$_type_15476',axiom,
! [Vvar__15477] :
( c_24__type__15476___24t(Vvar__15477)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3682___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__15477,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15506',axiom,
! [Vvar__15507] :
( c_24__type__15506___24t(Vvar__15507)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__15507,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15539',axiom,
! [Vvar__15540] :
( c_24__type__15539___24t(Vvar__15540)
<=> ! [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__15540,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15542',axiom,
! [Vvar__15543] :
( c_24__type__15542___24t(Vvar__15543)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__15543,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15554',axiom,
! [Vvar__15555] :
( c_24__type__15554___24t(Vvar__15555)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__15555,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15556',axiom,
! [Vvar__15557] :
( c_24__type__15556___24t(Vvar__15557)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__15557,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15575',axiom,
! [Vvar__15576] :
( c_24__type__15575___24t(Vvar__15576)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__15576,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15577',axiom,
! [Vvar__15578] :
( c_24__type__15577___24t(Vvar__15578)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__15578,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1575',axiom,
! [Vvar__1576] :
( c_24__type__1575___24t(Vvar__1576)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1430___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1593___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__1576,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_15765',axiom,
! [Vvar__15766] :
( c_24__type__15765___24t(Vvar__15766)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__15766,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15768',axiom,
! [Vvar__15769] :
( c_24__type__15768___24t(Vvar__15769)
<=> ! [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__15769,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15773',axiom,
! [Vvar__15774] :
( c_24__type__15773___24t(Vvar__15774)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__15774,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1593',axiom,
! [Vv__CANONICAL__0,Vvar__1594] :
( c_24__type__1593___24t(Vv__CANONICAL__0,Vvar__1594)
<=> ! [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__1594,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1598',axiom,
! [Vvar__1599] :
( c_24__type__1598___24t(Vvar__1599)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__1599,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1601',axiom,
! [Vvar__1602] :
( c_24__type__1601___24t(Vvar__1602)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__1602,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16900',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16901] :
( c_24__type__16900___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16901)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__16901,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_16914',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16915] :
( c_24__type__16914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16915)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__16915,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_16921',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16922] :
( c_24__type__16921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16922)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__16922,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_1780',axiom,
! [Vvar__1781] :
( c_24__type__1780___24t(Vvar__1781)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1430___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__1781,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_179',axiom,
! [Vvar__180] :
( c_24__type__179___24t(Vvar__180)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__180,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18146',axiom,
! [Vvar__18147] :
( c_24__type__18146___24t(Vvar__18147)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__18147,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18517] :
( c_24__type__18516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18517)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__18517,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_18930',axiom,
! [Vvar__18931] :
( c_24__type__18930___24t(Vvar__18931)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__891___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__18931,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('$_type_18953',axiom,
! [Vvar__18954] :
( c_24__type__18953___24t(Vvar__18954)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__18954,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18961',axiom,
! [Vv__CANONICAL__0,Vvar__18962] :
( c_24__type__18961___24t(Vv__CANONICAL__0,Vvar__18962)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__18962,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_18966',axiom,
! [Vvar__18967] :
( c_24__type__18966___24t(Vvar__18967)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__18967,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_194',axiom,
! [Vvar__195] :
( c_24__type__194___24t(Vvar__195)
<=> ! [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__195,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19415',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19416] :
( c_24__type__19415___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19416)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19416,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19517] :
( c_24__type__19516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19517)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19517,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19617',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19618] :
( c_24__type__19617___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19618)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19618,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19707',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19708] :
( c_24__type__19707___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19708)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__19708,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_198',axiom,
! [Vvar__199] :
( c_24__type__198___24t(Vvar__199)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__199,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19808',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19809] :
( c_24__type__19808___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19809)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__19809,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_19909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19910] :
( c_24__type__19909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19910)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__19910,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_2',axiom,
! [Vvar__3] :
( c_24__type__2___24t(Vvar__3)
<=> ! [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__4___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__3,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20010',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20011] :
( c_24__type__20010___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__20011)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20011,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_20093',axiom,
! [Vvar__20094] :
( c_24__type__20093___24t(Vvar__20094)
<=> ! [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__20094,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20105',axiom,
! [Vvar__20106] :
( c_24__type__20105___24t(Vvar__20106)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__20106,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20110',axiom,
! [Vvar__20111] :
( c_24__type__20110___24t(Vvar__20111)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__20111,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20115',axiom,
! [Vvar__20116] :
( c_24__type__20115___24t(Vvar__20116)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__20116,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20118',axiom,
! [Vvar__20119] :
( c_24__type__20118___24t(Vvar__20119)
<=> ! [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__20119,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20127',axiom,
! [Vvar__20128] :
( c_24__type__20127___24t(Vvar__20128)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__20128,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20131',axiom,
! [Vvar__20132] :
( c_24__type__20131___24t(Vvar__20132)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(Vvar__20132,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20140',axiom,
! [Vvar__20141] :
( c_24__type__20140___24t(Vvar__20141)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__20142___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__20141,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20151',axiom,
! [Vvar__20152] :
( c_24__type__20151___24t(Vvar__20152)
<=> ! [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__20152,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_20156',axiom,
! [Vvar__20157] :
( c_24__type__20156___24t(Vvar__20157)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__20157,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2029',axiom,
! [Vvar__2030] :
( c_24__type__2029___24t(Vvar__2030)
<=> ! [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__2030,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20303',axiom,
! [Vvar__20304] :
( c_24__type__20303___24t(Vvar__20304)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__20304,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20306',axiom,
! [Vvar__20307] :
( c_24__type__20306___24t(Vvar__20307)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__20307,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20308',axiom,
! [Vvar__20309] :
( c_24__type__20308___24t(Vvar__20309)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__20309,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20312',axiom,
! [Vvar__20313] :
( c_24__type__20312___24t(Vvar__20313)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRMicromega_2eRWitness,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__20313,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2032',axiom,
! [Vvar__2033] :
( c_24__type__2032___24t(Vvar__2033)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2033,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20326',axiom,
! [Vvar__20327] :
( c_24__type__20326___24t(Vvar__20327)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__20327,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20329',axiom,
! [Vvar__20330] :
( c_24__type__20329___24t(Vvar__20330)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__20330,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20331',axiom,
! [Vvar__20332] :
( c_24__type__20331___24t(Vvar__20332)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__20332,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2037',axiom,
! [Vvar__2038] :
( c_24__type__2037___24t(Vvar__2038)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2038,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20395',axiom,
! [Vvar__20396] :
( c_24__type__20395___24t(Vvar__20396)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__20396,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2040',axiom,
! [Vvar__2041] :
( c_24__type__2040___24t(Vvar__2041)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2041,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20432',axiom,
! [Vvar__20433] :
( c_24__type__20432___24t(Vvar__20433)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__20433,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20437',axiom,
! [Vvar__20438] :
( c_24__type__20437___24t(Vvar__20438)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__20438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20523',axiom,
! [Vvar__20524] :
( c_24__type__20523___24t(Vvar__20524)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__20524,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20594',axiom,
! [Vvar__20595] :
( c_24__type__20594___24t(Vvar__20595)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRIneq_2eposreal___24t(happ(Vvar__20595,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21186',axiom,
! [Vvar__21187] :
( c_24__type__21186___24t(Vvar__21187)
<=> ! [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__21187,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21191',axiom,
! [Vvar__21192] :
( c_24__type__21191___24t(Vvar__21192)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__21192,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_21197',axiom,
! [Vvar__21198] :
( c_24__type__21197___24t(Vvar__21198)
<=> ! [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__21198,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21220',axiom,
! [Vvar__21221] :
( c_24__type__21220___24t(Vvar__21221)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__21221,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21254',axiom,
! [Vvar__21255] :
( c_24__type__21254___24t(Vvar__21255)
<=> ! [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__21255,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_21469',axiom,
! [Vvar__21470] :
( c_24__type__21469___24t(Vvar__21470)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__899___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__904___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__913___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__21470,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_21729',axiom,
! [Vvar__21730] :
( c_24__type__21729___24t(Vvar__21730)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1200___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__899___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__904___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__913___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__21730,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_21830',axiom,
! [Vvar__21831] :
( c_24__type__21830___24t(Vvar__21831)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__21831,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_22084',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22085] :
( c_24__type__22084___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22085)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22085,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22147',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22148] :
( c_24__type__22147___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22148)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22148,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22210',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22211] :
( c_24__type__22210___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22211)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22211,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22264',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22265] :
( c_24__type__22264___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22265)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__22265,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_22327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22328] :
( c_24__type__22327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__22328)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22328,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_2248',axiom,
! [Vvar__2249] :
( c_24__type__2248___24t(Vvar__2249)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1430___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1593___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2249,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_22495',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22496] :
( c_24__type__22495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22496)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22496,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22525',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22526] :
( c_24__type__22525___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22526)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22526,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22549',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22550] :
( c_24__type__22549___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22550)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__22550,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_22579',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22580] :
( c_24__type__22579___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22580)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22580,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_22609',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22610] :
( c_24__type__22609___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22610)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22610,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22633',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22634] :
( c_24__type__22633___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22634)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__22634,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_22666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22667] :
( c_24__type__22666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22667)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22667,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22690',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22691] :
( c_24__type__22690___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22691)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__22691,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_22717',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22718] :
( c_24__type__22717___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22718)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__22718,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_228',axiom,
! [Vvar__229] :
( c_24__type__228___24t(Vvar__229)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__229,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23',axiom,
! [Vvar__24] :
( c_24__type__23___24t(Vvar__24)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__24,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23142',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23143] :
( c_24__type__23142___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23143)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23143,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23355',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23356] :
( c_24__type__23355___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23356)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23356,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_235',axiom,
! [Vvar__236] :
( c_24__type__235___24t(Vvar__236)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__236,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23568',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23569] :
( c_24__type__23568___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23569)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23569,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23763',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23764] :
( c_24__type__23763___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23764)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__23764,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_23976',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23977] :
( c_24__type__23976___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__23977)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23977,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_24189',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24190] :
( c_24__type__24189___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24190)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__24190,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_2424',axiom,
! [Vvar__2425] :
( c_24__type__2424___24t(Vvar__2425)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1430___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1593___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__2425,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_24402',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24403] :
( c_24__type__24402___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24403)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__24403,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_2445',axiom,
! [Vvar__2446] :
( c_24__type__2445___24t(Vvar__2446)
<=> ! [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__2446,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2457',axiom,
! [Vvar__2458] :
( c_24__type__2457___24t(Vvar__2458)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2458,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24616] :
( c_24__type__24615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24616)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__24616,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_2479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2480] :
( c_24__type__2479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2480)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__2480,Vv__CANONICAL__2)) ) ) ).
fof('$_type_24810',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24811] :
( c_24__type__24810___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__24811)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__24811,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_249',axiom,
! [Vvar__250] :
( c_24__type__249___24t(Vvar__250)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__250,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25023',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25024] :
( c_24__type__25023___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25024)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__25024,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_2515',axiom,
! [Vvar__2516] :
( c_24__type__2515___24t(Vvar__2516)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2516,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2518',axiom,
! [Vvar__2519] :
( c_24__type__2518___24t(Vvar__2519)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2519,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25218',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25219] :
( c_24__type__25218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__25219)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__25219,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_25406',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25407] :
( c_24__type__25406___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25407)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25407,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25450',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25451] :
( c_24__type__25450___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25451)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__25451,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_25486',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25487] :
( c_24__type__25486___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25487)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__25487,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_25530',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25531] :
( c_24__type__25530___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__25531)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__25531,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25665',axiom,
! [Vv__CANONICAL__0,Vvar__25666] :
( c_24__type__25665___24t(Vv__CANONICAL__0,Vvar__25666)
<=> ! [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__25666,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_25676',axiom,
! [Vvar__25677] :
( c_24__type__25676___24t(Vvar__25677)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__25677,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25771',axiom,
! [Vvar__25772] :
( c_24__type__25771___24t(Vvar__25772)
<=> ! [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__25772,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_25780',axiom,
! [Vvar__25781] :
( c_24__type__25780___24t(Vvar__25781)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__25781,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25786',axiom,
! [Vvar__25787] :
( c_24__type__25786___24t(Vvar__25787)
<=> ! [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__25789___24a1(Vv__CANONICAL__0),happ(Vvar__25787,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_25808',axiom,
! [Vvar__25809] :
( c_24__type__25808___24t(Vvar__25809)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3682___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__25809,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25829',axiom,
! [Vvar__25830] :
( c_24__type__25829___24t(Vvar__25830)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3682___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25830,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2586',axiom,
! [Vvar__2587] :
( c_24__type__2586___24t(Vvar__2587)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__2587,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25918',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25919] :
( c_24__type__25918___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25919)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25919,Vv__CANONICAL__2)) ) ) ).
fof('$_type_25922',axiom,
! [Vvar__25923] :
( c_24__type__25922___24t(Vvar__25923)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__25923,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25925',axiom,
! [Vv__CANONICAL__0,Vvar__25926] :
( c_24__type__25925___24t(Vv__CANONICAL__0,Vvar__25926)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25926,Vv__CANONICAL__1)) ) ) ).
fof('$_type_25942',axiom,
! [Vvar__25943] :
( c_24__type__25942___24t(Vvar__25943)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__25943,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_25959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25960] :
( c_24__type__25959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25960)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25960,Vv__CANONICAL__2)) ) ) ).
fof('$_type_25965',axiom,
! [Vvar__25966] :
( c_24__type__25965___24t(Vvar__25966)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__25966,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_25972',axiom,
! [Vvar__25973] :
( c_24__type__25972___24t(Vvar__25973)
<=> ! [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__25973,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_25977',axiom,
! [Vvar__25978] :
( c_24__type__25977___24t(Vvar__25978)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__25978,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_2600',axiom,
! [Vvar__2601] :
( c_24__type__2600___24t(Vvar__2601)
<=> ! [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__2601,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_26003',axiom,
! [Vvar__26004] :
( c_24__type__26003___24t(Vvar__26004)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__26007___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__26014___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__26021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__26004,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_26007',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26008] :
( c_24__type__26007___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26008)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__26008,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26014',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26015] :
( c_24__type__26014___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26015)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__26015,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_26021',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26022] :
( c_24__type__26021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26022)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__26022,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_2604',axiom,
! [Vvar__2605] :
( c_24__type__2604___24t(Vvar__2605)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2605,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2607',axiom,
! [Vvar__2608] :
( c_24__type__2607___24t(Vvar__2608)
<=> ! [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__2608,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26150',axiom,
! [Vvar__26151] :
( c_24__type__26150___24t(Vvar__26151)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__26151,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_263',axiom,
! [Vvar__264] :
( c_24__type__263___24t(Vvar__264)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__264,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26554',axiom,
! [Vvar__26555] :
( c_24__type__26554___24t(Vvar__26555)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__26555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_26577',axiom,
! [Vvar__26578] :
( c_24__type__26577___24t(Vvar__26578)
<=> ! [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__26578,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_26617',axiom,
! [Vvar__26618] :
( c_24__type__26617___24t(Vvar__26618)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(Vvar__26618,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26648',axiom,
! [Vvar__26649] :
( c_24__type__26648___24t(Vvar__26649)
<=> ! [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__26649,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_268',axiom,
! [Vvar__269] :
( c_24__type__268___24t(Vvar__269)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__269,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2702',axiom,
! [Vvar__2703] :
( c_24__type__2702___24t(Vvar__2703)
<=> ! [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__2703,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_280',axiom,
! [Vvar__281] :
( c_24__type__280___24t(Vvar__281)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__281,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29845',axiom,
! [Vvar__29846] :
( c_24__type__29845___24t(Vvar__29846)
<=> ! [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__29846,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29853',axiom,
! [Vvar__29854] :
( c_24__type__29853___24t(Vvar__29854)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__29854,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29893',axiom,
! [Vvar__29894] :
( c_24__type__29893___24t(Vvar__29894)
<=> ! [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__29894,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29915',axiom,
! [Vvar__29916] :
( c_24__type__29915___24t(Vvar__29916)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__29916,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29918',axiom,
! [Vvar__29919] :
( c_24__type__29918___24t(Vvar__29919)
<=> ! [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__29919,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29938',axiom,
! [Vvar__29939] :
( c_24__type__29938___24t(Vvar__29939)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__29939,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29966',axiom,
! [Vvar__29967] :
( c_24__type__29966___24t(Vvar__29967)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29967,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30501',axiom,
! [Vvar__30502] :
( c_24__type__30501___24t(Vvar__30502)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30502,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30513',axiom,
! [Vv__CANONICAL__0,Vvar__30514] :
( c_24__type__30513___24t(Vv__CANONICAL__0,Vvar__30514)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__30514,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30526',axiom,
! [Vvar__30527] :
( c_24__type__30526___24t(Vvar__30527)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__30528___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__30533___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__30527,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30528',axiom,
! [Vvar__30529] :
( c_24__type__30528___24t(Vvar__30529)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30529,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30533',axiom,
! [Vv__CANONICAL__0,Vvar__30534] :
( c_24__type__30533___24t(Vv__CANONICAL__0,Vvar__30534)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__30534,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_30573',axiom,
! [Vvar__30574] :
( c_24__type__30573___24t(Vvar__30574)
<=> ! [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__30574,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_30583',axiom,
! [Vvar__30584] :
( c_24__type__30583___24t(Vvar__30584)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__30584,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30595',axiom,
! [Vvar__30596] :
( c_24__type__30595___24t(Vvar__30596)
<=> ! [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__30596,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30600',axiom,
! [Vvar__30601] :
( c_24__type__30600___24t(Vvar__30601)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__30601,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30650',axiom,
! [Vvar__30651] :
( c_24__type__30650___24t(Vvar__30651)
<=> ! [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__30651,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30673',axiom,
! [Vvar__30674] :
( c_24__type__30673___24t(Vvar__30674)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__30674,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30883',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__30884] :
( c_24__type__30883___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__30884)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30884,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30976',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__30977] :
( c_24__type__30976___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__30977)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30977,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31069',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31070] :
( c_24__type__31069___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31070)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31070,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31151',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31152] :
( c_24__type__31151___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31152)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__31152,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_31244',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31245] :
( c_24__type__31244___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31245)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31245,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31326',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31327] :
( c_24__type__31326___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31327)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__31327,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_31419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31420] :
( c_24__type__31419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__31420)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31420,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_31450',axiom,
! [Vvar__31451] :
( c_24__type__31450___24t(Vvar__31451)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__31451,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_31521',axiom,
! [Vvar__31522] :
( c_24__type__31521___24t(Vvar__31522)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__31524___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__31522,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31524',axiom,
! [Vvar__31525] :
( c_24__type__31524___24t(Vvar__31525)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__31525,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31527',axiom,
! [Vv__CANONICAL__0,Vvar__31528] :
( c_24__type__31527___24t(Vv__CANONICAL__0,Vvar__31528)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__31528,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_31540',axiom,
! [Vvar__31541] :
( c_24__type__31540___24t(Vvar__31541)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eReals_2eRIneq_2enonnegreal___24t(happ(Vvar__31541,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_31570',axiom,
! [Vvar__31571] :
( c_24__type__31570___24t(Vvar__31571)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( Vv__CANONICAL__0 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRIneq_2enonzeroreal___24t(happ(Vvar__31571,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_31582',axiom,
! [Vvar__31583] :
( c_24__type__31582___24t(Vvar__31583)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRList_2eRlist___24t(happ(happ(Vvar__31583,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31589',axiom,
! [Vvar__31590] :
( c_24__type__31589___24t(Vvar__31590)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__31590,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31597',axiom,
! [Vvar__31598] :
( c_24__type__31597___24t(Vvar__31598)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__31598,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31617',axiom,
! [Vvar__31618] :
( c_24__type__31617___24t(Vvar__31618)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__31618,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31622',axiom,
! [Vvar__31623] :
( c_24__type__31622___24t(Vvar__31623)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__31623,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31628',axiom,
! [Vvar__31629] :
( c_24__type__31628___24t(Vvar__31629)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__31629,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31631',axiom,
! [Vv__CANONICAL__0,Vvar__31632] :
( c_24__type__31631___24t(Vv__CANONICAL__0,Vvar__31632)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(Vvar__31632,Vv__CANONICAL__1)) ) ) ).
fof('$_type_31633',axiom,
! [Vvar__31634] :
( c_24__type__31633___24t(Vvar__31634)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__31634,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31635',axiom,
! [Vvar__31636] :
( c_24__type__31635___24t(Vvar__31636)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eid,Vv__CANONICAL__0,happ(Vvar__31636,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31639',axiom,
! [Vvar__31640] :
( c_24__type__31639___24t(Vvar__31640)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRanalysis1_2ederivable___24t(c_24__lam__31642___24a1(Vv__CANONICAL__0),happ(Vvar__31640,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31643',axiom,
! [Vvar__31644] :
( c_24__type__31643___24t(Vvar__31644)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31644,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31645',axiom,
! [Vvar__31646] :
( c_24__type__31645___24t(Vvar__31646)
<=> ! [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__31646,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31647',axiom,
! [Vvar__31648] :
( c_24__type__31647___24t(Vvar__31648)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31648,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31763',axiom,
! [Vvar__31764] :
( c_24__type__31763___24t(Vvar__31764)
<=> ! [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__31764,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31768',axiom,
! [Vvar__31769] :
( c_24__type__31768___24t(Vvar__31769)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__31769,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31776',axiom,
! [Vvar__31777] :
( c_24__type__31776___24t(Vvar__31777)
<=> ! [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__31777,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_31779',axiom,
! [Vvar__31780] :
( c_24__type__31779___24t(Vvar__31780)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__31780,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31797',axiom,
! [Vvar__31798] :
( c_24__type__31797___24t(Vvar__31798)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__882___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__31798,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_32026',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32027] :
( c_24__type__32026___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32027)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32027,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32089',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32090] :
( c_24__type__32089___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32090)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32090,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32153] :
( c_24__type__32152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32153)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32153,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32206',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32207] :
( c_24__type__32206___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32207)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__32207,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_32269',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32270] :
( c_24__type__32269___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__32270)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__32270,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_32362',axiom,
! [Vvar__32363] :
( c_24__type__32362___24t(Vvar__32363)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1601___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__32363,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32381',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32382] :
( c_24__type__32381___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32382)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__32382,Vv__CANONICAL__2)) ) ) ).
fof('$_type_32385',axiom,
! [Vvar__32386] :
( c_24__type__32385___24t(Vvar__32386)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32388___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__32386,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32388',axiom,
! [Vv__CANONICAL__0,Vvar__32389] :
( c_24__type__32388___24t(Vv__CANONICAL__0,Vvar__32389)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__32389,Vv__CANONICAL__1)) ) ) ).
fof('$_type_32408',axiom,
! [Vvar__32409] :
( c_24__type__32408___24t(Vvar__32409)
<=> ! [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__32409,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_32425',axiom,
! [Vvar__32426] :
( c_24__type__32425___24t(Vvar__32426)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__32426,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_32437',axiom,
! [Vvar__32438] :
( c_24__type__32437___24t(Vvar__32438)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( 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)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__32438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_32439',axiom,
! [Vvar__32440] :
( c_24__type__32439___24t(Vvar__32440)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(Vvar__32440,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32447',axiom,
! [Vvar__32448] :
( c_24__type__32447___24t(Vvar__32448)
<=> ! [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__32448,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32750',axiom,
! [Vvar__32751] :
( c_24__type__32750___24t(Vvar__32751)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__32751,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32765',axiom,
! [Vvar__32766] :
( c_24__type__32765___24t(Vvar__32766)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__32766,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32805',axiom,
! [Vvar__32806] :
( c_24__type__32805___24t(Vvar__32806)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__32806,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32809',axiom,
! [Vvar__32810] :
( c_24__type__32809___24t(Vvar__32810)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__32810,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32913',axiom,
! [Vvar__32914] :
( c_24__type__32913___24t(Vvar__32914)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__32914,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32961',axiom,
! [Vvar__32962] :
( c_24__type__32961___24t(Vvar__32962)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1430___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__32962,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_32971',axiom,
! [Vvar__32972] :
( c_24__type__32971___24t(Vvar__32972)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__32972,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33355',axiom,
! [Vvar__33356] :
( c_24__type__33355___24t(Vvar__33356)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___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__16921___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__899___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__904___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__913___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__33387___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__33356,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_33387',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33388] :
( c_24__type__33387___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33388)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__33388,Vv__CANONICAL__3)) ) ) ).
fof('$_type_33406',axiom,
! [Vvar__33407] :
( c_24__type__33406___24t(Vvar__33407)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__33407,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33411',axiom,
! [Vvar__33412] :
( c_24__type__33411___24t(Vvar__33412)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__33412,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34140',axiom,
! [Vvar__34141] :
( c_24__type__34140___24t(Vvar__34141)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__34141,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34145',axiom,
! [Vvar__34146] :
( c_24__type__34145___24t(Vvar__34146)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__34146,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34148',axiom,
! [Vv__CANONICAL__0,Vvar__34149] :
( c_24__type__34148___24t(Vv__CANONICAL__0,Vvar__34149)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__34149,Vv__CANONICAL__1)) ) ) ).
fof('$_type_34306',axiom,
! [Vvar__34307] :
( c_24__type__34306___24t(Vvar__34307)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34307,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34344',axiom,
! [Vvar__34345] :
( c_24__type__34344___24t(Vvar__34345)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___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__34345,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34401',axiom,
! [Vvar__34402] :
( c_24__type__34401___24t(Vvar__34402)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__34403___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__34402,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34451',axiom,
! [Vvar__34452] :
( c_24__type__34451___24t(Vvar__34452)
<=> ! [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__34455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__34459___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__34452,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_34455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34456] :
( c_24__type__34455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34456)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__1,happ(Vvar__34456,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34459',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34460] :
( c_24__type__34459___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34460)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRlimit_2eBase___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__34460,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34468',axiom,
! [Vvar__34469] :
( c_24__type__34468___24t(Vvar__34469)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3682___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__34469,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34485',axiom,
! [Vvar__34486] :
( c_24__type__34485___24t(Vvar__34486)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__34486,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34714',axiom,
! [Vvar__34715] :
( c_24__type__34714___24t(Vvar__34715)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__34715,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34819',axiom,
! [Vvar__34820] :
( c_24__type__34819___24t(Vvar__34820)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__34820,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35030',axiom,
! [Vvar__35031] :
( c_24__type__35030___24t(Vvar__35031)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35031,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35033',axiom,
! [Vvar__35034] :
( c_24__type__35033___24t(Vvar__35034)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,happ(Vvar__35034,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35624',axiom,
! [Vv__CANONICAL__0,Vvar__35625] :
( c_24__type__35624___24t(Vv__CANONICAL__0,Vvar__35625)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__35625,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3682',axiom,
! [Vvar__3683] :
( c_24__type__3682___24t(Vvar__3683)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__3683,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37151] :
( c_24__type__37150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37151)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37151,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_37191',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37192] :
( c_24__type__37191___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37192)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37192,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_38426',axiom,
! [Vvar__38427] :
( c_24__type__38426___24t(Vvar__38427)
<=> ! [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__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__11] :
( c_24__type__16921___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__899___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cType___24t(Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__904___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__913___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__33387___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__17)
=> ! [Vv__CANONICAL__18] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__18)
=> ! [Vv__CANONICAL__19] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__19)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__38427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__19),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_48899',axiom,
! [Vv__CANONICAL__0,Vvar__48900] :
( c_24__type__48899___24t(Vv__CANONICAL__0,Vvar__48900)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__48901___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(Vvar__48900,Vv__CANONICAL__1)) ) ) ).
fof('$_type_48957',axiom,
! [Vvar__48958] :
( c_24__type__48957___24t(Vvar__48958)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__48959___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__48958,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_51705',axiom,
! [Vvar__51706] :
( c_24__type__51705___24t(Vvar__51706)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__51706,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_52101',axiom,
! [Vvar__52102] :
( c_24__type__52101___24t(Vvar__52102)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRaxioms_2ebound___24a1(Vv__CANONICAL__0)
=> ( ? [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
& p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) )
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__52105___24a1(Vv__CANONICAL__0),happ(Vvar__52102,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_6',axiom,
! [Vvar__7] :
( c_24__type__6___24t(Vvar__7)
<=> ! [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__7,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_610',axiom,
! [Vvar__611] :
( c_24__type__610___24t(Vvar__611)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__611,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_615',axiom,
! [Vvar__616] :
( c_24__type__615___24t(Vvar__616)
<=> ! [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__616,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_61958',axiom,
! [Vvar__61959] :
( c_24__type__61958___24t(Vvar__61959)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__61959,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61968',axiom,
! [Vvar__61969] :
( c_24__type__61968___24t(Vvar__61969)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__61969,Vv__CANONICAL__0)) ) ) ).
fof('$_type_61974',axiom,
! [Vvar__61975] :
( c_24__type__61974___24t(Vvar__61975)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__61975,Vv__CANONICAL__0)) ) ) ).
fof('$_type_61986',axiom,
! [Vvar__61987] :
( c_24__type__61986___24t(Vvar__61987)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__61987,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_62',axiom,
! [Vvar__63] :
( c_24__type__62___24t(Vvar__63)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__63,Vv__CANONICAL__0)) ) ) ).
fof('$_type_62002',axiom,
! [Vvar__62003] :
( c_24__type__62002___24t(Vvar__62003)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___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__62003,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_62020',axiom,
! [Vvar__62021] :
( c_24__type__62020___24t(Vvar__62021)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,happ(happ(Vvar__62021,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_62025',axiom,
! [Vvar__62026] :
( c_24__type__62025___24t(Vvar__62026)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___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__62026,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_62560',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__62561] :
( c_24__type__62560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__62561)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62561,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_62906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__62907] :
( c_24__type__62906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__62907)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__62907,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63252',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__63253] :
( c_24__type__63252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__63253)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__63253,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_63575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__63576] :
( c_24__type__63575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__63576)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__63576,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_63921',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__63922] :
( c_24__type__63921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__63922)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__63922,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_64267',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__64268] :
( c_24__type__64267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__64268)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__64268,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_64613',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__64614] :
( c_24__type__64613___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__64614)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__64614,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_64959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__64960] :
( c_24__type__64959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__64960)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__64960,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_65305',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__65306] :
( c_24__type__65305___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__65306)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__65306,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_65628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__65629] :
( c_24__type__65628___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__65629)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__65629,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_65974',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__65975] :
( c_24__type__65974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__65975)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__65975,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_66320',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__66321] :
( c_24__type__66320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__66321)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__66321,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_66643',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__66644] :
( c_24__type__66643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__66644)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__66644,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_66966',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__66967] :
( c_24__type__66966___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__66967)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__66967,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_67312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__67313] :
( c_24__type__67312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__67313)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__67313,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_67816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67817] :
( c_24__type__67816___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67817)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__67817,Vv__CANONICAL__2)) ) ) ).
fof('$_type_67840',axiom,
! [Vvar__67841] :
( c_24__type__67840___24t(Vvar__67841)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__67846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__67858___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__67841,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_67846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67847] :
( c_24__type__67846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__67847)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__67847,Vv__CANONICAL__2)) ) ) ).
fof('$_type_67858',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67859] :
( c_24__type__67858___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67859)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(Vvar__67859,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).
fof('$_type_67867',axiom,
! [Vvar__67868] :
( c_24__type__67867___24t(Vvar__67868)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32388___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__67868,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_67892',axiom,
! [Vvar__67893] :
( c_24__type__67892___24t(Vvar__67893)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__67893,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_70096',axiom,
! [Vvar__70097] :
( c_24__type__70096___24t(Vvar__70097)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__70097,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_70972',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__70973] :
( c_24__type__70972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__70973)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(Vvar__70973,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_70984',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70985] :
( c_24__type__70984___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70985)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__4,Vv__CANONICAL__3)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__1,Vv__CANONICAL__4,happ(Vvar__70985,Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_71084',axiom,
! [Vvar__71085] :
( c_24__type__71084___24t(Vvar__71085)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__71085,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_71124',axiom,
! [Vvar__71125] :
( c_24__type__71124___24t(Vvar__71125)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__31524___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__71125,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_71172',axiom,
! [Vvar__71173] :
( c_24__type__71172___24t(Vvar__71173)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__71173,Vv__CANONICAL__0)) ) ) ).
fof('$_type_71224',axiom,
! [Vvar__71225] :
( c_24__type__71224___24t(Vvar__71225)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRList_2eRlist___24t(happ(happ(Vvar__71225,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_71311',axiom,
! [Vvar__71312] :
( c_24__type__71311___24t(Vvar__71312)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__71312,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_71316',axiom,
! [Vvar__71317] :
( c_24__type__71316___24t(Vvar__71317)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(Vv__CANONICAL__0),happ(Vvar__71317,Vv__CANONICAL__0)) ) ) ).
fof('$_type_71322',axiom,
! [Vvar__71323] :
( c_24__type__71322___24t(Vvar__71323)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(c_24__lam__31642___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,happ(happ(Vvar__71323,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_71598',axiom,
! [Vvar__71599] :
( c_24__type__71598___24t(Vvar__71599)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___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)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))) )
=> ( ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__7)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__7))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__7,happ(Vv__CANONICAL__0,Vv__CANONICAL__3)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__7) = cCoq_2eReals_2eRanalysis1_2eid___24a1(Vv__CANONICAL__7) ) ) )
=> ( ! [Vv__CANONICAL__8] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__8)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__8))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__8,happ(Vv__CANONICAL__0,Vv__CANONICAL__3)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__8)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__1,Vv__CANONICAL__8),Vv__CANONICAL__3)) ) ) ) )
=> ( ! [Vv__CANONICAL__9] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__10)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__9))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__9,Vv__CANONICAL__10))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__10,Vv__CANONICAL__3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__9),happ(Vv__CANONICAL__0,Vv__CANONICAL__10))) ) ) ) ) )
=> ! [Vv__CANONICAL__10] :
( c_24__type__71618___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__10)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(happ(happ(happ(happ(happ(Vvar__71599,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_71618',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__71619] :
( c_24__type__71618___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__71619)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(Vvar__71619,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_71814',axiom,
! [Vvar__71815] :
( c_24__type__71814___24t(Vvar__71815)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___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)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))) )
=> ( ! [Vv__CANONICAL__7] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__7)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__7))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__7,happ(Vv__CANONICAL__0,Vv__CANONICAL__3)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__7) = cCoq_2eReals_2eRanalysis1_2eid___24a1(Vv__CANONICAL__7) ) ) )
=> ( ! [Vv__CANONICAL__8] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__8)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__8))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__8,happ(Vv__CANONICAL__0,Vv__CANONICAL__3)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__8)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__1,Vv__CANONICAL__8),Vv__CANONICAL__3)) ) ) ) )
=> ( ! [Vv__CANONICAL__9] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__10)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__9))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__9,Vv__CANONICAL__10))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__10,Vv__CANONICAL__3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__9),happ(Vv__CANONICAL__0,Vv__CANONICAL__10))) ) ) ) ) )
=> ! [Vv__CANONICAL__10] :
( c_24__type__71618___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__10)
=> ( cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__4),cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv__prelim1___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__10)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__1,Vv__CANONICAL__4,happ(happ(happ(happ(happ(happ(Vvar__71815,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_71884',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__71885] :
( c_24__type__71884___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__71885)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(Vvar__71885,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_71937',axiom,
! [Vvar__71938] :
( c_24__type__71937___24t(Vvar__71938)
<=> ! [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__20377___24a1(Vv__CANONICAL__0),happ(Vvar__71938,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_72',axiom,
! [Vvar__73] :
( c_24__type__72___24t(Vvar__73)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__73,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_72005',axiom,
! [Vvar__72006] :
( c_24__type__72005___24t(Vvar__72006)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__23___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__72006,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_72588',axiom,
! [Vvar__72589] :
( c_24__type__72588___24t(Vvar__72589)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__72589,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_74836',axiom,
! [Vvar__74837] :
( c_24__type__74836___24t(Vvar__74837)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__74837,Vv__CANONICAL__0)) ) ) ).
fof('$_type_74873',axiom,
! [Vvar__74874] :
( c_24__type__74873___24t(Vvar__74874)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__74836___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(happ(Vvar__74874,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_75033',axiom,
! [Vvar__75034] :
( c_24__type__75033___24t(Vvar__75034)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__75036___24a1(Vv__CANONICAL__0),happ(Vvar__75034,Vv__CANONICAL__0)) ) ) ).
fof('$_type_75845',axiom,
! [Vvar__75846] :
( c_24__type__75845___24t(Vvar__75846)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__75846,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_75963',axiom,
! [Vvar__75964] :
( c_24__type__75963___24t(Vvar__75964)
<=> ! [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_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive),happ(happ(Vvar__75964,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_76247',axiom,
! [Vvar__76248] :
( c_24__type__76247___24t(Vvar__76248)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ),happ(happ(Vvar__76248,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_76347',axiom,
! [Vv__CANONICAL__0,Vvar__76348] :
( c_24__type__76347___24t(Vv__CANONICAL__0,Vvar__76348)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2ePSeries__reg_2eCVN__r___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(Vvar__76348,Vv__CANONICAL__1)) ) ) ).
fof('$_type_76350',axiom,
! [Vvar__76351] :
( c_24__type__76350___24t(Vvar__76351)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__31524___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__76351,Vv__CANONICAL__0)) ) ) ).
fof('$_type_76360',axiom,
! [Vvar__76361] :
( c_24__type__76360___24t(Vvar__76361)
<=> ! [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_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__76361,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_76398',axiom,
! [Vvar__76399] :
( c_24__type__76398___24t(Vvar__76399)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__76399,Vv__CANONICAL__0)) ) ) ).
fof('$_type_76465',axiom,
! [Vvar__76466] :
( c_24__type__76465___24t(Vvar__76466)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1601___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)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eplus__fct___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__76466,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_76585',axiom,
! [Vvar__76586] :
( c_24__type__76585___24t(Vvar__76586)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(happ(Vvar__76586,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_76883',axiom,
! [Vvar__76884] :
( c_24__type__76883___24t(Vvar__76884)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___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_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__76884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_76888',axiom,
! [Vvar__76889] :
( c_24__type__76888___24t(Vvar__76889)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__76889,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_77040',axiom,
! [Vvar__77041] :
( c_24__type__77040___24t(Vvar__77041)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__31524___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__77041,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_77217',axiom,
! [Vvar__77218] :
( c_24__type__77217___24t(Vvar__77218)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__77220___24a1(Vv__CANONICAL__0),happ(Vvar__77218,Vv__CANONICAL__0)) ) ) ).
fof('$_type_78057',axiom,
! [Vvar__78058] :
( c_24__type__78057___24t(Vvar__78058)
<=> ! [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_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,happ(happ(Vvar__78058,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_78091',axiom,
! [Vvar__78092] :
( c_24__type__78091___24t(Vvar__78092)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__78092,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_78162',axiom,
! [Vvar__78163] :
( c_24__type__78162___24t(Vvar__78163)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3682___24t(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(Vv__CANONICAL__0)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__78167___24a1(Vv__CANONICAL__0),happ(Vvar__78163,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_877',axiom,
! [Vvar__878] :
( c_24__type__877___24t(Vvar__878)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__899___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__904___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__913___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__878,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_88',axiom,
! [Vvar__89] :
( c_24__type__88___24t(Vvar__89)
<=> ! [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__89,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_882',axiom,
! [Vv__CANONICAL__0,Vvar__883] :
( c_24__type__882___24t(Vv__CANONICAL__0,Vvar__883)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__883,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_891',axiom,
! [Vv__CANONICAL__0,Vvar__892] :
( c_24__type__891___24t(Vv__CANONICAL__0,Vvar__892)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__892,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_899',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__900] :
( c_24__type__899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__900)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__900,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_904',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__905] :
( c_24__type__904___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__905)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__905,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_913',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__914] :
( c_24__type__913___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__914)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__914,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__93] :
( c_24__type__92___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__93)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__93,Vv__CANONICAL__2)) ) ) ).
fof('$_type_935',axiom,
! [Vvar__936] :
( c_24__type__935___24t(Vvar__936)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__936,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_946',axiom,
! [Vvar__947] :
( c_24__type__946___24t(Vvar__947)
<=> ! [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__947,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_966',axiom,
! [Vvar__967] :
( c_24__type__966___24t(Vvar__967)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__967,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_98171',axiom,
! [Vvar__98172] :
( c_24__type__98171___24t(Vvar__98172)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__98172,Vv__CANONICAL__0)) ) ) ).
fof('$_type_98207',axiom,
! [Vvar__98208] :
( c_24__type__98207___24t(Vvar__98208)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__20377___24a1(Vv__CANONICAL__0),happ(Vvar__98208,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_98212',axiom,
! [Vvar__98213] :
( c_24__type__98212___24t(Vvar__98213)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__98214___24a1(Vv__CANONICAL__0),c_24__prop__98215___24a1(Vv__CANONICAL__0),happ(Vvar__98213,Vv__CANONICAL__0)) ) ) ).
fof('$_type_98295',axiom,
! [Vvar__98296] :
( c_24__type__98295___24t(Vvar__98296)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4) = happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3) ) )
=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ( happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> Vv__CANONICAL__4 = Vv__CANONICAL__5 ) ) )
=> ( ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__6),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__7),Vv__CANONICAL__6)))) ) ) )
=> cCoq_2eReals_2eRlimit_2eMetric__Space___24t(happ(happ(Vvar__98296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ) ).
fof('$_type_98342',axiom,
! [Vvar__98343] :
( c_24__type__98342___24t(Vvar__98343)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___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__98347___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__98343,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ).
fof('$_type_98351',axiom,
! [Vvar__98352] :
( c_24__type__98351___24t(Vvar__98352)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__98354___24a1(Vv__CANONICAL__0),happ(Vvar__98352,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_98618',axiom,
! [Vvar__98619] :
( c_24__type__98618___24t(Vvar__98619)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__98619,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_98628',axiom,
! [Vvar__98629] :
( c_24__type__98628___24t(Vvar__98629)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__98629,Vv__CANONICAL__0)) ) ) ).
fof('$_type_98636',axiom,
! [Vvar__98637] :
( c_24__type__98636___24t(Vvar__98637)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___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)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(cCoq_2eReals_2eRanalysis1_2eid,Vv__CANONICAL__2,happ(happ(happ(Vvar__98637,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_98673',axiom,
! [Vvar__98674] :
( c_24__type__98673___24t(Vvar__98674)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__98347___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__98674,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ) ).
fof('$_type_98690',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__98691] :
( c_24__type__98690___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__98691)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__4)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__4))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))) )
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,happ(Vvar__98691,Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_98785',axiom,
! [Vvar__98786] :
( c_24__type__98785___24t(Vvar__98786)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1601___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)))
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__98347___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__98786,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ) ).
fof('$_type_99',axiom,
! [Vvar__100] :
( c_24__type__99___24t(Vvar__100)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__100,Vv__CANONICAL__0)) ) ) ).
fof('$_typeof_Coq.Arith.Compare_dec.le_gt_dec',axiom,
c_24__type__98618___24t(cCoq_2eArith_2eCompare__dec_2ele__gt__dec) ).
fof('$_typeof_Coq.Arith.Compare_dec.lt_eq_lt_dec',axiom,
c_24__type__48957___24t(cCoq_2eArith_2eCompare__dec_2elt__eq__lt__dec) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__15554___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_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__15577___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__15554___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__15575___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__15539___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__280___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__268___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__30573___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__34140___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__34145___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__30583___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__249___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__30526___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__15542___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__263___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__249___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__88___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__72___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__2600___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__72___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_typeof_Coq.Init.Datatypes.true',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).
fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__18966___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__15554___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__18966___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__18966___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__15554___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__18966___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__20093___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__20093___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__20093___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__25942___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__67867___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__25972___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__25965___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__25977___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__25922___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__32385___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
c_24__type__67840___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__124___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__26003___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__2457___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__51705___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__18953___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__29853___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__29845___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__18953___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__32750___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__2518___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_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__15506___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__62___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__62___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__235___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__235___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__29918___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__29918___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__32765___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__29893___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__29915___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.gcd',axiom,
c_24__type__29893___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.ggcd',axiom,
c_24__type__75963___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__29893___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__32809___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__29893___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__32805___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__20115___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__20118___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq_bool',axiom,
c_24__type__34306___24t(cCoq_2eQArith_2eQArith__base_2eQeq__bool) ).
fof('$_typeof_Coq.QArith.QArith_base.Qinv',axiom,
c_24__type__20131___24t(cCoq_2eQArith_2eQArith__base_2eQinv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__20105___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__20127___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__20110___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.QArith.Qreals.Q2R',axiom,
c_24__type__33406___24t(cCoq_2eQArith_2eQreals_2eQ2R) ).
fof('$_typeof_Coq.Reals.AltSeries.Alt_PI',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eAltSeries_2eAlt__PI) ).
fof('$_typeof_Coq.Reals.AltSeries.PI_tg',axiom,
c_24__type__3682___24t(cCoq_2eReals_2eAltSeries_2ePI__tg) ).
fof('$_typeof_Coq.Reals.AltSeries.alternated_series',axiom,
c_24__type__78162___24t(cCoq_2eReals_2eAltSeries_2ealternated__series) ).
fof('$_typeof_Coq.Reals.AltSeries.positivity_seq',axiom,
c_24__type__25829___24t(cCoq_2eReals_2eAltSeries_2epositivity__seq) ).
fof('$_typeof_Coq.Reals.AltSeries.tg_alt',axiom,
c_24__type__15476___24t(cCoq_2eReals_2eAltSeries_2etg__alt) ).
fof('$_typeof_Coq.Reals.Cos_plus.Majxy',axiom,
c_24__type__70096___24t(cCoq_2eReals_2eCos__plus_2eMajxy) ).
fof('$_typeof_Coq.Reals.Machin.atan_sub',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eMachin_2eatan__sub) ).
fof('$_typeof_Coq.Reals.NewtonInt.Newton_integrable',axiom,
c_24__type__20523___24t(cCoq_2eReals_2eNewtonInt_2eNewton__integrable) ).
fof('$_typeof_Coq.Reals.PSeries_reg.Boule',axiom,
c_24__type__71084___24t(cCoq_2eReals_2ePSeries__reg_2eBoule) ).
fof('$_typeof_Coq.Reals.PSeries_reg.CVN_R',axiom,
c_24__type__76350___24t(cCoq_2eReals_2ePSeries__reg_2eCVN__R) ).
fof('$_typeof_Coq.Reals.PSeries_reg.CVN_r',axiom,
c_24__type__77040___24t(cCoq_2eReals_2ePSeries__reg_2eCVN__r) ).
fof('$_typeof_Coq.Reals.PSeries_reg.CVU',axiom,
c_24__type__71124___24t(cCoq_2eReals_2ePSeries__reg_2eCVU) ).
fof('$_typeof_Coq.Reals.PartSum.SP',axiom,
c_24__type__31521___24t(cCoq_2eReals_2ePartSum_2eSP) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_dec',axiom,
c_24__type__20140___24t(cCoq_2eReals_2eRIneq_2eRle__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_lt_dec',axiom,
c_24__type__61958___24t(cCoq_2eReals_2eRIneq_2eRle__lt__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rlt_le_dec',axiom,
c_24__type__76360___24t(cCoq_2eReals_2eRIneq_2eRlt__le__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.mknonnegreal',axiom,
c_24__type__31540___24t(cCoq_2eReals_2eRIneq_2emknonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.mknonzeroreal',axiom,
c_24__type__31570___24t(cCoq_2eReals_2eRIneq_2emknonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.mkposreal',axiom,
c_24__type__20151___24t(cCoq_2eReals_2eRIneq_2emkposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonneg',axiom,
c_24__type__34485___24t(cCoq_2eReals_2eRIneq_2enonneg) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonpos',axiom,
c_24__type__98171___24t(cCoq_2eReals_2eRIneq_2enonpos) ).
fof('$_typeof_Coq.Reals.RIneq.nonzero',axiom,
c_24__type__61968___24t(cCoq_2eReals_2eRIneq_2enonzero) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.pos',axiom,
c_24__type__20156___24t(cCoq_2eReals_2eRIneq_2epos) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.RList.In',axiom,
c_24__type__31589___24t(cCoq_2eReals_2eRList_2eIn) ).
fof('$_typeof_Coq.Reals.RList.MinRlist',axiom,
c_24__type__76398___24t(cCoq_2eReals_2eRList_2eMinRlist) ).
fof('$_typeof_Coq.Reals.RList.Rlength',axiom,
c_24__type__61974___24t(cCoq_2eReals_2eRList_2eRlength) ).
fof('$_typeof_Coq.Reals.RList.Rlist',axiom,
cType___24t(cCoq_2eReals_2eRList_2eRlist) ).
fof('$_typeof_Coq.Reals.RList.cons',axiom,
c_24__type__31582___24t(cCoq_2eReals_2eRList_2econs) ).
fof('$_typeof_Coq.Reals.RList.mid_Rlist',axiom,
c_24__type__71224___24t(cCoq_2eReals_2eRList_2emid__Rlist) ).
fof('$_typeof_Coq.Reals.RList.nil',axiom,
cCoq_2eReals_2eRList_2eRlist___24t(cCoq_2eReals_2eRList_2enil) ).
fof('$_typeof_Coq.Reals.RList.pos_Rl',axiom,
c_24__type__61986___24t(cCoq_2eReals_2eRList_2epos__Rl) ).
fof('$_typeof_Coq.Reals.R_Ifp.Int_part',axiom,
c_24__type__31647___24t(cCoq_2eReals_2eR__Ifp_2eInt__part) ).
fof('$_typeof_Coq.Reals.R_Ifp.frac_part',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eR__Ifp_2efrac__part) ).
fof('$_typeof_Coq.Reals.R_sqrt.Delta',axiom,
c_24__type__76883___24t(cCoq_2eReals_2eR__sqrt_2eDelta) ).
fof('$_typeof_Coq.Reals.R_sqrt.Delta_is_pos',axiom,
c_24__type__76888___24t(cCoq_2eReals_2eR__sqrt_2eDelta__is__pos) ).
fof('$_typeof_Coq.Reals.R_sqrt.sol_x1',axiom,
c_24__type__76883___24t(cCoq_2eReals_2eR__sqrt_2esol__x1) ).
fof('$_typeof_Coq.Reals.R_sqrt.sol_x2',axiom,
c_24__type__76883___24t(cCoq_2eReals_2eR__sqrt_2esol__x2) ).
fof('$_typeof_Coq.Reals.R_sqrt.sqrt',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eR__sqrt_2esqrt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.antiderivative',axiom,
c_24__type__62002___24t(cCoq_2eReals_2eRanalysis1_2eantiderivative) ).
fof('$_typeof_Coq.Reals.Ranalysis1.comp',axiom,
c_24__type__20326___24t(cCoq_2eReals_2eRanalysis1_2ecomp) ).
fof('$_typeof_Coq.Reals.Ranalysis1.constant',axiom,
c_24__type__20331___24t(cCoq_2eReals_2eRanalysis1_2econstant) ).
fof('$_typeof_Coq.Reals.Ranalysis1.constant_D_eq',axiom,
c_24__type__31617___24t(cCoq_2eReals_2eRanalysis1_2econstant__D__eq) ).
fof('$_typeof_Coq.Reals.Ranalysis1.continuity',axiom,
c_24__type__20331___24t(cCoq_2eReals_2eRanalysis1_2econtinuity) ).
fof('$_typeof_Coq.Reals.Ranalysis1.continuity_pt',axiom,
c_24__type__20329___24t(cCoq_2eReals_2eRanalysis1_2econtinuity__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.decreasing',axiom,
c_24__type__20331___24t(cCoq_2eReals_2eRanalysis1_2edecreasing) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable',axiom,
c_24__type__31633___24t(cCoq_2eReals_2eRanalysis1_2ederivable) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_Rsqr',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRIneq_2eRsqr,cCoq_2eReals_2eRanalysis1_2ederivable__Rsqr) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_const',axiom,
c_24__type__71316___24t(cCoq_2eReals_2eRanalysis1_2ederivable__const) ).
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_pow',axiom,
c_24__type__31639___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pow) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt',axiom,
c_24__type__31628___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_abs',axiom,
c_24__type__31622___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__abs) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_const',axiom,
c_24__type__62020___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__const) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_id',axiom,
c_24__type__31635___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__id) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_lim',axiom,
c_24__type__31622___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_mult',axiom,
c_24__type__71311___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__mult) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_plus',axiom,
c_24__type__76465___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__plus) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derivable_pt_pow',axiom,
c_24__type__71322___24t(cCoq_2eReals_2eRanalysis1_2ederivable__pt__pow) ).
fof('$_typeof_Coq.Reals.Ranalysis1.derive_pt',axiom,
c_24__type__34344___24t(cCoq_2eReals_2eRanalysis1_2ederive__pt) ).
fof('$_typeof_Coq.Reals.Ranalysis1.div_fct',axiom,
c_24__type__20326___24t(cCoq_2eReals_2eRanalysis1_2ediv__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.fct_cte',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRanalysis1_2efct__cte) ).
fof('$_typeof_Coq.Reals.Ranalysis1.id',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRanalysis1_2eid) ).
fof('$_typeof_Coq.Reals.Ranalysis1.increasing',axiom,
c_24__type__20331___24t(cCoq_2eReals_2eRanalysis1_2eincreasing) ).
fof('$_typeof_Coq.Reals.Ranalysis1.minus_fct',axiom,
c_24__type__20326___24t(cCoq_2eReals_2eRanalysis1_2eminus__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.mult_fct',axiom,
c_24__type__20326___24t(cCoq_2eReals_2eRanalysis1_2emult__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.no_cond',axiom,
c_24__type__23___24t(cCoq_2eReals_2eRanalysis1_2eno__cond) ).
fof('$_typeof_Coq.Reals.Ranalysis1.opp_fct',axiom,
c_24__type__31597___24t(cCoq_2eReals_2eRanalysis1_2eopp__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.plus_fct',axiom,
c_24__type__20326___24t(cCoq_2eReals_2eRanalysis1_2eplus__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.pow_fct',axiom,
c_24__type__31524___24t(cCoq_2eReals_2eRanalysis1_2epow__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis4.derivable_exp',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable___24t(cCoq_2eReals_2eRtrigo__def_2eexp,cCoq_2eReals_2eRanalysis4_2ederivable__exp) ).
fof('$_typeof_Coq.Reals.Ranalysis5.IVT_interv',axiom,
c_24__type__98673___24t(cCoq_2eReals_2eRanalysis5_2eIVT__interv) ).
fof('$_typeof_Coq.Reals.Ranalysis5.derivable_pt_id_interv',axiom,
c_24__type__98636___24t(cCoq_2eReals_2eRanalysis5_2ederivable__pt__id__interv) ).
fof('$_typeof_Coq.Reals.Ranalysis5.derivable_pt_recip_interv',axiom,
c_24__type__71814___24t(cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv) ).
fof('$_typeof_Coq.Reals.Ranalysis5.derivable_pt_recip_interv_prelim1',axiom,
c_24__type__71598___24t(cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv__prelim1) ).
fof('$_typeof_Coq.Reals.Ratan.Datan_seq',axiom,
c_24__type__2445___24t(cCoq_2eReals_2eRatan_2eDatan__seq) ).
fof('$_typeof_Coq.Reals.Ratan.Ratan_seq',axiom,
c_24__type__2445___24t(cCoq_2eReals_2eRatan_2eRatan__seq) ).
fof('$_typeof_Coq.Reals.Ratan.atan',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRatan_2eatan) ).
fof('$_typeof_Coq.Reals.Ratan.frame_tan',axiom,
c_24__type__77217___24t(cCoq_2eReals_2eRatan_2eframe__tan) ).
fof('$_typeof_Coq.Reals.Ratan.in_int',axiom,
c_24__type__98212___24t(cCoq_2eReals_2eRatan_2ein__int) ).
fof('$_typeof_Coq.Reals.Ratan.pos_half',axiom,
cCoq_2eReals_2eRIneq_2eposreal___24t(cCoq_2eReals_2eRatan_2epos__half) ).
fof('$_typeof_Coq.Reals.Ratan.ps_atan',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRatan_2eps__atan) ).
fof('$_typeof_Coq.Reals.Ratan.ps_atan_exists_01',axiom,
c_24__type__98207___24t(cCoq_2eReals_2eRatan_2eps__atan__exists__01) ).
fof('$_typeof_Coq.Reals.Ratan.ps_atan_exists_1',axiom,
c_24__type__71937___24t(cCoq_2eReals_2eRatan_2eps__atan__exists__1) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__3682___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Raxioms.bound',axiom,
c_24__type__31643___24t(cCoq_2eReals_2eRaxioms_2ebound) ).
fof('$_typeof_Coq.Reals.Raxioms.completeness',axiom,
c_24__type__52101___24t(cCoq_2eReals_2eRaxioms_2ecompleteness) ).
fof('$_typeof_Coq.Reals.Raxioms.is_lub',axiom,
c_24__type__20395___24t(cCoq_2eReals_2eRaxioms_2eis__lub) ).
fof('$_typeof_Coq.Reals.Raxioms.is_upper_bound',axiom,
c_24__type__20395___24t(cCoq_2eReals_2eRaxioms_2eis__upper__bound) ).
fof('$_typeof_Coq.Reals.Raxioms.total_order_T',axiom,
c_24__type__34401___24t(cCoq_2eReals_2eRaxioms_2etotal__order__T) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rabs',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRbasic__fun_2eRabs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rcase_abs',axiom,
c_24__type__31645___24t(cCoq_2eReals_2eRbasic__fun_2eRcase__abs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmax',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRbasic__fun_2eRmax) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmin',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRbasic__fun_2eRmin) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IPR',axiom,
c_24__type__20432___24t(cCoq_2eReals_2eRdefinitions_2eIPR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IPR_2',axiom,
c_24__type__20432___24t(cCoq_2eReals_2eRdefinitions_2eIPR__2) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__112___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__1598___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__107___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__107___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__107___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__107___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__31647___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rderiv.D_in',axiom,
c_24__type__72005___24t(cCoq_2eReals_2eRderiv_2eD__in) ).
fof('$_typeof_Coq.Reals.Rderiv.D_x',axiom,
c_24__type__20437___24t(cCoq_2eReals_2eRderiv_2eD__x) ).
fof('$_typeof_Coq.Reals.Rderiv.continue_in',axiom,
c_24__type__31617___24t(cCoq_2eReals_2eRderiv_2econtinue__in) ).
fof('$_typeof_Coq.Reals.Rfunctions.R_dist',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRfunctions_2eR__dist) ).
fof('$_typeof_Coq.Reals.Rfunctions.infinite_sum',axiom,
c_24__type__25808___24t(cCoq_2eReals_2eRfunctions_2einfinite__sum) ).
fof('$_typeof_Coq.Reals.Rfunctions.powerRZ',axiom,
c_24__type__33411___24t(cCoq_2eReals_2eRfunctions_2epowerRZ) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_f_R0',axiom,
c_24__type__15476___24t(cCoq_2eReals_2eRfunctions_2esum__f__R0) ).
fof('$_typeof_Coq.Reals.Rgeom.dist_euc',axiom,
c_24__type__76585___24t(cCoq_2eReals_2eRgeom_2edist__euc) ).
fof('$_typeof_Coq.Reals.RiemannInt.RinvN',axiom,
c_24__type__20594___24t(cCoq_2eReals_2eRiemannInt_2eRinvN) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.Int_SF',axiom,
c_24__type__72588___24t(cCoq_2eReals_2eRiemannInt__SF_2eInt__SF) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.open_interval',axiom,
c_24__type__62025___24t(cCoq_2eReals_2eRiemannInt__SF_2eopen__interval) ).
fof('$_typeof_Coq.Reals.Rlimit.Base',axiom,
c_24__type__25676___24t(cCoq_2eReals_2eRlimit_2eBase) ).
fof('$_typeof_Coq.Reals.Rlimit.Build_Metric_Space',axiom,
c_24__type__98295___24t(cCoq_2eReals_2eRlimit_2eBuild__Metric__Space) ).
fof('$_typeof_Coq.Reals.Rlimit.Dgf',axiom,
c_24__type__32362___24t(cCoq_2eReals_2eRlimit_2eDgf) ).
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('$_typeof_Coq.Reals.Rlimit.dist',axiom,
c_24__type__25771___24t(cCoq_2eReals_2eRlimit_2edist) ).
fof('$_typeof_Coq.Reals.Rlimit.limit1_in',axiom,
c_24__type__25780___24t(cCoq_2eReals_2eRlimit_2elimit1__in) ).
fof('$_typeof_Coq.Reals.Rlimit.limit_in',axiom,
c_24__type__34451___24t(cCoq_2eReals_2eRlimit_2elimit__in) ).
fof('$_typeof_Coq.Reals.Rlimit.mul_factor',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRlimit_2emul__factor) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__2445___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Reals.Rpower.Rpower',axiom,
c_24__type__1598___24t(cCoq_2eReals_2eRpower_2eRpower) ).
fof('$_typeof_Coq.Reals.Rpower.arcsinh',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRpower_2earcsinh) ).
fof('$_typeof_Coq.Reals.Rpower.ln',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRpower_2eln) ).
fof('$_typeof_Coq.Reals.Rpower.ln_exists1',axiom,
c_24__type__25786___24t(cCoq_2eReals_2eRpower_2eln__exists1) ).
fof('$_typeof_Coq.Reals.Rprod.prod_f_R0',axiom,
c_24__type__15476___24t(cCoq_2eReals_2eRprod_2eprod__f__R0) ).
fof('$_typeof_Coq.Reals.Rseries.EUn',axiom,
c_24__type__25808___24t(cCoq_2eReals_2eRseries_2eEUn) ).
fof('$_typeof_Coq.Reals.Rseries.Pser',axiom,
c_24__type__34468___24t(cCoq_2eReals_2eRseries_2ePser) ).
fof('$_typeof_Coq.Reals.Rseries.Un_cv',axiom,
c_24__type__25808___24t(cCoq_2eReals_2eRseries_2eUn__cv) ).
fof('$_typeof_Coq.Reals.Rseries.Un_growing',axiom,
c_24__type__25829___24t(cCoq_2eReals_2eRseries_2eUn__growing) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.Dichotomy_lb',axiom,
c_24__type__74873___24t(cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.Dichotomy_ub',axiom,
c_24__type__74873___24t(cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.IVT',axiom,
c_24__type__98785___24t(cCoq_2eReals_2eRsqrt__def_2eIVT) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.IVT_cor',axiom,
c_24__type__98342___24t(cCoq_2eReals_2eRsqrt__def_2eIVT__cor) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.Rsqrt',axiom,
c_24__type__34485___24t(cCoq_2eReals_2eRsqrt__def_2eRsqrt) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.Rsqrt_exists',axiom,
c_24__type__98351___24t(cCoq_2eReals_2eRsqrt__def_2eRsqrt__exists) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.cond_positivity',axiom,
c_24__type__74836___24t(cCoq_2eReals_2eRsqrt__def_2econd__positivity) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.dicho_lb',axiom,
c_24__type__74873___24t(cCoq_2eReals_2eRsqrt__def_2edicho__lb) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.dicho_up',axiom,
c_24__type__74873___24t(cCoq_2eReals_2eRsqrt__def_2edicho__up) ).
fof('$_typeof_Coq.Reals.Rsqrt_def.pow_2_n',axiom,
c_24__type__3682___24t(cCoq_2eReals_2eRsqrt__def_2epow__2__n) ).
fof('$_typeof_Coq.Reals.Rtrigo1.PI',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRtrigo1_2ePI) ).
fof('$_typeof_Coq.Reals.Rtrigo1.PI2',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRtrigo1_2ePI2) ).
fof('$_typeof_Coq.Reals.Rtrigo1.PI_2_aux',axiom,
cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__98355,cCoq_2eReals_2eRtrigo1_2ePI__2__aux) ).
fof('$_typeof_Coq.Reals.Rtrigo1.tan',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRtrigo1_2etan) ).
fof('$_typeof_Coq.Reals.Rtrigo_alt.cos_approx',axiom,
c_24__type__2445___24t(cCoq_2eReals_2eRtrigo__alt_2ecos__approx) ).
fof('$_typeof_Coq.Reals.Rtrigo_alt.cos_term',axiom,
c_24__type__2445___24t(cCoq_2eReals_2eRtrigo__alt_2ecos__term) ).
fof('$_typeof_Coq.Reals.Rtrigo_alt.sin_approx',axiom,
c_24__type__2445___24t(cCoq_2eReals_2eRtrigo__alt_2esin__approx) ).
fof('$_typeof_Coq.Reals.Rtrigo_alt.sin_term',axiom,
c_24__type__2445___24t(cCoq_2eReals_2eRtrigo__alt_2esin__term) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.cos',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRtrigo__def_2ecos) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.cos_in',axiom,
c_24__type__107___24t(cCoq_2eReals_2eRtrigo__def_2ecos__in) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.cos_n',axiom,
c_24__type__3682___24t(cCoq_2eReals_2eRtrigo__def_2ecos__n) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.cosh',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRtrigo__def_2ecosh) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.exist_cos',axiom,
c_24__type__75033___24t(cCoq_2eReals_2eRtrigo__def_2eexist__cos) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.exp',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRtrigo__def_2eexp) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.exp_in',axiom,
c_24__type__107___24t(cCoq_2eReals_2eRtrigo__def_2eexp__in) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.sin',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRtrigo__def_2esin) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.sin_in',axiom,
c_24__type__107___24t(cCoq_2eReals_2eRtrigo__def_2esin__in) ).
fof('$_typeof_Coq.Reals.Rtrigo_def.sinh',axiom,
c_24__type__1601___24t(cCoq_2eReals_2eRtrigo__def_2esinh) ).
fof('$_typeof_Coq.Reals.SeqProp.Un_decreasing',axiom,
c_24__type__25829___24t(cCoq_2eReals_2eSeqProp_2eUn__decreasing) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__179___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__179___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__179___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__179___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__179___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__179___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__228___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ggcd',axiom,
c_24__type__76247___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__2515___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
c_24__type__2515___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__18146___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__29966___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pos_div_eucl',axiom,
c_24__type__2702___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__div__eucl) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
c_24__type__29938___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__2586___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.shiftr',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__194___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__2515___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.Zmod_POS',axiom,
c_24__type__78091___24t(cCoq_2eZArith_2eZdiv_2eZmod__POS) ).
fof('$_typeof_Coq.ZArith.Znumtheory.rel_prime',axiom,
c_24__type__179___24t(cCoq_2eZArith_2eZnumtheory_2erel__prime) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest',axiom,
c_24__type__75845___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__15768___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__15773___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__15765___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEmul',axiom,
c_24__type__15773___24t(cCoq_2emicromega_2eEnvRing_2ePEmul) ).
fof('$_typeof_Coq.micromega.EnvRing.PEopp',axiom,
c_24__type__30595___24t(cCoq_2emicromega_2eEnvRing_2ePEopp) ).
fof('$_typeof_Coq.micromega.EnvRing.PEpow',axiom,
c_24__type__30600___24t(cCoq_2emicromega_2eEnvRing_2ePEpow) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__15773___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__30650___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__249___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__20308___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
c_24__type__20306___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).
fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
c_24__type__20306___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__20303___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.INZ',axiom,
c_24__type__98628___24t(cCoq_2emicromega_2eRMicromega_2eINZ) ).
fof('$_typeof_Coq.micromega.RMicromega.RTautoChecker',axiom,
c_24__type__20312___24t(cCoq_2emicromega_2eRMicromega_2eRTautoChecker) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.RingMicromega.Build_Formula',axiom,
c_24__type__21220___24t(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.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.PolC',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__21191___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__21197___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__21186___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__21191___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__26554___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.Cj',axiom,
c_24__type__32425___24t(cCoq_2emicromega_2eTauto_2eCj) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__67892___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__26150___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.I',axiom,
c_24__type__26577___24t(cCoq_2emicromega_2eTauto_2eI) ).
fof('$_typeof_Coq.micromega.Tauto.N',axiom,
c_24__type__32437___24t(cCoq_2emicromega_2eTauto_2eN) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__32408___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.VarMap.Branch',axiom,
c_24__type__32447___24t(cCoq_2emicromega_2eVarMap_2eBranch) ).
fof('$_typeof_Coq.micromega.VarMap.Elt',axiom,
c_24__type__26617___24t(cCoq_2emicromega_2eVarMap_2eElt) ).
fof('$_typeof_Coq.micromega.VarMap.Empty',axiom,
c_24__type__32439___24t(cCoq_2emicromega_2eVarMap_2eEmpty) ).
fof('$_typeof_Coq.micromega.VarMap.find',axiom,
c_24__type__26648___24t(cCoq_2emicromega_2eVarMap_2efind) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__249___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZgcdM',axiom,
c_24__type__194___24t(cCoq_2emicromega_2eZMicromega_2eZgcdM) ).
fof('$_typeof_Coq.micromega.ZMicromega.Zgcd_pol',axiom,
c_24__type__34714___24t(cCoq_2emicromega_2eZMicromega_2eZgcd__pol) ).
fof('$_typeof_Coq.micromega.ZMicromega.ceiling',axiom,
c_24__type__194___24t(cCoq_2emicromega_2eZMicromega_2eceiling) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__610___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__615___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__2604___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__615___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__877___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__2607___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__615___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__2607___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__30673___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__615___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__249___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__1448___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__1575___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fnorm',axiom,
c_24__type__1415___24t(cCoq_2esetoid__ring_2eField__theory_2eFnorm) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__1185___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__966___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__946___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
c_24__type__38426___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__249___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__935___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__946___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__249___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__32913___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__32913___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__32961___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__31450___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__18930___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__32971___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__2032___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__2037___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__2029___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__21469___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__2037___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__2040___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__21254___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__2037___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__249___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__31776___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__31763___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__1780___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__31768___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__249___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__33355___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__21729___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__2424___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__2248___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__31779___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__21830___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__31797___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Fermat4.ArithCompl.frac',axiom,
c_24__type__6___24t(cFermat4_2eArithCompl_2efrac) ).
fof('$_typeof_Fermat4.ArithCompl.is_rat',axiom,
c_24__type__23___24t(cFermat4_2eArithCompl_2eis__rat) ).
fof('$_typeof_Fermat4.ArithCompl.is_ratp',axiom,
c_24__type__34819___24t(cFermat4_2eArithCompl_2eis__ratp) ).
fof('$_typeof_Fermat4.ArithCompl.rel_prime_dec',axiom,
c_24__type__2___24t(cFermat4_2eArithCompl_2erel__prime__dec) ).
fof('$_typeof_Pythagorean.D_r',axiom,
c_24__type__62025___24t(cPythagorean_2eD__r) ).
fof('$_typeof_Pythagorean.cond_pqb',axiom,
c_24__type__179___24t(cPythagorean_2econd__pqb) ).
fof('$_typeof_Pythagorean.eqp',axiom,
c_24__type__35030___24t(cPythagorean_2eeqp) ).
fof('$_typeof_Pythagorean.in_ucirc',axiom,
c_24__type__107___24t(cPythagorean_2ein__ucirc) ).
fof('$_typeof_Pythagorean.in_ucp_setb',axiom,
c_24__type__107___24t(cPythagorean_2ein__ucp__setb) ).
fof('$_typeof_Pythagorean.interCDr',axiom,
c_24__type__62025___24t(cPythagorean_2einterCDr) ).
fof('$_typeof_Pythagorean.is_posp',axiom,
c_24__type__34819___24t(cPythagorean_2eis__posp) ).
fof('$_typeof_Pythagorean.is_ucp',axiom,
c_24__type__34819___24t(cPythagorean_2eis__ucp) ).
fof('$_typeof_Pythagorean.p1',axiom,
cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cPythagorean_2ep1) ).
fof('$_typeof_Pythagorean.p2',axiom,
c_24__type__35033___24t(cPythagorean_2ep2) ).
fof('$_typeof_Pythagorean.ucp',axiom,
c_24__type__78057___24t(cPythagorean_2eucp) ).
fof('Coq.Arith.Compare_dec.dec_ge',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_2ege___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_le',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_2ele___24a2(V0__n,V1__m)) ) ) ).
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_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
=> p(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)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(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))
=> p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Factorial.fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2eFactorial_2efact___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eO ) ).
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)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.lt_S_n',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(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,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))
=> p(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)
=> p(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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Arith.Minus.le_plus_minus',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> V1__m = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n)) ) ) ) ).
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_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> 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.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO)) ) ).
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__98626___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__35624___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__15556___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.Datatypes.prod_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__92___24t(V0__A,V1__B,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
=> ! [V4__p] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
=> p(happ(V2__P,V4__p)) ) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__31527___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_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__15556___24t(V1__P)
=> ( p(happ(V1__P,V0__n))
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V3__m))
=> ( p(happ(V1__P,V3__m))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V4__n))
=> p(happ(V1__P,V4__n)) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Specif.proj2_sig',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__25925___24t(V0__A,V1__P)
=> ! [V2__e] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> p(happ(V1__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e))) ) ) ) ).
fof('Coq.Init.Specif.sig_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__25925___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__67816___24t(V0__A,V1__P,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,V3__x))) ) )
=> ! [V4__s] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
=> p(happ(V2__P,V4__s)) ) ) ) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__146___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.Init.Specif.sumor_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__2479___24t(V0__A,V1__B,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,V3__a))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2einright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
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__30585___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_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.positive_ind',axiom,
! [V0__P] :
( c_24__type__30501___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__29921___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.PArith.BinPos.Pos.ggcd_gcd',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__b)
=> cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive),cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(V0__a,V1__b)) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V0__a,V1__b) ) ) ).
fof('Coq.QArith.Qreals.IZR_nz',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.AltSeries.PI_tg_cv',axiom,
cCoq_2eReals_2eRseries_2eUn__cv___24a2(cCoq_2eReals_2eAltSeries_2ePI__tg,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ).
fof('Coq.Reals.AltSeries.alternated_series_ineq',axiom,
! [V0__Un] :
( c_24__type__3682___24t(V0__Un)
=> ! [V1__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V0__Un)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__78171___24a1(V0__Un),V1__l)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(V0__Un),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V2__N))),V1__l))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__l,cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(V0__Un),cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V2__N)))) ) ) ) ) ) ) ) ).
fof('Coq.Reals.ArithProp.euclidian_division',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( V1__y != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ? [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
& ? [V4__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__r)
& V0__x = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V3__k),V1__y),V4__r)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V4__r))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__r,cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.ArithProp.even_odd_cor',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__p)
& ( V0__n = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__p)
| V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__p)) ) ) ) ).
fof('Coq.Reals.ArithProp.tech8',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__i))) ) ) ).
fof('Coq.Reals.Cos_plus.cos_plus',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V1__y)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V1__y))) ) ) ).
fof('Coq.Reals.Cos_rel.pow_sqr',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> 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__i)) = cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V0__x),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.Exp_prop.derivable_pt_lim_exp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRtrigo__def_2eexp,V0__x,cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x)) ) ).
fof('Coq.Reals.Exp_prop.derivable_pt_lim_exp_0',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRtrigo__def_2eexp,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.Exp_prop.exp_plus',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V1__y)) ) ) ).
fof('Coq.Reals.Exp_prop.exp_pos',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),cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x))) ) ).
fof('Coq.Reals.MVT.MVT',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___24t(V1__g)
=> ! [V2__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__a)
=> ! [V3__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__b)
=> ! [V4__pr1] :
( c_24__type__70972___24t(V0__f,V2__a,V3__b,V4__pr1)
=> ! [V5__pr2] :
( c_24__type__70984___24t(V0__f,V1__g,V2__a,V3__b,V5__pr2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__a,V3__b))
=> ( ! [V7__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V7__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V7__c,V3__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V7__c) ) )
=> ( ! [V8__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__c)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__a,V8__c))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__c,V3__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V1__g,V8__c) ) )
=> ? [V9__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__c)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__a,V9__c))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V9__c,V3__b))
& cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V1__g,V3__b),happ(V1__g,V2__a)),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V9__c,happ(V4__pr1,V9__c))) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f,V3__b),happ(V0__f,V2__a)),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V9__c,happ(V5__pr2,V9__c))) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.MVT.MVT_cor1',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable___24t(V0__f,V3__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V2__b))
=> ? [V5__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V5__c)
& cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V0__f,V2__b),happ(V0__f,V1__a)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V5__c,happ(V3__pr,V5__c)),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V2__b,V1__a))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V5__c))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V5__c,V2__b)) ) ) ) ) ) ) ).
fof('Coq.Reals.MVT.Rolle',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__pr] :
( c_24__type__70972___24t(V0__f,V1__a,V2__b,V3__pr)
=> ( ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__a,V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V4__x,V2__b)) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f,V4__x) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V2__b))
=> ( happ(V0__f,V1__a) = happ(V0__f,V2__b)
=> ? [V7__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__c)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V7__c))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__c,V2__b))
& cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V7__c,happ(V3__pr,V7__c)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.PartSum.cond_pos_sum',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__An,V2__n))) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___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.decomp_sum',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V1__N))
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(V0__An,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__98621___24a1(V0__An),cCoq_2eInit_2eNat_2epred___24a1(V1__N))) ) ) ) ).
fof('Coq.Reals.PartSum.scal_sum',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__x,cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V1__N)) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__76355___24a2(V0__An,V2__x),V1__N) ) ) ) ).
fof('Coq.Reals.PartSum.sum_cte',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(c_24__lam__98623___24a1(V0__x),V1__N) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__N))) ) ) ).
fof('Coq.Reals.PartSum.sum_eq',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__3682___24t(V1__Bn)
=> ! [V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ! [V3__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__i)
=> ( p(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__3682___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(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__3682___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(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.tech11',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__3682___24t(V1__Bn)
=> ! [V2__Cn] :
( c_24__type__3682___24t(V2__Cn)
=> ! [V3__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__N)
=> ( ! [V4__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__i)
=> happ(V0__An,V4__i) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(happ(V1__Bn,V4__i),happ(V2__Cn,V4__i)) )
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__An,V3__N) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__Bn,V3__N),cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V2__Cn,V3__N)) ) ) ) ) ) ).
fof('Coq.Reals.PartSum.tech2',axiom,
! [V0__An] :
( c_24__type__3682___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__52086___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__52088___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__3682___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__3682___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__52088___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.PartSum.uniqueness_sum',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l2)
=> ( cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V0__An,V1__l1)
=> ( cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V0__An,V2__l2)
=> V1__l1 = V2__l2 ) ) ) ) ) ).
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)))
=> p(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__101___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__1595___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__1595___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.RField_ring_lemma2',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__lH] :
( 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)),V1__lH)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V2__l)
=> ( 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,V2__l,V1__lH)
=> ! [V4__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)),V4__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,V1__lH) = V4__lmp
=> ! [V6__pe] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V6__pe)
=> ! [V7__npe] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,V7__npe)
=> ( 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,V4__lmp,V6__pe) = V7__npe
=> 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,V2__l,V6__pe) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(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_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V2__l,V7__npe) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.R_rm',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(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_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_2eReals_2eRdefinitions_2eIZR) ).
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_ge_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_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le',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_2eRle___24a2(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_ge_eq',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(V1__r2,V0__r1)) )
<=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rge_gt_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_2eRgt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
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_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_1',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRle___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.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_le_eq',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_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_minus',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(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_or_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.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_Rminus',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__b,V0__a))) ) ) ) ).
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_ge',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_2eRge___24a2(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.Rlt_plus_1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,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.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_ge',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_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_le',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_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
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_ge_compat_neg_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(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___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_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_ne',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
& 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.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_gt',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_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ).
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_Ropp_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)) ) ).
fof('Coq.Reals.RIneq.Ropp_eq_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_2eRopp___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Ropp_eq_compat',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_2eRopp___24a1(V0__r1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_ge_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_2eRge___24a2(V0__r1,V1__r2))
=> 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_gt_lt_0_contravar',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)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
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_inv_permute',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) ) ) ).
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_cancel',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_2eRopp___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,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_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(V1__r2,V0__r1)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) ) ) ).
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_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_2eRopp___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
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_0_r_uniq',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = V0__r
=> V1__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_0_l',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))
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_R0',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))
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ).
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_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_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)
=> V1__r1 = V2__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_ge_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_2eRge___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_gt_ge_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_2eRgt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___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',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.Rsqr_0',axiom,
cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.Rsqr_0_uniq',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> 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.Zeq_bool_IZR',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__y)
=> cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Reals.RIneq.cond_nonneg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2enonneg___24a1(V0__n))) ) ).
fof('Coq.Reals.RIneq.cond_nonpos',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2enonpos___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ).
fof('Coq.Reals.RIneq.cond_nonzero',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V0__n)
=> cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
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.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)
=> ( p(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.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_1_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRaxioms_2eINR___24a1(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.minus_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_2esub___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(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_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
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.not_1_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)
=> 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.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.opp_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)) ) ).
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.succ_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
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.RList.Rlist_ind',axiom,
! [V0__P] :
( c_24__type__71172___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eReals_2eRList_2enil))
=> ( ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ! [V3__r] :
( cCoq_2eReals_2eRList_2eRlist___24t(V3__r)
=> ( p(happ(V0__P,V3__r))
=> p(happ(V0__P,cCoq_2eReals_2eRList_2econs___24a2(V2__r,V3__r))) ) ) )
=> ! [V3__r] :
( cCoq_2eReals_2eRList_2eRlist___24t(V3__r)
=> p(happ(V0__P,V3__r)) ) ) ) ) ).
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.for_base_fp',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___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_2eZ0)))
& 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.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.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_div',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( V1__y != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)) ) ) ) ).
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_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.Rle_mult_inv_pos',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_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y)))) ) ) ) ) ).
fof('Coq.Reals.R_sqrt.Rsqr_sol_eq_0_0',axiom,
! [V0__a] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__c)
=> ! [V3__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__x)
=> ( cCoq_2eReals_2eR__sqrt_2eDelta__is__pos___24a3(V0__a,V1__b,V2__c)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__a),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V3__x)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__b,V3__x)),V2__c) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V3__x = cCoq_2eReals_2eR__sqrt_2esol__x1___24a3(V0__a,V1__b,V2__c)
| V3__x = cCoq_2eReals_2eR__sqrt_2esol__x2___24a3(V0__a,V1__b,V2__c) ) ) ) ) ) ) ) ).
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_0',axiom,
cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
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_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_lt_1_alt',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_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_lt_R0',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_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(V0__x))) ) ) ).
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.R_sqrt.sqrt_square',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_2eRdefinitions_2eRmult___24a2(V0__x,V0__x)) = V0__x ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_div',axiom,
! [V0__f1] :
( c_24__type__1601___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__1601___24t(V1__f2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f1)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V1__f2)
=> ( ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> happ(V1__f2,V4__x) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2ediv__fct___24a2(V0__f1,V1__f2)) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_minus',axiom,
! [V0__f1] :
( c_24__type__1601___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__1601___24t(V1__f2)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f1)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V1__f2)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2eminus__fct___24a2(V0__f1,V1__f2)) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_opp',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V0__f)
=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRanalysis1_2eopp__fct___24a1(V0__f)) ) ) ).
fof('Coq.Reals.Ranalysis1.continuity_pt_mult',axiom,
! [V0__f1] :
( c_24__type__1601___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__1601___24t(V1__f2)
=> ! [V2__x0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x0)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V0__f1,V2__x0)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V1__f2,V2__x0)
=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(V0__f1,V1__f2),V2__x0) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.deriv_constant2',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V3__c,V4__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V3__c))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V3__c,V2__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V2__b))
=> happ(V0__f,V7__x) = happ(V0__f,V3__c) ) ) )
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V3__c,V4__pr) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.deriv_maximum',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V3__c,V4__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V3__c))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V3__c,V2__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V2__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V7__x),happ(V0__f,V3__c))) ) ) )
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V3__c,V4__pr) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.deriv_minimum',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ! [V4__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V3__c,V4__pr)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V3__c))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V3__c,V2__b))
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__a,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V2__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V3__c),happ(V0__f,V7__x))) ) ) )
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V3__c,V4__pr) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_continuous',axiom,
! [V0__f] :
( c_24__type__1601___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__1601___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_derive',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__pr] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,V1__x,V2__pr)
=> ? [V3__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l)
& cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,V1__x,V2__pr) = V3__l ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derivable_pt_lim_const',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(V0__a),V1__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
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.derivable_pt_lim_mult',axiom,
! [V0__f1] :
( c_24__type__1601___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__1601___24t(V1__f2)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__l2)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f1,V2__x,V3__l1)
=> ( cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V1__f2,V2__x,V4__l2)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(V0__f1,V1__f2),V2__x,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V3__l1,happ(V1__f2,V2__x)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__f1,V2__x),V4__l2))) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_const',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(cCoq_2eReals_2eRanalysis1_2efct__cte___24a1(V0__a),V1__x,cCoq_2eReals_2eRanalysis1_2ederivable__pt__const___24a2(V0__a,V1__x)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_eq',axiom,
! [V0__f] :
( c_24__type__1601___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_2ederive__pt___24a3(V0__f,V1__x,V3__pr) = V2__l
<=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_eq_0',axiom,
! [V0__f] :
( c_24__type__1601___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.derive_pt_eq_1',axiom,
! [V0__f] :
( c_24__type__1601___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_2ederive__pt___24a3(V0__f,V1__x,V3__pr) = V2__l
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V0__f,V1__x,V2__l) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_id',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(cCoq_2eReals_2eRanalysis1_2eid,V0__x,cCoq_2eReals_2eRanalysis1_2ederivable__pt__id___24a1(V0__x)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_mult',axiom,
! [V0__f1] :
( c_24__type__1601___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__1601___24t(V1__f2)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f1,V2__x,V3__pr1)
=> ! [V4__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__f2,V2__x,V4__pr2)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(V0__f1,V1__f2),V2__x,cCoq_2eReals_2eRanalysis1_2ederivable__pt__mult___24a5(V0__f1,V1__f2,V2__x,V3__pr1,V4__pr2)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f1,V2__x,V3__pr1),happ(V1__f2,V2__x)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__f1,V2__x),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__f2,V2__x,V4__pr2))) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.derive_pt_plus',axiom,
! [V0__f1] :
( c_24__type__1601___24t(V0__f1)
=> ! [V1__f2] :
( c_24__type__1601___24t(V1__f2)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__pr1] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f1,V2__x,V3__pr1)
=> ! [V4__pr2] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__f2,V2__x,V4__pr2)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(cCoq_2eReals_2eRanalysis1_2eplus__fct___24a2(V0__f1,V1__f2),V2__x,cCoq_2eReals_2eRanalysis1_2ederivable__pt__plus___24a5(V0__f1,V1__f2,V2__x,V3__pr1,V4__pr2)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f1,V2__x,V3__pr1),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__f2,V2__x,V4__pr2)) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis1.pr_nu',axiom,
! [V0__f] :
( c_24__type__1601___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.Ranalysis2.quadruple_var',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> V0__x = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ) ).
fof('Coq.Reals.Ranalysis4.Rabs_derive_1',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_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRbasic__fun_2eRabs,V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ).
fof('Coq.Reals.Ranalysis5.derivable_pt_lim_recip_interv',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___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__Prf] :
( c_24__type__98690___24t(V0__f,V1__g,V2__lb,V3__ub,V5__Prf)
=> ( cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V1__g,V4__x)
=> ( 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)) )
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V2__lb),happ(V1__g,V4__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V4__x),happ(V1__g,V3__ub))) )
=> ( ! [V10__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V10__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V10__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V10__x,V3__ub)) )
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V10__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V10__x) ) )
=> ( cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,happ(V1__g,V4__x),happ(V5__Prf,happ(V1__g,V4__x))) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(V1__g,V4__x,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,happ(V1__g,V4__x),happ(V5__Prf,happ(V1__g,V4__x))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.derive_pt_recip_interv',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V2__lb),V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,happ(V0__f,V3__ub))) )
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ! [V8__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V8__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V7__x),happ(V0__f,V8__y))) ) ) ) ) )
=> ( ! [V8__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V8__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V8__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V8__x),V3__ub)) ) ) ) )
=> ! [V9__Prf] :
( c_24__type__71884___24t(V0__f,V2__lb,V3__ub,V9__Prf)
=> ( ! [V10__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V10__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V10__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V10__x,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V10__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V10__x) ) ) )
=> ( cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,happ(V1__g,V4__x),cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv__prelim1___24a6(V0__f,V1__g,V2__lb,V3__ub,V4__x,V9__Prf)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V4__x,cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv___24a6(V0__f,V1__g,V2__lb,V3__ub,V4__x,V9__Prf)) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,happ(V1__g,V4__x),happ(happ(V9__Prf,happ(V1__g,V4__x)),cCoq_2eReals_2eRanalysis5_2ederive__pt__recip__interv__prelim1__1___24a5(V0__f,V1__g,V2__lb,V3__ub,V4__x)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.derive_pt_recip_interv_prelim0',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___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__Prf] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V0__f,happ(V1__g,V4__x),V5__Prf)
=> ! [V6__Prg] :
( cCoq_2eReals_2eRanalysis1_2ederivable__pt___24t(V1__g,V4__x,V6__Prg)
=> ( 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__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__x)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V9__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V9__x,V3__ub)) )
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V9__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V9__x) ) )
=> ( cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,happ(V1__g,V4__x),V5__Prf) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V1__g,V4__x,V6__Prg) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V0__f,happ(V1__g,V4__x),V5__Prf)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.derive_pt_recip_interv_prelim1_0',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V2__lb),V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,happ(V0__f,V3__ub))) )
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ! [V8__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V8__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V7__x),happ(V0__f,V8__y))) ) ) ) ) )
=> ( ! [V8__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V8__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V8__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V8__x),V3__ub)) ) ) ) )
=> ( ! [V9__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V9__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V9__x,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V9__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V9__x) ) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,happ(V1__g,V4__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V1__g,V4__x),V3__ub)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.derive_pt_recip_interv_prelim1_1',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V3__ub))
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V2__lb),V4__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__x,happ(V0__f,V3__ub))) )
=> ( ! [V7__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__x)
=> ! [V8__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,V7__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V7__x,V8__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__y,V3__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(V0__f,V7__x),happ(V0__f,V8__y))) ) ) ) ) )
=> ( ! [V8__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V8__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V8__x,happ(V0__f,V3__ub)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V8__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V8__x),V3__ub)) ) ) ) )
=> ( ! [V9__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__f,V2__lb),V9__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V9__x,happ(V0__f,V3__ub)))
=> cCoq_2eReals_2eRanalysis1_2ecomp___24a3(V0__f,V1__g,V9__x) = cCoq_2eReals_2eRanalysis1_2eid___24a1(V9__x) ) ) )
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__lb,happ(V1__g,V4__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__g,V4__x),V3__ub)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Ranalysis5.pr_nu_var2_interv',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___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.Ranalysis5.ub_lt_2_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__ub] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__ub)
=> ! [V2__lb] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__lb)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__lb,V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__ub))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__ub,V2__lb),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ) ) ) ) ) ).
fof('Coq.Reals.Ratan.Alt_PI_tg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eAltSeries_2ePI__tg___24a1(V0__n) = cCoq_2eReals_2eRatan_2eRatan__seq___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n) ) ).
fof('Coq.Reals.Ratan.Boule_half_to_interval',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2ePSeries__reg_2eBoule___24a3(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRatan_2epos__half,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)))) ) ) ) ).
fof('Coq.Reals.Ratan.Datan_seq_CV_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_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___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_2eDatan__seq___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('Coq.Reals.Ratan.PI2_1',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___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)))))) ).
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__3682___24t(V0__un)
=> ! [V1__vn] :
( c_24__type__3682___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.atan_1',axiom,
cCoq_2eReals_2eRatan_2eatan___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___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_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('Coq.Reals.Ratan.atan_bound',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( 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)))),cCoq_2eReals_2eRatan_2eatan___24a1(V0__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRatan_2eatan___24a1(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)))))) ) ) ).
fof('Coq.Reals.Ratan.atan_eq_ps_atan',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_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> cCoq_2eReals_2eRatan_2eatan___24a1(V0__x) = cCoq_2eReals_2eRatan_2eps__atan___24a1(V0__x) ) ) ).
fof('Coq.Reals.Ratan.atan_right_inv',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo1_2etan___24a1(cCoq_2eReals_2eRatan_2eatan___24a1(V0__x)) = V0__x ) ).
fof('Coq.Reals.Ratan.plus_Rsqr_gt_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ).
fof('Coq.Reals.Ratan.pos_half_prf',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ).
fof('Coq.Reals.Ratan.pos_opp_lt',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_2eRopp___24a1(V0__x),V0__x)) ) ) ).
fof('Coq.Reals.Ratan.pow2_abs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ) ).
fof('Coq.Reals.Ratan.pow2_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),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))) ) ).
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_atan0_0',axiom,
cCoq_2eReals_2eRatan_2eps__atan___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
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__20388___24a1(V0__N),V1__x) ) ) ) ) ).
fof('Coq.Reals.Ratan.sum_Ratan_seq_opp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x))),V1__n) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(cCoq_2eReals_2eAltSeries_2etg__alt___24a1(cCoq_2eReals_2eRatan_2eRatan__seq___24a1(V0__x)),V1__n)) ) ) ).
fof('Coq.Reals.Ratan.tan_1_gt_1',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRtrigo1_2etan___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.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_asym',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(V1__r2,V0__r1)) ) ) ) ).
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_R1',axiom,
cCoq_2eReals_2eRbasic__fun_2eRabs___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.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_def1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__a),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),V1__a)) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_def2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),V1__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__a))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__a),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.Rmax_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(V0__x,cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y))) ) ) ).
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_pos',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_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y))) ) ) ) ) ).
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.Rderiv.Dx',axiom,
! [V0__D] :
( c_24__type__23___24t(V0__D)
=> ! [V1__x0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x0)
=> cCoq_2eReals_2eRderiv_2eD__in___24a4(c_24__lam__72010,c_24__lam__72011,V0__D,V1__x0) ) ) ).
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.RPow_abs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),V1__n) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n)) ) ) ).
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.R_dist_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y),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))
=> ( p(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.poly',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(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_2eRaxioms_2eINR___24a1(V0__n),V1__x)),cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__x),V0__n))) ) ) ) ).
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_1_even',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_1_odd',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_O',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_R1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eReals_2eRpow__def_2epow___24a2(V0__r,V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))
=> ( cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))
| V1__n = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
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_maj_Rabs',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_2eRbasic__fun_2eRabs___24a1(V1__y),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V2__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n))) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_mult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n1)
=> ! [V2__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n2)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2emul___24a2(V1__n1,V2__n2)) = cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n1),V2__n2) ) ) ) ).
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.Rfunctions.powerRZ_O',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_R1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___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.tech_pow_Rmult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n)) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)) ) ) ).
fof('Coq.Reals.RiemannInt.RiemannInt_P9',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__a)
=> ! [V2__pr] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V0__f,V1__a,V1__a,V2__pr)
=> cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V0__f,V1__a,V1__a,V2__pr) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RiemannInt.RinvN_pos',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(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.Rlimit.dist_pos',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ! [V1__x] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V2__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRlimit_2edist___24a3(V0__m,V1__x,V2__y),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.Rlimit.dist_refl',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ! [V1__x] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V2__y)
=> ( cCoq_2eReals_2eRlimit_2edist___24a3(V0__m,V1__x,V2__y) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> V1__x = V2__y ) ) ) ) ).
fof('Coq.Reals.Rlimit.dist_sym',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ! [V1__x] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V2__y)
=> cCoq_2eReals_2eRlimit_2edist___24a3(V0__m,V1__x,V2__y) = cCoq_2eReals_2eRlimit_2edist___24a3(V0__m,V2__y,V1__x) ) ) ) ).
fof('Coq.Reals.Rlimit.dist_tri',axiom,
! [V0__m] :
( cCoq_2eReals_2eRlimit_2eMetric__Space___24t(V0__m)
=> ! [V1__x] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V2__y)
=> ! [V3__z] :
( cCoq_2eReals_2eRlimit_2eBase___24t(V0__m,V3__z)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRlimit_2edist___24a3(V0__m,V1__x,V2__y),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRlimit_2edist___24a3(V0__m,V1__x,V3__z),cCoq_2eReals_2eRlimit_2edist___24a3(V0__m,V3__z,V2__y)))) ) ) ) ) ).
fof('Coq.Reals.Rlimit.eps2',axiom,
! [V0__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__eps)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__eps,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__eps,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) = V0__eps ) ).
fof('Coq.Reals.Rlimit.eps2_Rgt_R0',axiom,
! [V0__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__eps,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(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.Rlimit.limit_inv',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__D] :
( c_24__type__23___24t(V1__D)
=> ! [V2__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l)
=> ! [V3__x0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__x0)
=> ( cCoq_2eReals_2eRlimit_2elimit1__in___24a4(V0__f,V1__D,V2__l,V3__x0)
=> ( V2__l != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRlimit_2elimit1__in___24a4(c_24__lam__34462___24a1(V0__f),V1__D,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V2__l),V3__x0) ) ) ) ) ) ) ).
fof('Coq.Reals.Rlimit.mul_factor_gt_f',axiom,
! [V0__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__eps)
=> ! [V1__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l)
=> ! [V2__l_27] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l_27)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__eps,cCoq_2eReals_2eRlimit_2emul__factor___24a2(V1__l,V2__l_27))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ).
fof('Coq.Reals.Rlimit.mul_factor_wd',axiom,
! [V0__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__l)
=> ! [V1__l_27] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l_27)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__l),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__l_27))) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rlimit.prop_eps',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( ! [V1__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V1__eps)) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.Reals.Rpower.D_in_ext',axiom,
! [V0__f] :
( c_24__type__1601___24t(V0__f)
=> ! [V1__g] :
( c_24__type__1601___24t(V1__g)
=> ! [V2__h] :
( c_24__type__1601___24t(V2__h)
=> ! [V3__D] :
( c_24__type__23___24t(V3__D)
=> ! [V4__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__x)
=> ( happ(V0__f,V4__x) = happ(V1__g,V4__x)
=> ( cCoq_2eReals_2eRderiv_2eD__in___24a4(V2__h,V0__f,V3__D,V4__x)
=> cCoq_2eReals_2eRderiv_2eD__in___24a4(V2__h,V1__g,V3__D,V4__x) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rpower.Dpower',axiom,
! [V0__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__y)
=> ! [V1__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__y))
=> cCoq_2eReals_2eRderiv_2eD__in___24a4(c_24__lam__74805___24a1(V1__z),c_24__lam__74807___24a1(V1__z),c_24__lam__74801,V0__y) ) ) ) ).
fof('Coq.Reals.Rpower.Rpower_1',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_2eRpower_2eRpower___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = V0__x ) ) ).
fof('Coq.Reals.Rpower.Rpower_O',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_2eRpower_2eRpower___24a2(V0__x,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.Rpower.Rpower_Ropp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRpower_2eRpower___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__y)) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpower_2eRpower___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.Reals.Rpower.Rpower_plus',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> cCoq_2eReals_2eRpower_2eRpower___24a2(V2__z,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpower_2eRpower___24a2(V2__z,V0__x),cCoq_2eReals_2eRpower_2eRpower___24a2(V2__z,V1__y)) ) ) ) ).
fof('Coq.Reals.Rpower.exp_increasing',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_2eRlt___24a2(cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V1__y))) ) ) ) ).
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.exp_le_3',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2eexp___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_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('Coq.Reals.Rpower.exp_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_2eRtrigo__def_2eexp___24a1(cCoq_2eReals_2eRpower_2eln___24a1(V0__x)) = 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.Rpower.ln_exp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRpower_2eln___24a1(cCoq_2eReals_2eRtrigo__def_2eexp___24a1(V0__x)) = V0__x ) ).
fof('Coq.Reals.Rpower.ln_inv',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_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( cCoq_2eReals_2eRpower_2eln___24a1(V0__x) = cCoq_2eReals_2eRpower_2eln___24a1(V1__y)
=> V0__x = V1__y ) ) ) ) ) ).
fof('Coq.Reals.Rprod.INR_fact_lt_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)))) ) ).
fof('Coq.Reals.Rprod.fact_prodSO',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)) = cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(c_24__lam__98744,V0__n) ) ).
fof('Coq.Reals.Rprod.prod_SO_pos',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__N)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V1__N))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__An,V2__n))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V0__An,V1__N))) ) ) ) ).
fof('Coq.Reals.Rseries.Un_cv_crit_lub',axiom,
! [V0__Un] :
( c_24__type__3682___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.Rseries.growing_prop',axiom,
! [V0__Un] :
( c_24__type__3682___24t(V0__Un)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
=> ( p(cCoq_2eInit_2ePeano_2ege___24a2(V1__n,V2__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(V0__Un,V1__n),happ(V0__Un,V2__m))) ) ) ) ) ) ).
fof('Coq.Reals.Rsqrt_def.Rsqrt_positivity',axiom,
! [V0__x] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRsqrt__def_2eRsqrt___24a1(V0__x))) ) ).
fof('Coq.Reals.Rsqrt_def.pow_2_n_infty',axiom,
cCoq_2eReals_2eSeqProp_2ecv__infty___24a1(cCoq_2eReals_2eRsqrt__def_2epow__2__n) ).
fof('Coq.Reals.Rsqrt_def.pow_2_n_neq_R0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRsqrt__def_2epow__2__n___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rtrigo1.COS_bound',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
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.PI2_Rlt_PI',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(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_2ePI)) ).
fof('Coq.Reals.Rtrigo1.PI4_RLT_PI2',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(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_2exO___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)))))) ).
fof('Coq.Reals.Rtrigo1.PI_4',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo1_2ePI,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___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.SIN_bound',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('Coq.Reals.Rtrigo1._PI2_RLT_0',axiom,
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))))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ).
fof('Coq.Reals.Rtrigo1.continuity_cos',axiom,
cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(cCoq_2eReals_2eRtrigo__def_2ecos) ).
fof('Coq.Reals.Rtrigo1.cos2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x))) ) ).
fof('Coq.Reals.Rtrigo1.cos_2PI',axiom,
cCoq_2eReals_2eRtrigo__def_2ecos___24a1(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_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.Rtrigo1.cos_2a_sin',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(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__x)) = cCoq_2eReals_2eRdefinitions_2eRminus___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(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x)),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x))) ) ).
fof('Coq.Reals.Rtrigo1.cos_3PI2',axiom,
cCoq_2eReals_2eRtrigo__def_2ecos___24a1(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_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo1.cos_PI',axiom,
cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRtrigo1_2ePI) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
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_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ? [V2__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__k)
& V0__x = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V2__k),cCoq_2eReals_2eRtrigo1_2ePI),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.cos_eq_0_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_2ecos___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( 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))))) ) ) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_ge_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___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_2eRle___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_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x))) ) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_ge_0_3PI2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(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))))),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)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x))) ) ) ) ).
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_le_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(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_2eRle___24a2(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)))))))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
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.cos_period',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(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_2eRaxioms_2eINR___24a1(V1__k)),cCoq_2eReals_2eRtrigo1_2ePI))) = cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) ) ) ).
fof('Coq.Reals.Rtrigo1.cos_pi2',axiom,
cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRtrigo1_2ePI2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo1.cos_shift',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(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_2eRtrigo__def_2esin___24a1(V0__x) ) ).
fof('Coq.Reals.Rtrigo1.cos_sin',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x) = cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(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)) ) ).
fof('Coq.Reals.Rtrigo1.neg_cos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x)) ) ).
fof('Coq.Reals.Rtrigo1.neg_sin',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,cCoq_2eReals_2eRtrigo1_2ePI)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x)) ) ).
fof('Coq.Reals.Rtrigo1.pi2_int',axiom,
( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),cCoq_2eReals_2eRtrigo1_2ePI2))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo1_2ePI2,cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) ) ).
fof('Coq.Reals.Rtrigo1.sin2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x))) ) ).
fof('Coq.Reals.Rtrigo1.sin2_cos2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x)),cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rtrigo1.sin_2PI',axiom,
cCoq_2eReals_2eRtrigo__def_2esin___24a1(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_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo1.sin_2a',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(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__x)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(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_2eRtrigo__def_2esin___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_PI2',axiom,
cCoq_2eReals_2eRtrigo__def_2esin___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_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.Rtrigo1.sin_eq_0_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ? [V2__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__k)
& V0__x = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V2__k),cCoq_2eReals_2eRtrigo1_2ePI) ) ) ) ).
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_gt_cos_7_8',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))))) ).
fof('Coq.Reals.Rtrigo1.sin_le_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo1_2ePI,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)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x)) ) ).
fof('Coq.Reals.Rtrigo1.sin_period',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(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_2eRaxioms_2eINR___24a1(V1__k)),cCoq_2eReals_2eRtrigo1_2ePI))) = cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_plus',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2esin___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V1__y)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__x),cCoq_2eReals_2eRtrigo__def_2esin___24a1(V1__y))) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_pos_tech',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_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_2esin___24a1(V0__x))) ) ) ).
fof('Coq.Reals.Rtrigo1.sin_shift',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRtrigo__def_2esin___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(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_2eRtrigo__def_2ecos___24a1(V0__x) ) ).
fof('Coq.Reals.Rtrigo1.tan_0',axiom,
cCoq_2eReals_2eRtrigo1_2etan___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo_alt.pre_cos_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_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),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_2exH)))))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__alt_2ecos__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_2ecos___24a1(V0__a)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRtrigo__def_2ecos___24a1(V0__a),cCoq_2eReals_2eRtrigo__alt_2ecos__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_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.PI4_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_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) ).
fof('Coq.Reals.Rtrigo_calc.PI6_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_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) ).
fof('Coq.Reals.Rtrigo_calc.R1_sqrt2_neq_0',axiom,
cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(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.Rtrigo_calc.Rlt_sqrt2_0',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ).
fof('Coq.Reals.Rtrigo_calc.Rlt_sqrt3_0',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) ).
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_calc.sqrt2_neq_0',axiom,
cCoq_2eReals_2eR__sqrt_2esqrt___24a1(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.Rtrigo_calc.sqrt3_2_neq_0',axiom,
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_2eR__sqrt_2esqrt___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo_calc.tan_2PI',axiom,
cCoq_2eReals_2eRtrigo1_2etan___24a1(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_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rtrigo_def.cos_0',axiom,
cCoq_2eReals_2eRtrigo__def_2ecos___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.cosh_0',axiom,
cCoq_2eReals_2eRtrigo__def_2ecosh___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.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.Rtrigo_reg.derivable_pt_lim_sin_0',axiom,
cCoq_2eReals_2eRanalysis1_2ederivable__pt__lim___24a3(cCoq_2eReals_2eRtrigo__def_2esin,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.SeqProp.CV_mult',axiom,
! [V0__An] :
( c_24__type__3682___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__3682___24t(V1__Bn)
=> ! [V2__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__l2)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__An,V2__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V1__Bn,V3__l2)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__75083___24a2(V0__An,V1__Bn),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__l1,V3__l2)) ) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.UL_sequence',axiom,
! [V0__Un] :
( c_24__type__3682___24t(V0__Un)
=> ! [V1__l1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__l2)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l1)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V2__l2)
=> V1__l1 = V2__l2 ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.cv_infty_cv_R0',axiom,
! [V0__Un] :
( c_24__type__3682___24t(V0__Un)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> happ(V0__Un,V1__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> ( cCoq_2eReals_2eSeqProp_2ecv__infty___24a1(V0__Un)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__98796___24a1(V0__Un),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('Coq.Reals.SeqProp.cv_speed_pow_fact',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__98365___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ) ).
fof('Coq.Reals.SeqProp.decreasing_ineq',axiom,
! [V0__Un] :
( c_24__type__3682___24t(V0__Un)
=> ! [V1__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l)
=> ( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V0__Un)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__l,happ(V0__Un,V4__n))) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.growing_ineq',axiom,
! [V0__Un] :
( c_24__type__3682___24t(V0__Un)
=> ! [V1__l] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__l)
=> ( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
=> ( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V4__n),V1__l)) ) ) ) ) ) ).
fof('Coq.Reals.SeqProp.tech13',axiom,
! [V0__An] :
( c_24__type__3682___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__98792___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)
=> ( p(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.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.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__234___24a2(V0__n,V1__m)) ) ) ).
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.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_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.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.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_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.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_2430477___24a2(V0__p,V1__q) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.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.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_sub',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___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.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)
=> ( p(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)
=> ( p(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)
=> ( p(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)
=> ( p(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.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.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.EnvRing.Pol_ind',axiom,
! [V0__C] :
( cType___24t(V0__C)
=> ! [V1__P] :
( c_24__type__34148___24t(V0__C,V1__P)
=> ( ! [V2__c] :
( t(V2__c,V0__C)
=> p(happ(V1__P,cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,V2__c))) )
=> ( ! [V3__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ! [V4__p] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V4__p)
=> ( p(happ(V1__P,V4__p))
=> p(happ(V1__P,cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,V3__p,V4__p))) ) ) )
=> ( ! [V4__p] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V4__p)
=> ( p(happ(V1__P,V4__p))
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__p] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V7__p)
=> ( p(happ(V1__P,V7__p))
=> p(happ(V1__P,cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,V4__p,V6__p,V7__p))) ) ) ) ) )
=> ! [V5__p] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V5__p)
=> p(happ(V1__P,V5__p)) ) ) ) ) ) ) ).
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.Fourier_util.Rlt_zero_pos_plus1',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_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.Q2R_0',axiom,
cCoq_2eQArith_2eQreals_2eQ2R___24a1(cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.micromega.RMicromega.Q2R_1',axiom,
cCoq_2eQArith_2eQreals_2eQ2R___24a1(cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
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.micromega.RMicromega.Rinv_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) = V0__x ) ).
fof('Coq.omega.OmegaLemmas.OMEGA1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA17',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.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__99___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__99___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__99___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__99___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__99___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__99___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__99___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k))))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zmult_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__99___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zmult_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__99___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zmult_plus_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__99___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__99___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__99___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__99___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__99___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__99___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__99___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__99___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__99___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__99___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__99___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__99___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__99___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__99___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__882___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__882___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__882___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__891___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__882___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__891___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1200___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Ztriv_div_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__1200___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> ! [V3__zphi] :
( c_24__type__18961___24t(V0__R,V3__zphi)
=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V1__req,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V3__zphi,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.gen_phiZ_morph',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__882___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__882___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__882___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__891___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1200___24t(V0__R,V7__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___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_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,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_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V6__ropp)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.get_signZ_th',axiom,
cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
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__20439___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__20439___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.RTheory',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(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)) ).
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.RealField.Rfield',axiom,
cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(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,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR)) ).
fof('Coq.setoid_ring.RealField.Rgen_phiPOS',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ).
fof('Coq.setoid_ring.RealField.Rgen_phiPOS_not_0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,V0__x) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.setoid_ring.RealField.Rlt_0_2',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.setoid_ring.RealField.Rlt_n_Sn',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__882___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__882___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__891___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__882___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__882___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__882___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__891___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1200___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_rt',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__882___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__882___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__882___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__891___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1200___24t(V0__R,V7__req)
=> ( ! [V8__x] :
( t(V8__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
=> ( ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
=> ( ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
=> ( ! [V12__x] :
( t(V12__x,V0__R)
=> ! [V13__y] :
( t(V13__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V12__x),V13__y)),happ(happ(V4__rmul,V13__y),V12__x))) ) )
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ! [V15__z] :
( t(V15__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),happ(happ(V4__rmul,V14__y),V15__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V13__x),V14__y)),V15__z))) ) ) )
=> ( ! [V14__x] :
( t(V14__x,V0__R)
=> ! [V15__y] :
( t(V15__y,V0__R)
=> ! [V16__z] :
( t(V16__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V14__x),V15__y)),V16__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V14__x),V16__z)),happ(happ(V4__rmul,V15__y),V16__z)))) ) ) )
=> ( ! [V15__x] :
( t(V15__x,V0__R)
=> ! [V16__y] :
( t(V16__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V15__x),V16__y)),happ(happ(V3__radd,V15__x),happ(V6__ropp,V16__y)))) ) )
=> ( ! [V16__x] :
( t(V16__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V16__x),happ(V6__ropp,V16__x))),V1__rO)) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mkmorph',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__882___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__882___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__882___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__891___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1200___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__16900___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__16900___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__16900___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__16914___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__16921___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__899___24t(V0__R,V8__C,V16__phi)
=> ( p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO))
=> ( p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI))
=> ( ! [V19__x] :
( t(V19__x,V8__C)
=> ! [V20__y] :
( t(V20__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V19__x),V20__y))),happ(happ(V3__radd,happ(V16__phi,V19__x)),happ(V16__phi,V20__y)))) ) )
=> ( ! [V20__x] :
( t(V20__x,V8__C)
=> ! [V21__y] :
( t(V21__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V13__csub,V20__x),V21__y))),happ(happ(V5__rsub,happ(V16__phi,V20__x)),happ(V16__phi,V21__y)))) ) )
=> ( ! [V21__x] :
( t(V21__x,V8__C)
=> ! [V22__y] :
( t(V22__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V21__x),V22__y))),happ(happ(V4__rmul,happ(V16__phi,V21__x)),happ(V16__phi,V22__y)))) ) )
=> ( ! [V22__x] :
( t(V22__x,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V22__x))),happ(V6__ropp,happ(V16__phi,V22__x)))) )
=> ( ! [V23__x] :
( t(V23__x,V8__C)
=> ! [V24__y] :
( t(V24__y,V8__C)
=> ( happ(happ(V15__ceqb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,happ(V16__phi,V23__x)),happ(V16__phi,V24__y))) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Fermat4.ArithCompl.Rdiv_ge_0',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__a,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__b,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__a,V1__b),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ).
fof('Fermat4.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('Fermat4.ArithCompl.frac_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
=> cFermat4_2eArithCompl_2efrac___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__b)) = cFermat4_2eArithCompl_2efrac___24a2(V0__a,V1__b) ) ) ) ).
fof('Fermat4.ArithCompl.frac_rat',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_2eReals_2eRdefinitions_2eRge___24a2(cFermat4_2eArithCompl_2efrac___24a2(V0__a,V1__b),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cFermat4_2eArithCompl_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)) ) ) ) ) ) ) ) ).
fof('Fermat4.ArithCompl.frac_simp',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V2__c != cCoq_2eNumbers_2eBinNums_2eZ0
=> cFermat4_2eArithCompl_2efrac___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V0__a),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c,V1__b)) = cFermat4_2eArithCompl_2efrac___24a2(V0__a,V1__b) ) ) ) ) ) ).
fof('Fermat4.ArithCompl.gcd_rel_prime',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_2eZnumtheory_2eZis__gcd___24a3(V0__x,V1__y,V2__d)
=> ? [V4__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__a)
& ? [V5__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__b)
& V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__d,V4__a)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__d,V5__b)
& p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V4__a,V5__b)) ) ) ) ) ) ) ).
fof('Fermat4.ArithCompl.not_IZR_0',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__a) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__a != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Fermat4.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('Fermat4.ArithCompl.rel_prime_opp',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))
=> p(cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))) ) ) ) ).
fof('Fermat4.ArithCompl.relp_rat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cFermat4_2eArithCompl_2eis__rat___24a1(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> ? [V4__pq] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,V4__pq)
& c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432___24a2(V0__r,V4__pq) ) ) ) ) ) ).
fof('Fermat4.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('Fermat4.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('Pythagorean.interCDr_sol',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> ( cPythagorean_2einterCDr___24a3(V0__r,V1__x,V2__y)
=> ( cPythagorean_2eeqp___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V1__x,V2__y),cPythagorean_2ep1)
| cPythagorean_2eeqp___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V1__x,V2__y),cPythagorean_2ep2___24a1(V0__r)) ) ) ) ) ) ).
fof('Pythagorean.rat_coo2',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( cPythagorean_2ein__ucirc___24a2(V0__x,V1__y)
& cFermat4_2eArithCompl_2eis__ratp___24a1(cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__x,V1__y)) )
=> ? [V3__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r)
& cFermat4_2eArithCompl_2eis__rat___24a1(V3__r)
& cPythagorean_2einterCDr___24a3(V3__r,V0__x,V1__y) ) ) ) ) ).
fof('$adef_$_prop_20418_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__20418,V_24X1),V_24X2) = c_24__prop__20418___24a2(V_24X1,V_24X2) ).
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('$adef_$_let_1_den_35032_$a1',axiom,
! [V_24X1] : happ(c_24__let__1__den__35032,V_24X1) = c_24__let__1__den__35032___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis5.derivable_pt_recip_interv_prelim1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv__prelim1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv__prelim1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.Ranalysis1.constant_D_eq_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2econstant__D__eq,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRanalysis1_2econstant__D__eq___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_48908_$a1',axiom,
! [V_24X1] : happ(c_24__prop__48908,V_24X1) = c_24__prop__48908___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsqrt_def.dicho_up_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2edicho__up,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2edicho__up___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_16_mkpow_33075_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__33075,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__33075___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_31510_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31510,V_24X1),V_24X2),V_24X3) = c_24__lam__31510___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_$_let_var_8_up_74878_74894_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__8__up__74878__74894,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__8__up__74878__74894___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_let_var_var_15_s2_1255_1259_1317_$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__1255__1259__1317,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__1255__1259__1317___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_31516_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31516,V_24X1),V_24X2),V_24X3) = c_24__lam__31516___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_lam_77220_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__77220,V_24X1),V_24X2))
<=> c_24__lam__77220___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Ratan.ps_atan_exists_1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eps__atan__exists__1,V_24X1) = cCoq_2eReals_2eRatan_2eps__atan__exists__1___24a1(V_24X1) ).
fof('$adef_$_prop_25805_$a1',axiom,
! [V_24X1] : happ(c_24__prop__25805,V_24X1) = c_24__prop__25805___24a1(V_24X1) ).
fof('$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_$_prop_98319_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98319,V_24X1) = c_24__prop__98319___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2emkposreal___24a2(V_24X1,V_24X2) ).
fof('$adef_Pythagorean.cond_pqb_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cPythagorean_2econd__pqb,V_24X1),V_24X2))
<=> cPythagorean_2econd__pqb___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rsqrt_def.dicho_lb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2edicho__lb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2edicho__lb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_71916_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__71916,V_24X1),V_24X2))
<=> c_24__lam__71916___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_34462_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34462,V_24X1),V_24X2) = c_24__lam__34462___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.plus_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2eplus__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2eplus__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_12_x_1226_1229_1299_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__1226__1229__1299,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__1226__1229__1299___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_let_var_9_z_74879_74895_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__9__z__74879__74895,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__9__z__74879__74895___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_31510_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__31510,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__31510___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_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.micromega.RingMicromega.map_Formula_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__Formula,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2emap__Formula___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2ederivable,V_24X1) = cCoq_2eReals_2eRanalysis1_2ederivable___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$74835_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474835,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474835___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$74902_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474902,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474902___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEc_$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_52086_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__52086,V_24X1),V_24X2) = c_24__lam__52086___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_31783_31786_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__31783__31786,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__31783__31786___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_var_v_CANONICAL_4_48951_48954_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__var__v__CANONICAL__4__48951__48954,V_24X1),V_24X2),V_24X3) = c_24__let__var__v__CANONICAL__4__48951__48954___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_$_let_18_mkmult_pow_33077_$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__33077,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__33077___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_var_var_12_x_1239_1242_1305_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__1239__1242__1305,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__1239__1242__1305___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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_$_let_var_var_14_s_1241_1244_1307_$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__1241__1244__1307,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__1241__1244__1307___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$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('$adef_Coq.micromega.RMicromega.CMult_$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('$adef_$_lam_71995_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__71995,V_24X1),V_24X2) = c_24__lam__71995___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20377_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__20377,V_24X1),V_24X2))
<=> c_24__lam__20377___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('$adef_Coq.Reals.Rsqrt_def.Rsqrt_exists_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRsqrt__def_2eRsqrt__exists,V_24X1),V_24X2) = cCoq_2eReals_2eRsqrt__def_2eRsqrt__exists___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('$adef_$_let_var_5_r\'_78069_78086_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__var__5__r_27__78069__78086,V_24X1),V_24X2) = c_24__let__var__5__r_27__78069__78086___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_$_lam_98354_$a1',axiom,
! [V_24X1] : happ(c_24__lam__98354,V_24X1) = c_24__lam__98354___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$74864_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474864,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2474864___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_72011_$a1',axiom,
! [V_24X1] : happ(c_24__lam__72011,V_24X1) = c_24__lam__72011___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_$_lam_25789_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__25789,V_24X1),V_24X2))
<=> c_24__lam__25789___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.ZMicromega.ceiling_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eceiling,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RList.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRList_2eIn,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRList_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Datatypes.app_$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('$adef_Coq.Reals.RIneq.Rle_dec_$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('$adef_$_let_var_var_13_y_1277_1281_1327_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__1277__1281__1327,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__1277__1281__1327___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.PArith.BinPosDef.Pos.gcdn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcdn,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcdn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_5_r\'_78062_78078_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__var__5__r_27__78062__78078,V_24X1),V_24X2) = c_24__let__var__5__r_27__78062__78078___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_12_x_1252_1256_1314_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__1252__1256__1314,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__1252__1256__1314___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_lam_71995_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__71995,V_24X1),V_24X2),V_24X3) = c_24__lam__71995___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('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$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('$adef_$_lam_25825_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__25825,V_24X1),V_24X2))
<=> c_24__lam__25825___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_31642_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31642,V_24X1) = c_24__lam__31642___24a1(V_24X1) ).
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_48955_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__48955,V_24X1),V_24X2) = c_24__prop__48955___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_25812_$a1',axiom,
! [V_24X1] : happ(c_24__lam__25812,V_24X1) = c_24__lam__25812___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_98744_$a1',axiom,
! [V_24X1] : happ(c_24__lam__98744,V_24X1) = c_24__lam__98744___24a1(V_24X1) ).
fof('$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_$_lam_20310_$a1',axiom,
! [V_24X1] : happ(c_24__lam__20310,V_24X1) = c_24__lam__20310___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.derive_pt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederive__pt,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2ederive__pt___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.fct_cte_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2efct__cte,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
fof('$adef_$_lam_52105_$a1',axiom,
! [V_24X1] : happ(c_24__lam__52105,V_24X1) = c_24__lam__52105___24a1(V_24X1) ).
fof('$adef_$_prop_234_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__234,V_24X1),V_24X2) = c_24__prop__234___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.nonneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonneg,V_24X1) = cCoq_2eReals_2eRIneq_2enonneg___24a1(V_24X1) ).
fof('$adef_$_lam_2116_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__2116,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__2116___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Reals.RList.pos_Rl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2epos__Rl,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2epos__Rl___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_70508_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__70508,V_24X1),V_24X2) = c_24__lam__70508___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Raxioms.INR_$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('$adef_$_lam_76355_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76355,V_24X1),V_24X2),V_24X3) = c_24__lam__76355___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_77035_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__77035,V_24X1),V_24X2) = c_24__lam__77035___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_25804_$a1',axiom,
! [V_24X1] : happ(c_24__prop__25804,V_24X1) = c_24__prop__25804___24a1(V_24X1) ).
fof('$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_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_$_lam_98621_$a1',axiom,
! [V_24X1] : happ(c_24__lam__98621,V_24X1) = c_24__lam__98621___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('$adef_$_let_6_lmp_20439_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__20439,V_24X1) = c_24__let__6__lmp__20439___24a1(V_24X1) ).
fof('$adef_$_prop_20385_$a1',axiom,
! [V_24X1] : happ(c_24__prop__20385,V_24X1) = c_24__prop__20385___24a1(V_24X1) ).
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('$adef_Coq.Init.Datatypes.nat_rec_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2enat__rec___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_let_var_var_var_6_r\'_2674_2684_2686_2696_$a1',axiom,
! [V_24X1] : happ(c_24__let__var__var__var__6__r_27__2674__2684__2686__2696,V_24X1) = c_24__let__var__var__var__6__r_27__2674__2684__2686__2696___24a1(V_24X1) ).
fof('$adef_$_lam_98347_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__98347,V_24X1),V_24X2),V_24X3) = c_24__lam__98347___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_77220_$a1',axiom,
! [V_24X1] : happ(c_24__lam__77220,V_24X1) = c_24__lam__77220___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_$_lam_98623_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__98623,V_24X1),V_24X2) = c_24__lam__98623___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.SeqProp.cv_infty_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eSeqProp_2ecv__infty,V_24X1))
<=> cCoq_2eReals_2eSeqProp_2ecv__infty___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('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_$_lam_98792_$a1',axiom,
! [V_24X1] : happ(c_24__lam__98792,V_24X1) = c_24__lam__98792___24a1(V_24X1) ).
fof('$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_Fermat4.ArithCompl.is_rat_$a1',axiom,
! [V_24X1] :
( p(happ(cFermat4_2eArithCompl_2eis__rat,V_24X1))
<=> cFermat4_2eArithCompl_2eis__rat___24a1(V_24X1) ) ).
fof('$adef_$_prop_20142_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__20142,V_24X1),V_24X2) = c_24__prop__20142___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_13_y_1240_1243_1306_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__1240__1243__1306,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__1240__1243__1306___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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_Pythagorean.is_posp_$a1',axiom,
! [V_24X1] :
( p(happ(cPythagorean_2eis__posp,V_24X1))
<=> cPythagorean_2eis__posp___24a1(V_24X1) ) ).
fof('$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_$_let_11_subst_l_2044_$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__2044,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__2044___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEadd_$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('$adef_Coq.Reals.Rgeom.dist_euc_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRgeom_2edist__euc,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRgeom_2edist__euc___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_let_var_var_14_s1_1278_1282_1328_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__14__s1__1278__1282__1328,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s1__1278__1282__1328___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_48949_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__48949,V_24X1),V_24X2),V_24X3) = c_24__lam__48949___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_17_mkopp_pow_33076_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__33076,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__33076___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Reals.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_$_fix_74875_0_Dichotomy_lb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__fix__74875__0__Dichotomy__lb,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__fix__74875__0__Dichotomy__lb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rtrigo_alt.sin_term_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__alt_2esin__term,V_24X1) = cCoq_2eReals_2eRtrigo__alt_2esin__term___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.display_pow_linear_$a20',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20) = cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RMicromega.Reval_formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eReval__formula,V_24X1) = cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$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('$adef_$_fix_74808_1_Dichotomy_ub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__fix__74808__1__Dichotomy__ub,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__fix__74808__1__Dichotomy__ub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_20_lnum_37765_$a18',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__20__lnum__37765,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18) = c_24__let__20__lnum__37765___24a18(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18) ).
fof('$adef_$_lam_78171_$a1',axiom,
! [V_24X1] : happ(c_24__lam__78171,V_24X1) = c_24__lam__78171___24a1(V_24X1) ).
fof('$adef_$_fix_29863_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__29863__1__add__carry,V_24X1),V_24X2) = c_24__fix__29863__1__add__carry___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.Ratan.in_int_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2ein__int,V_24X1) = cCoq_2eReals_2eRatan_2ein__int___24a1(V_24X1) ).
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('$adef_Coq.Reals.Rpower.ln_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRpower_2eln,V_24X1) = cCoq_2eReals_2eRpower_2eln___24a1(V_24X1) ).
fof('$adef_$_prop_48959_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__48959,V_24X1),V_24X2) = c_24__prop__48959___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_77035_$a1',axiom,
! [V_24X1] : happ(c_24__lam__77035,V_24X1) = c_24__lam__77035___24a1(V_24X1) ).
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('$adef_$_lam_67809_$a1',axiom,
! [V_24X1] : happ(c_24__lam__67809,V_24X1) = c_24__lam__67809___24a1(V_24X1) ).
fof('$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_Pythagorean.p2_$a1',axiom,
! [V_24X1] : happ(cPythagorean_2ep2,V_24X1) = cPythagorean_2ep2___24a1(V_24X1) ).
fof('$adef_$_prop_48952_$a1',axiom,
! [V_24X1] : happ(c_24__prop__48952,V_24X1) = c_24__prop__48952___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('$adef_$_lam_75083_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__75083,V_24X1),V_24X2) = c_24__lam__75083___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_48904_$a1',axiom,
! [V_24X1] : happ(c_24__lam__48904,V_24X1) = c_24__lam__48904___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('$adef_Coq.Reals.Rtrigo_def.cosh_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2ecosh,V_24X1) = cCoq_2eReals_2eRtrigo__def_2ecosh___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('$adef_$_prop_30585_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__30585,V_24X1),V_24X2) = c_24__prop__30585___24a2(V_24X1,V_24X2) ).
fof('$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_$_case_Coq.Init.Datatypes.comparison$30477_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2430477,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2430477___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('$adef_Coq.micromega.RMicromega.CPlus_$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('$adef_$_lam_67809_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__67809,V_24X1),V_24X2))
<=> c_24__lam__67809___24a2(V_24X1,V_24X2) ) ).
fof('$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_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.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.PArith.BinPosDef.Pos.ggcdn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eggcdn,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2eggcdn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.opp_fct_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2eopp__fct,V_24X1) = cCoq_2eReals_2eRanalysis1_2eopp__fct___24a1(V_24X1) ).
fof('$adef_$_let_2_pr_78053_$a1',axiom,
! [V_24X1] : happ(c_24__let__2__pr__78053,V_24X1) = c_24__let__2__pr__78053___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_var_11_x_1271_1319_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__1271__1319,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__1271__1319___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.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_$_lam_77031_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77031,V_24X1),V_24X2),V_24X3) = c_24__lam__77031___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_8_up_74840_74856_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__8__up__74840__74856,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__8__up__74840__74856___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.opp_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2eopp__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2eopp__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_20406_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__20406,V_24X1),V_24X2) = c_24__prop__20406___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.Rfunctions.infinite_sum_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRfunctions_2einfinite__sum,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_25812_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__25812,V_24X1),V_24X2))
<=> c_24__lam__25812___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_var_4_r_78068_78085_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__var__4__r__78068__78085,V_24X1),V_24X2) = c_24__let__var__4__r__78068__78085___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_78171_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__78171,V_24X1),V_24X2) = c_24__lam__78171___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_98796_$a1',axiom,
! [V_24X1] : happ(c_24__lam__98796,V_24X1) = c_24__lam__98796___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RList.MinRlist_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRList_2eMinRlist,V_24X1) = cCoq_2eReals_2eRList_2eMinRlist___24a1(V_24X1) ).
fof('$adef_$_lam_77001_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__77001,V_24X1),V_24X2) = c_24__lam__77001___24a2(V_24X1,V_24X2) ).
fof('$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.RList.mid_Rlist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2emid__Rlist,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2emid__Rlist___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a18',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18) ).
fof('$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.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.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_$_lam_75083_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__75083,V_24X1),V_24X2),V_24X3) = c_24__lam__75083___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_case_Coq.Init.Datatypes.prod$15_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.Un_cv_$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('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_id_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__id,V_24X1) = cCoq_2eReals_2eRanalysis1_2ederivable__pt__id___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RMicromega.Rnegate_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eRnegate,V_24X1) = cCoq_2emicromega_2eRMicromega_2eRnegate___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RiemannInt.RinvN_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRiemannInt_2eRinvN__pos,V_24X1) = cCoq_2eReals_2eRiemannInt_2eRinvN__pos___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('$adef_$_lam_98354_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__98354,V_24X1),V_24X2))
<=> c_24__lam__98354___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_let_4_den_78055_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__4__den__78055,V_24X1),V_24X2) = c_24__let__4__den__78055___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_77251_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__77251,V_24X1),V_24X2) = c_24__lam__77251___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo_def.cos_n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2ecos__n,V_24X1) = cCoq_2eReals_2eRtrigo__def_2ecos__n___24a1(V_24X1) ).
fof('$adef_Coq.Reals.NewtonInt.Newton_integrable_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eNewtonInt_2eNewton__integrable,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eNewtonInt_2eNewton__integrable___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.map_bformula_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2emap__bformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2emap__bformula___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_prop_98753_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98753,V_24X1) = c_24__prop__98753___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.PartSum.SP_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2ePartSum_2eSP,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2ePartSum_2eSP___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.Zpower.Zdiv_rest_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest___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('$adef_Pythagorean.D_r_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cPythagorean_2eD__r,V_24X1),V_24X2),V_24X3))
<=> cPythagorean_2eD__r___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34302_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34302,V_24X1),V_24X2) = c_24__lam__34302___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_avoid_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rsqrt_def.pow_2_n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRsqrt__def_2epow__2__n,V_24X1) = cCoq_2eReals_2eRsqrt__def_2epow__2__n___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$_lam_52088_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__52088,V_24X1),V_24X2) = c_24__lam__52088___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2116_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__2116,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__2116___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.micromega.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_$_lam_31626_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__31626,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__31626___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Pythagorean.interCDr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cPythagorean_2einterCDr,V_24X1),V_24X2),V_24X3))
<=> cPythagorean_2einterCDr___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_let_var_var_12_x_1293_1295_1330_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__1293__1295__1330,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__1293__1295__1330___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.micromega.RMicromega.Rnormalise_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eRnormalise,V_24X1) = cCoq_2emicromega_2eRMicromega_2eRnormalise___24a1(V_24X1) ).
fof('$adef_$_let_var_9_z_74812_74828_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__9__z__74812__74828,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__9__z__74812__74828___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_78167_$a1',axiom,
! [V_24X1] : happ(c_24__lam__78167,V_24X1) = c_24__lam__78167___24a1(V_24X1) ).
fof('$adef_Pythagorean.in_ucirc_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cPythagorean_2ein__ucirc,V_24X1),V_24X2))
<=> cPythagorean_2ein__ucirc___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78169_$a1',axiom,
! [V_24X1] : happ(c_24__lam__78169,V_24X1) = c_24__lam__78169___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rmin_$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('$adef_Coq.ZArith.BinInt.Z.ge_$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('$adef_Coq.ZArith.Zbool.Zeq_bool_$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('$adef_Coq.micromega.EnvRing.PEc_$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('$adef_Coq.Reals.RiemannInt.RiemannInt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt_2eRiemannInt,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRiemannInt_2eRiemannInt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Ranalysis1.plus_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eplus__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_31626_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31626,V_24X1),V_24X2) = c_24__lam__31626___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2efst___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_$_lam_52086_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__52086,V_24X1),V_24X2),V_24X3) = c_24__lam__52086___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rlimit.mul_factor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRlimit_2emul__factor,V_24X1),V_24X2) = cCoq_2eReals_2eRlimit_2emul__factor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_prop_98756_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98756,V_24X1) = c_24__prop__98756___24a1(V_24X1) ).
fof('$adef_$_lam_78167_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__78167,V_24X1),V_24X2))
<=> c_24__lam__78167___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_common_$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('$adef_$_lam_20388_$a1',axiom,
! [V_24X1] : happ(c_24__lam__20388,V_24X1) = c_24__lam__20388___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.R_sqrt.sol_x2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eR__sqrt_2esol__x2,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eR__sqrt_2esol__x2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rtrigo_def.sinh_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2esinh,V_24X1) = cCoq_2eReals_2eRtrigo__def_2esinh___24a1(V_24X1) ).
fof('$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_$_prop_4_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__4,V_24X1),V_24X2) = c_24__prop__4___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] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_$_lam_74805_$a1',axiom,
! [V_24X1] : happ(c_24__lam__74805,V_24X1) = c_24__lam__74805___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.ZMicromega.ZgcdM_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eZgcdM,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.Ranalysis1.derivable_pt_const_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__const,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2ederivable__pt__const___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq__bool,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RiemannInt_SF.open_interval_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eopen__interval,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRiemannInt__SF_2eopen__interval___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_case_Coq.Init.Datatypes.bool$78089_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478089,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478089___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.INZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eINZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_def.exist_cos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2eexist__cos,V_24X1) = cCoq_2eReals_2eRtrigo__def_2eexist__cos___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).
fof('$adef_$_lam_77001_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77001,V_24X1),V_24X2),V_24X3) = c_24__lam__77001___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_98626_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__98626,V_24X1),V_24X2) = c_24__prop__98626___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_98215_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98215,V_24X1) = c_24__prop__98215___24a1(V_24X1) ).
fof('$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_$_lam_31516_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31516,V_24X1),V_24X2) = c_24__lam__31516___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.AltSeries.positivity_seq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eAltSeries_2epositivity__seq,V_24X1))
<=> cCoq_2eReals_2eAltSeries_2epositivity__seq___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.tauto_checker_$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_2emicromega_2eTauto_2etauto__checker,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2emicromega_2eTauto_2etauto__checker___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_48909_$a1',axiom,
! [V_24X1] : happ(c_24__prop__48909,V_24X1) = c_24__prop__48909___24a1(V_24X1) ).
fof('$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_Coq.Reals.RList.Rlength_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRList_2eRlength,V_24X1) = cCoq_2eReals_2eRList_2eRlength___24a1(V_24X1) ).
fof('$adef_Coq.Reals.R_sqrt.sol_x1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eR__sqrt_2esol__x1,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eR__sqrt_2esol__x1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_let_var_7_down_74810_74826_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__7__down__74810__74826,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__7__down__74810__74826___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_48901_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__48901,V_24X1),V_24X2) = c_24__prop__48901___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RiemannInt.RinvN_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRiemannInt_2eRinvN,V_24X1) = cCoq_2eReals_2eRiemannInt_2eRinvN___24a1(V_24X1) ).
fof('$adef_Fermat4.ArithCompl.is_ratp_$a1',axiom,
! [V_24X1] :
( p(happ(cFermat4_2eArithCompl_2eis__ratp,V_24X1))
<=> cFermat4_2eArithCompl_2eis__ratp___24a1(V_24X1) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.shiftr_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eshiftr___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.mult_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2emult__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ratan.Datan_seq_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eDatan__seq,V_24X1) = cCoq_2eReals_2eRatan_2eDatan__seq___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Zgcd_pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eZgcd__pol,V_24X1) = cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_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_Pythagorean.ucp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPythagorean_2eucp,V_24X1),V_24X2) = cPythagorean_2eucp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_20386_$a1',axiom,
! [V_24X1] : happ(c_24__prop__20386,V_24X1) = c_24__prop__20386___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsqrt_def.cond_positivity_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRsqrt__def_2econd__positivity,V_24X1) = cCoq_2eReals_2eRsqrt__def_2econd__positivity___24a1(V_24X1) ).
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('$adef_$_lam_74807_$a1',axiom,
! [V_24X1] : happ(c_24__lam__74807,V_24X1) = c_24__lam__74807___24a1(V_24X1) ).
fof('$adef_Coq.QArith.Qreals.Q2R_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQreals_2eQ2R,V_24X1) = cCoq_2eQArith_2eQreals_2eQ2R___24a1(V_24X1) ).
fof('$adef_$_let_var_var_13_y_1253_1257_1315_$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__1253__1257__1315,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__1253__1257__1315___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$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('$adef_Coq.Reals.Rderiv.continue_in_$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('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.ZArith.Zdiv.Zmod_POS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZdiv_2eZmod__POS,V_24X1),V_24X2) = cCoq_2eZArith_2eZdiv_2eZmod__POS___24a2(V_24X1,V_24X2) ).
fof('$adef_Pythagorean.eqp_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cPythagorean_2eeqp,V_24X1),V_24X2))
<=> cPythagorean_2eeqp___24a2(V_24X1,V_24X2) ) ).
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('$adef_$_lam_20388_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__20388,V_24X1),V_24X2) = c_24__lam__20388___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.Ranalysis1.pow_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2epow__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2epow__fct___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.AltSeries.PI_tg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eAltSeries_2ePI__tg,V_24X1) = cCoq_2eReals_2eAltSeries_2ePI__tg___24a1(V_24X1) ).
fof('$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_Coq.Reals.Ranalysis1.minus_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2eminus__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2eminus__fct___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_25825_$a1',axiom,
! [V_24X1] : happ(c_24__lam__25825,V_24X1) = c_24__lam__25825___24a1(V_24X1) ).
fof('$adef_$_lam_34482_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34482,V_24X1) = c_24__lam__34482___24a1(V_24X1) ).
fof('$adef_$_lam_20377_$a1',axiom,
! [V_24X1] : happ(c_24__lam__20377,V_24X1) = c_24__lam__20377___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$78081_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478081,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2478081___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.PSeries_reg.CVU_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2ePSeries__reg_2eCVU,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2ePSeries__reg_2eCVU___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_75030_$a1',axiom,
! [V_24X1] : happ(c_24__lam__75030,V_24X1) = c_24__lam__75030___24a1(V_24X1) ).
fof('$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_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_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Compare_dec.le_lt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__lt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_75036_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__75036,V_24X1),V_24X2))
<=> c_24__lam__75036___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_18_mkmult_pow_33077_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__33077,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__33077___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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_$_let_var_var_13_y_1227_1230_1300_$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__1227__1230__1300,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__1227__1230__1300___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_$_let_3_qr_78054_$a1',axiom,
! [V_24X1] : happ(c_24__let__3__qr__78054,V_24X1) = c_24__let__3__qr__78054___24a1(V_24X1) ).
fof('$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_$_lam_34462_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34462,V_24X1) = c_24__lam__34462___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.increasing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2eincreasing,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2eincreasing___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RiemannInt_SF.Int_SF_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eInt__SF,V_24X1),V_24X2) = cCoq_2eReals_2eRiemannInt__SF_2eInt__SF___24a2(V_24X1,V_24X2) ).
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('$adef_$_let_var_var_var_6_r\'_2656_2666_2668_2690_$a1',axiom,
! [V_24X1] : happ(c_24__let__var__var__var__6__r_27__2656__2666__2668__2690,V_24X1) = c_24__let__var__var__var__6__r_27__2656__2666__2668__2690___24a1(V_24X1) ).
fof('$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_Coq.Reals.PSeries_reg.CVN_r_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2ePSeries__reg_2eCVN__r,V_24X1),V_24X2) = cCoq_2eReals_2ePSeries__reg_2eCVN__r___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.Reals.Rderiv.D_x_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRderiv_2eD__x,V_24X1),V_24X2) = cCoq_2eReals_2eRderiv_2eD__x___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_78169_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__78169,V_24X1),V_24X2) = c_24__lam__78169___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ratan.ps_atan_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eps__atan,V_24X1) = cCoq_2eReals_2eRatan_2eps__atan___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('$adef_Coq.Init.Specif.inright_$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('$adef_$_let_var_4_r_78061_78077_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__var__4__r__78061__78077,V_24X1),V_24X2) = c_24__let__var__4__r__78061__78077___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_98621_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__98621,V_24X1),V_24X2) = c_24__lam__98621___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_98320_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98320,V_24X1) = c_24__prop__98320___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_20417_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__20417,V_24X1),V_24X2) = c_24__prop__20417___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Compare_dec.lt_eq_lt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2elt__eq__lt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2elt__eq__lt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Ranalysis1.antiderivative_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eantiderivative,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2eRanalysis1_2eantiderivative___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEsub_$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('$adef_$_lam_74805_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74805,V_24X1),V_24X2) = c_24__lam__74805___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_aux_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$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_$_let_var_7_down_74877_74893_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__7__down__74877__74893,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__7__down__74877__74893___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.R_sqrt.Delta_is_pos_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eR__sqrt_2eDelta__is__pos,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eR__sqrt_2eDelta__is__pos___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_20373_$a1',axiom,
! [V_24X1] : happ(c_24__prop__20373,V_24X1) = c_24__prop__20373___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$32_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rlimit.Dgf_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2eRlimit_2eDgf,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2eRlimit_2eDgf___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_lam_20379_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__20379,V_24X1),V_24X2) = c_24__lam__20379___24a2(V_24X1,V_24X2) ).
fof('$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_$_case_Coq.Init.Datatypes.bool$2694_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_242694,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242694___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rpower.arcsinh_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRpower_2earcsinh,V_24X1) = cCoq_2eReals_2eRpower_2earcsinh___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rtrigo_alt.sin_term_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtrigo__alt_2esin__term,V_24X1),V_24X2) = cCoq_2eReals_2eRtrigo__alt_2esin__term___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('$adef_Coq.Reals.Ranalysis5.derivable_pt_recip_interv_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eReals_2eRanalysis5_2ederivable__pt__recip__interv___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Pythagorean.in_ucp_setb_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cPythagorean_2ein__ucp__setb,V_24X1),V_24X2))
<=> cPythagorean_2ein__ucp__setb___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_15479_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__15479,V_24X1))
<=> c_24__lam__15479___24a1(V_24X1) ) ).
fof('$adef_$_lam_98623_$a1',axiom,
! [V_24X1] : happ(c_24__lam__98623,V_24X1) = c_24__lam__98623___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.nonzero_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonzero,V_24X1) = cCoq_2eReals_2eRIneq_2enonzero___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_74801_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__74801,V_24X1))
<=> c_24__lam__74801___24a1(V_24X1) ) ).
fof('$adef_$_let_17_mkopp_pow_33076_$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__33076,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__33076___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Reals.Rprod.prod_f_R0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRprod_2eprod__f__R0,V_24X1),V_24X2) = cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_76355_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__76355,V_24X1),V_24X2) = c_24__lam__76355___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.RWeakChecker_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eRWeakChecker,V_24X1) = cCoq_2emicromega_2eRMicromega_2eRWeakChecker___24a1(V_24X1) ).
fof('$adef_Fermat4.ArithCompl.frac_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cFermat4_2eArithCompl_2efrac,V_24X1),V_24X2) = cFermat4_2eArithCompl_2efrac___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_98355_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__98355,V_24X1))
<=> c_24__lam__98355___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.get_signZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V_24X1) ).
fof('$adef_$_lam_98792_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__98792,V_24X1),V_24X2) = c_24__lam__98792___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_70508_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70508,V_24X1) = c_24__lam__70508___24a1(V_24X1) ).
fof('$adef_$_prop_98755_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98755,V_24X1) = c_24__prop__98755___24a1(V_24X1) ).
fof('$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.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.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_$_let_var_var_12_x_1276_1280_1326_$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__1276__1280__1326,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__1276__1280__1326___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_Coq.micromega.RMicromega.CInv_$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('$adef_$_lam_34302_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__34302,V_24X1),V_24X2),V_24X3) = c_24__lam__34302___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_71916_$a1',axiom,
! [V_24X1] : happ(c_24__lam__71916,V_24X1) = c_24__lam__71916___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.ggcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eggcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$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('$adef_Coq.Reals.RIneq.mknonnegreal_$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('$adef_$_let_var_6_p_31785_31787_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__31785__31787,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__31785__31787___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_98347_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__98347,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__98347___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$38069_$a20',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2438069,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2438069___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20) ).
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('$adef_Coq.Reals.Ranalysis1.constant_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2econstant,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2econstant___24a1(V_24X1) ) ).
fof('$adef_$_lam_77037_$a1',axiom,
! [V_24X1] : happ(c_24__lam__77037,V_24X1) = c_24__lam__77037___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_var_9_z_74841_74857_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__9__z__74841__74857,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__9__z__74841__74857___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR__2,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V_24X1) ).
fof('$adef_$_prop_98214_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98214,V_24X1) = c_24__prop__98214___24a1(V_24X1) ).
fof('$adef_$_lam_15480_$a1',axiom,
! [V_24X1] : happ(c_24__lam__15480,V_24X1) = c_24__lam__15480___24a1(V_24X1) ).
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('$adef_$_lam_25789_$a1',axiom,
! [V_24X1] : happ(c_24__lam__25789,V_24X1) = c_24__lam__25789___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rderiv.D_in_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eReals_2eRderiv_2eD__in,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eReals_2eRderiv_2eD__in___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Reals.Ranalysis5.derive_pt_recip_interv_prelim1_1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis5_2ederive__pt__recip__interv__prelim1__1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eReals_2eRanalysis5_2ederive__pt__recip__interv__prelim1__1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_75030_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__75030,V_24X1),V_24X2) = c_24__lam__75030___24a2(V_24X1,V_24X2) ).
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('$adef_$_prop_34403_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__34403,V_24X1),V_24X2) = c_24__prop__34403___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_14_s1_1254_1258_1316_$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__1254__1258__1316,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__1254__1258__1316___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Reals.RIneq.cond_nonneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2econd__nonneg,V_24X1) = cCoq_2eReals_2eRIneq_2econd__nonneg___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('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$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('$adef_Coq.micromega.EnvRing.Pc_$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_20379_$a1',axiom,
! [V_24X1] : happ(c_24__lam__20379,V_24X1) = c_24__lam__20379___24a1(V_24X1) ).
fof('$adef_$_lam_98365_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__98365,V_24X1),V_24X2) = c_24__lam__98365___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ratan.atan_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRatan_2eatan,V_24X1) = cCoq_2eReals_2eRatan_2eatan___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.nonpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonpos,V_24X1) = cCoq_2eReals_2eRIneq_2enonpos___24a1(V_24X1) ).
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('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rsqrt_def.Dichotomy_lb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__lb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RList.cons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRList_2econs,V_24X1),V_24X2) = cCoq_2eReals_2eRList_2econs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.decreasing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2edecreasing,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2edecreasing___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_14_s_1228_1231_1301_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__14__s__1228__1231__1301,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s__1228__1231__1301___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.ZArith.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.Arith.Compare_dec.le_gt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__gt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_20372_$a1',axiom,
! [V_24X1] : happ(c_24__prop__20372,V_24X1) = c_24__prop__20372___24a1(V_24X1) ).
fof('$adef_$_lam_74807_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74807,V_24X1),V_24X2) = c_24__lam__74807___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_29921_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__29921,V_24X1),V_24X2) = c_24__prop__29921___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.Rsqrt_def.Dichotomy_ub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRsqrt__def_2eDichotomy__ub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_20407_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__20407,V_24X1),V_24X2) = c_24__prop__20407___24a2(V_24X1,V_24X2) ).
fof('$adef_Pythagorean.is_ucp_$a1',axiom,
! [V_24X1] :
( p(happ(cPythagorean_2eis__ucp,V_24X1))
<=> cPythagorean_2eis__ucp___24a1(V_24X1) ) ).
fof('$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_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Ranalysis1.mult_fct_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRanalysis1_2emult__fct,V_24X1),V_24X2) = cCoq_2eReals_2eRanalysis1_2emult__fct___24a2(V_24X1,V_24X2) ).
fof('$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.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_$_let_var_7_down_74839_74855_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__7__down__74839__74855,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__7__down__74839__74855___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rabs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRabs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec,V_24X1),V_24X2) = cCoq_2eArith_2ePeanoNat_2eNat_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_98796_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__98796,V_24X1),V_24X2) = c_24__lam__98796___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.Rtrigo_alt.cos_approx_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtrigo__alt_2ecos__approx,V_24X1),V_24X2) = cCoq_2eReals_2eRtrigo__alt_2ecos__approx___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34482_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__34482,V_24X1),V_24X2))
<=> c_24__lam__34482___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.ggcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___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('$adef_Coq.Reals.Rtrigo_alt.cos_term_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__alt_2ecos__term,V_24X1) = cCoq_2eReals_2eRtrigo__alt_2ecos__term___24a1(V_24X1) ).
fof('$adef_$_let_6_lmp_1595_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__1595,V_24X1) = c_24__let__6__lmp__1595___24a1(V_24X1) ).
fof('$adef_Coq.Reals.R_sqrt.Delta_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eR__sqrt_2eDelta,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eR__sqrt_2eDelta___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Cos_plus.Majxy_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eCos__plus_2eMajxy,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eCos__plus_2eMajxy___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_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_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.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_mult_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__mult,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eReals_2eRanalysis1_2ederivable__pt__mult___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_75036_$a1',axiom,
! [V_24X1] : happ(c_24__lam__75036,V_24X1) = c_24__lam__75036___24a1(V_24X1) ).
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('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_33075_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__33075,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__33075___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.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_$_case_Coq.Init.Datatypes.bool$2700_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_242700,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242700___24a3(V_24X1,V_24X2,V_24X3) ).
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_72010_$a1',axiom,
! [V_24X1] : happ(c_24__lam__72010,V_24X1) = c_24__lam__72010___24a1(V_24X1) ).
fof('$adef_$_let_var_8_up_74811_74827_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__8__up__74811__74827,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__8__up__74811__74827___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_52088_$a1',axiom,
! [V_24X1] : happ(c_24__lam__52088,V_24X1) = c_24__lam__52088___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rseries.Pser_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRseries_2ePser,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRseries_2ePser___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_var_var_15_s2_1279_1283_1329_$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__1279__1283__1329,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__1279__1283__1329___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$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('$adef_$_lam_48897_$a1',axiom,
! [V_24X1] : happ(c_24__lam__48897,V_24X1) = c_24__lam__48897___24a1(V_24X1) ).
fof('$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_$_lam_77031_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__77031,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__77031___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_98365_$a1',axiom,
! [V_24X1] : happ(c_24__lam__98365,V_24X1) = c_24__lam__98365___24a1(V_24X1) ).
fof('$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_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Machin.atan_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eMachin_2eatan__sub,V_24X1),V_24X2) = cCoq_2eReals_2eMachin_2eatan__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_98754_$a1',axiom,
! [V_24X1] : happ(c_24__prop__98754,V_24X1) = c_24__prop__98754___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$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('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_11_x_1268_1318_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__1268__1318,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__1268__1318___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Reals.Ranalysis1.derivable_pt_plus_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eReals_2eRanalysis1_2ederivable__pt__plus,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eReals_2eRanalysis1_2ederivable__pt__plus___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Reals.Rtrigo_alt.cos_term_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRtrigo__alt_2ecos__term,V_24X1),V_24X2) = cCoq_2eReals_2eRtrigo__alt_2ecos__term___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.PSeries_reg.CVN_R_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2ePSeries__reg_2eCVN__R,V_24X1) = cCoq_2eReals_2ePSeries__reg_2eCVN__R___24a1(V_24X1) ).
fof('$adef_$_lam_77251_$a1',axiom,
! [V_24X1] : happ(c_24__lam__77251,V_24X1) = c_24__lam__77251___24a1(V_24X1) ).
fof('$adef_$_lam_52105_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__52105,V_24X1),V_24X2))
<=> c_24__lam__52105___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_77037_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__77037,V_24X1),V_24X2) = c_24__lam__77037___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31642_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31642,V_24X1),V_24X2) = c_24__lam__31642___24a2(V_24X1,V_24X2) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rtrigo_def.sin_n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRtrigo__def_2esin__n,V_24X1) = cCoq_2eReals_2eRtrigo__def_2esin__n___24a1(V_24X1) ).
fof('$tdef_$_type_75845',axiom,
! [V_24Y] :
( c_24__type__75845___24t(V_24Y)
<=> t(V_24Y,c_24__type__75845) ) ).
fof('$tdef_$_type_15556',axiom,
! [V_24Y] :
( c_24__type__15556___24t(V_24Y)
<=> t(V_24Y,c_24__type__15556) ) ).
fof('$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_22609',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22609___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22609___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2586',axiom,
! [V_24Y] :
( c_24__type__2586___24t(V_24Y)
<=> t(V_24Y,c_24__type__2586) ) ).
fof('$tdef_$_type_32026',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32026___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32026___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_98628',axiom,
! [V_24Y] :
( c_24__type__98628___24t(V_24Y)
<=> t(V_24Y,c_24__type__98628) ) ).
fof('$tdef_$_type_67858',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__67858___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__67858___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_61968',axiom,
! [V_24Y] :
( c_24__type__61968___24t(V_24Y)
<=> t(V_24Y,c_24__type__61968) ) ).
fof('$tdef_$_type_2424',axiom,
! [V_24Y] :
( c_24__type__2424___24t(V_24Y)
<=> t(V_24Y,c_24__type__2424) ) ).
fof('$tdef_$_type_22495',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22495___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22495___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_23',axiom,
! [V_24Y] :
( c_24__type__23___24t(V_24Y)
<=> t(V_24Y,c_24__type__23) ) ).
fof('$tdef_$_type_2032',axiom,
! [V_24Y] :
( c_24__type__2032___24t(V_24Y)
<=> t(V_24Y,c_24__type__2032) ) ).
fof('$tdef_$_type_64613',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__64613___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__64613___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_19415',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19415___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19415___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2604',axiom,
! [V_24Y] :
( c_24__type__2604___24t(V_24Y)
<=> t(V_24Y,c_24__type__2604) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_891',axiom,
! [V_24X1,V_24Y] :
( c_24__type__891___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__891___24a1(V_24X1)) ) ).
fof('$tdef_$_type_67816',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__67816___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__67816___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_70972',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__70972___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__70972___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_78057',axiom,
! [V_24Y] :
( c_24__type__78057___24t(V_24Y)
<=> t(V_24Y,c_24__type__78057) ) ).
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_$_type_615',axiom,
! [V_24Y] :
( c_24__type__615___24t(V_24Y)
<=> t(V_24Y,c_24__type__615) ) ).
fof('$tdef_$_type_29853',axiom,
! [V_24Y] :
( c_24__type__29853___24t(V_24Y)
<=> t(V_24Y,c_24__type__29853) ) ).
fof('$tdef_$_type_65628',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__65628___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__65628___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_32089',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32089___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32089___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_64959',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__64959___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__64959___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_32388',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32388___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32388___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15575',axiom,
! [V_24Y] :
( c_24__type__15575___24t(V_24Y)
<=> t(V_24Y,c_24__type__15575) ) ).
fof('$tdef_$_type_32381',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32381___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32381___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31645',axiom,
! [V_24Y] :
( c_24__type__31645___24t(V_24Y)
<=> t(V_24Y,c_24__type__31645) ) ).
fof('$tdef_$_type_30583',axiom,
! [V_24Y] :
( c_24__type__30583___24t(V_24Y)
<=> t(V_24Y,c_24__type__30583) ) ).
fof('$tdef_$_type_71322',axiom,
! [V_24Y] :
( c_24__type__71322___24t(V_24Y)
<=> t(V_24Y,c_24__type__71322) ) ).
fof('$tdef_$_type_25925',axiom,
! [V_24X1,V_24Y] :
( c_24__type__25925___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__25925___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32269',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32269___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32269___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_76888',axiom,
! [V_24Y] :
( c_24__type__76888___24t(V_24Y)
<=> t(V_24Y,c_24__type__76888) ) ).
fof('$tdef_$_type_194',axiom,
! [V_24Y] :
( c_24__type__194___24t(V_24Y)
<=> t(V_24Y,c_24__type__194) ) ).
fof('$tdef_$_type_2457',axiom,
! [V_24Y] :
( c_24__type__2457___24t(V_24Y)
<=> t(V_24Y,c_24__type__2457) ) ).
fof('$tdef_$_type_71124',axiom,
! [V_24Y] :
( c_24__type__71124___24t(V_24Y)
<=> t(V_24Y,c_24__type__71124) ) ).
fof('$tdef_$_type_31582',axiom,
! [V_24Y] :
( c_24__type__31582___24t(V_24Y)
<=> t(V_24Y,c_24__type__31582) ) ).
fof('$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_$_type_2515',axiom,
! [V_24Y] :
( c_24__type__2515___24t(V_24Y)
<=> t(V_24Y,c_24__type__2515) ) ).
fof('$tdef_$_type_77040',axiom,
! [V_24Y] :
( c_24__type__77040___24t(V_24Y)
<=> t(V_24Y,c_24__type__77040) ) ).
fof('$tdef_$_type_31419',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31419___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31419___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25676',axiom,
! [V_24Y] :
( c_24__type__25676___24t(V_24Y)
<=> t(V_24Y,c_24__type__25676) ) ).
fof('$tdef_$_type_15765',axiom,
! [V_24Y] :
( c_24__type__15765___24t(V_24Y)
<=> t(V_24Y,c_24__type__15765) ) ).
fof('$tdef_$_type_22549',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22549___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22549___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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('$tdef_$_type_25959',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__25959___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__25959___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_198',axiom,
! [V_24Y] :
( c_24__type__198___24t(V_24Y)
<=> t(V_24Y,c_24__type__198) ) ).
fof('$tdef_$_type_98212',axiom,
! [V_24Y] :
( c_24__type__98212___24t(V_24Y)
<=> t(V_24Y,c_24__type__98212) ) ).
fof('$tdef_$_type_25918',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__25918___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__25918___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25780',axiom,
! [V_24Y] :
( c_24__type__25780___24t(V_24Y)
<=> t(V_24Y,c_24__type__25780) ) ).
fof('$tdef_$_type_67312',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__67312___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__67312___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Specif.sumbool',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21469',axiom,
! [V_24Y] :
( c_24__type__21469___24t(V_24Y)
<=> t(V_24Y,c_24__type__21469) ) ).
fof('$tdef_$_type_18146',axiom,
! [V_24Y] :
( c_24__type__18146___24t(V_24Y)
<=> t(V_24Y,c_24__type__18146) ) ).
fof('$tdef_$_type_67867',axiom,
! [V_24Y] :
( c_24__type__67867___24t(V_24Y)
<=> t(V_24Y,c_24__type__67867) ) ).
fof('$tdef_$_type_31589',axiom,
! [V_24Y] :
( c_24__type__31589___24t(V_24Y)
<=> t(V_24Y,c_24__type__31589) ) ).
fof('$tdef_$_type_78091',axiom,
! [V_24Y] :
( c_24__type__78091___24t(V_24Y)
<=> t(V_24Y,c_24__type__78091) ) ).
fof('$tdef_$_type_15476',axiom,
! [V_24Y] :
( c_24__type__15476___24t(V_24Y)
<=> t(V_24Y,c_24__type__15476) ) ).
fof('$tdef_$_type_48899',axiom,
! [V_24X1,V_24Y] :
( c_24__type__48899___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__48899___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16900',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16900___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16900___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31527',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31527___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31527___24a1(V_24X1)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$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_25808',axiom,
! [V_24Y] :
( c_24__type__25808___24t(V_24Y)
<=> t(V_24Y,c_24__type__25808) ) ).
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_$_type_235',axiom,
! [V_24Y] :
( c_24__type__235___24t(V_24Y)
<=> t(V_24Y,c_24__type__235) ) ).
fof('$tdef_$_type_98618',axiom,
! [V_24Y] :
( c_24__type__98618___24t(V_24Y)
<=> t(V_24Y,c_24__type__98618) ) ).
fof('$tdef_$_type_15542',axiom,
! [V_24Y] :
( c_24__type__15542___24t(V_24Y)
<=> t(V_24Y,c_24__type__15542) ) ).
fof('$tdef_$_type_71224',axiom,
! [V_24Y] :
( c_24__type__71224___24t(V_24Y)
<=> t(V_24Y,c_24__type__71224) ) ).
fof('$tdef_$_type_24402',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__24402___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__24402___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_70984',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__70984___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__70984___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_71598',axiom,
! [V_24Y] :
( c_24__type__71598___24t(V_24Y)
<=> t(V_24Y,c_24__type__71598) ) ).
fof('$tdef_$_type_52101',axiom,
! [V_24Y] :
( c_24__type__52101___24t(V_24Y)
<=> t(V_24Y,c_24__type__52101) ) ).
fof('$tdef_$_type_32913',axiom,
! [V_24Y] :
( c_24__type__32913___24t(V_24Y)
<=> t(V_24Y,c_24__type__32913) ) ).
fof('$tdef_$_type_26577',axiom,
! [V_24Y] :
( c_24__type__26577___24t(V_24Y)
<=> t(V_24Y,c_24__type__26577) ) ).
fof('$tdef_$_type_62560',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__62560___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__62560___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_31763',axiom,
! [V_24Y] :
( c_24__type__31763___24t(V_24Y)
<=> t(V_24Y,c_24__type__31763) ) ).
fof('$tdef_$_type_23355',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__23355___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__23355___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_76360',axiom,
! [V_24Y] :
( c_24__type__76360___24t(V_24Y)
<=> t(V_24Y,c_24__type__76360) ) ).
fof('$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_20010',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__20010___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__20010___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34714',axiom,
! [V_24Y] :
( c_24__type__34714___24t(V_24Y)
<=> t(V_24Y,c_24__type__34714) ) ).
fof('$tdef_$_type_32750',axiom,
! [V_24Y] :
( c_24__type__32750___24t(V_24Y)
<=> t(V_24Y,c_24__type__32750) ) ).
fof('$tdef_$_type_26007',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26007___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26007___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22525',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22525___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22525___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_31643',axiom,
! [V_24Y] :
( c_24__type__31643___24t(V_24Y)
<=> t(V_24Y,c_24__type__31643) ) ).
fof('$tdef_$_type_2702',axiom,
! [V_24Y] :
( c_24__type__2702___24t(V_24Y)
<=> t(V_24Y,c_24__type__2702) ) ).
fof('$tdef_$_type_76247',axiom,
! [V_24Y] :
( c_24__type__76247___24t(V_24Y)
<=> t(V_24Y,c_24__type__76247) ) ).
fof('$tdef_$_type_228',axiom,
! [V_24Y] :
( c_24__type__228___24t(V_24Y)
<=> t(V_24Y,c_24__type__228) ) ).
fof('$tdef_$_type_61986',axiom,
! [V_24Y] :
( c_24__type__61986___24t(V_24Y)
<=> t(V_24Y,c_24__type__61986) ) ).
fof('$tdef_$_type_24810',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__24810___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__24810___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_19909',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19909___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19909___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32362',axiom,
! [V_24Y] :
( c_24__type__32362___24t(V_24Y)
<=> t(V_24Y,c_24__type__32362) ) ).
fof('$tdef_$_type_3682',axiom,
! [V_24Y] :
( c_24__type__3682___24t(V_24Y)
<=> t(V_24Y,c_24__type__3682) ) ).
fof('$tdef_$_type_25530',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25530___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25530___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_62906',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__62906___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__62906___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_25922',axiom,
! [V_24Y] :
( c_24__type__25922___24t(V_24Y)
<=> t(V_24Y,c_24__type__25922) ) ).
fof('$tdef_$_type_35033',axiom,
! [V_24Y] :
( c_24__type__35033___24t(V_24Y)
<=> t(V_24Y,c_24__type__35033) ) ).
fof('$tdef_$_type_2029',axiom,
! [V_24Y] :
( c_24__type__2029___24t(V_24Y)
<=> t(V_24Y,c_24__type__2029) ) ).
fof('$tdef_$_type_2479',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2479___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2479___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_98207',axiom,
! [V_24Y] :
( c_24__type__98207___24t(V_24Y)
<=> t(V_24Y,c_24__type__98207) ) ).
fof('$tdef_$_type_1448',axiom,
! [V_24Y] :
( c_24__type__1448___24t(V_24Y)
<=> t(V_24Y,c_24__type__1448) ) ).
fof('$tdef_$_type_1593',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1593___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1593___24a1(V_24X1)) ) ).
fof('$tdef_$_type_112',axiom,
! [V_24Y] :
( c_24__type__112___24t(V_24Y)
<=> t(V_24Y,c_24__type__112) ) ).
fof('$tdef_$_type_61958',axiom,
! [V_24Y] :
( c_24__type__61958___24t(V_24Y)
<=> t(V_24Y,c_24__type__61958) ) ).
fof('$tdef_$_type_20115',axiom,
! [V_24Y] :
( c_24__type__20115___24t(V_24Y)
<=> t(V_24Y,c_24__type__20115) ) ).
fof('$tdef_$_type_20140',axiom,
! [V_24Y] :
( c_24__type__20140___24t(V_24Y)
<=> t(V_24Y,c_24__type__20140) ) ).
fof('$tdef_$_type_25450',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25450___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25450___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_34306',axiom,
! [V_24Y] :
( c_24__type__34306___24t(V_24Y)
<=> t(V_24Y,c_24__type__34306) ) ).
fof('$tdef_$_type_29938',axiom,
! [V_24Y] :
( c_24__type__29938___24t(V_24Y)
<=> t(V_24Y,c_24__type__29938) ) ).
fof('$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_20110',axiom,
! [V_24Y] :
( c_24__type__20110___24t(V_24Y)
<=> t(V_24Y,c_24__type__20110) ) ).
fof('$tdef_$_type_99',axiom,
! [V_24Y] :
( c_24__type__99___24t(V_24Y)
<=> t(V_24Y,c_24__type__99) ) ).
fof('$tdef_$_type_71316',axiom,
! [V_24Y] :
( c_24__type__71316___24t(V_24Y)
<=> t(V_24Y,c_24__type__71316) ) ).
fof('$tdef_$_type_913',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__913___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__913___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_67846',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__67846___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__67846___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31524',axiom,
! [V_24Y] :
( c_24__type__31524___24t(V_24Y)
<=> t(V_24Y,c_24__type__31524) ) ).
fof('$tdef_$_type_98785',axiom,
! [V_24Y] :
( c_24__type__98785___24t(V_24Y)
<=> t(V_24Y,c_24__type__98785) ) ).
fof('$tdef_$_type_88',axiom,
! [V_24Y] :
( c_24__type__88___24t(V_24Y)
<=> t(V_24Y,c_24__type__88) ) ).
fof('$tdef_$_type_64267',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__64267___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__64267___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_2248',axiom,
! [V_24Y] :
( c_24__type__2248___24t(V_24Y)
<=> t(V_24Y,c_24__type__2248) ) ).
fof('$tdef_$_type_67892',axiom,
! [V_24Y] :
( c_24__type__67892___24t(V_24Y)
<=> t(V_24Y,c_24__type__67892) ) ).
fof('$tdef_$_type_21197',axiom,
! [V_24Y] :
( c_24__type__21197___24t(V_24Y)
<=> t(V_24Y,c_24__type__21197) ) ).
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_$_type_30600',axiom,
! [V_24Y] :
( c_24__type__30600___24t(V_24Y)
<=> t(V_24Y,c_24__type__30600) ) ).
fof('$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_31631',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31631___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31631___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2518',axiom,
! [V_24Y] :
( c_24__type__2518___24t(V_24Y)
<=> t(V_24Y,c_24__type__2518) ) ).
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_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_31540',axiom,
! [V_24Y] :
( c_24__type__31540___24t(V_24Y)
<=> t(V_24Y,c_24__type__31540) ) ).
fof('$tdef_$_type_20523',axiom,
! [V_24Y] :
( c_24__type__20523___24t(V_24Y)
<=> t(V_24Y,c_24__type__20523) ) ).
fof('$tdef_$_type_31069',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31069___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31069___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_280',axiom,
! [V_24Y] :
( c_24__type__280___24t(V_24Y)
<=> t(V_24Y,c_24__type__280) ) ).
fof('$tdef_$_type_65974',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__65974___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__65974___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_20331',axiom,
! [V_24Y] :
( c_24__type__20331___24t(V_24Y)
<=> t(V_24Y,c_24__type__20331) ) ).
fof('$tdef_$_type_31597',axiom,
! [V_24Y] :
( c_24__type__31597___24t(V_24Y)
<=> t(V_24Y,c_24__type__31597) ) ).
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_$_type_71084',axiom,
! [V_24Y] :
( c_24__type__71084___24t(V_24Y)
<=> t(V_24Y,c_24__type__71084) ) ).
fof('$tdef_$_type_15554',axiom,
! [V_24Y] :
( c_24__type__15554___24t(V_24Y)
<=> t(V_24Y,c_24__type__15554) ) ).
fof('$tdef_$_type_31326',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31326___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31326___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.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_32408',axiom,
! [V_24Y] :
( c_24__type__32408___24t(V_24Y)
<=> t(V_24Y,c_24__type__32408) ) ).
fof('$tdef_$_type_15539',axiom,
! [V_24Y] :
( c_24__type__15539___24t(V_24Y)
<=> t(V_24Y,c_24__type__15539) ) ).
fof('$tdef_$_type_76585',axiom,
! [V_24Y] :
( c_24__type__76585___24t(V_24Y)
<=> t(V_24Y,c_24__type__76585) ) ).
fof('$tdef_$_type_31779',axiom,
! [V_24Y] :
( c_24__type__31779___24t(V_24Y)
<=> t(V_24Y,c_24__type__31779) ) ).
fof('$tdef_$_type_20105',axiom,
! [V_24Y] :
( c_24__type__20105___24t(V_24Y)
<=> t(V_24Y,c_24__type__20105) ) ).
fof('$tdef_$_type_62020',axiom,
! [V_24Y] :
( c_24__type__62020___24t(V_24Y)
<=> t(V_24Y,c_24__type__62020) ) ).
fof('$tdef_$_type_63921',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__63921___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__63921___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_22666',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22666___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22666___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_20151',axiom,
! [V_24Y] :
( c_24__type__20151___24t(V_24Y)
<=> t(V_24Y,c_24__type__20151) ) ).
fof('$tdef_$_type_15773',axiom,
! [V_24Y] :
( c_24__type__15773___24t(V_24Y)
<=> t(V_24Y,c_24__type__15773) ) ).
fof('$tdef_$_type_98295',axiom,
! [V_24Y] :
( c_24__type__98295___24t(V_24Y)
<=> t(V_24Y,c_24__type__98295) ) ).
fof('$tdef_$_type_63252',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__63252___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__63252___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_946',axiom,
! [V_24Y] :
( c_24__type__946___24t(V_24Y)
<=> t(V_24Y,c_24__type__946) ) ).
fof('$tdef_$_type_31647',axiom,
! [V_24Y] :
( c_24__type__31647___24t(V_24Y)
<=> t(V_24Y,c_24__type__31647) ) ).
fof('$tdef_$_type_2037',axiom,
! [V_24Y] :
( c_24__type__2037___24t(V_24Y)
<=> t(V_24Y,c_24__type__2037) ) ).
fof('$tdef_$_type_22147',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__22147___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__22147___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_34140',axiom,
! [V_24Y] :
( c_24__type__34140___24t(V_24Y)
<=> t(V_24Y,c_24__type__34140) ) ).
fof('$tdef_$_type_1575',axiom,
! [V_24Y] :
( c_24__type__1575___24t(V_24Y)
<=> t(V_24Y,c_24__type__1575) ) ).
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_$_type_2607',axiom,
! [V_24Y] :
( c_24__type__2607___24t(V_24Y)
<=> t(V_24Y,c_24__type__2607) ) ).
fof('$tdef_$_type_1430',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1430___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1430___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32809',axiom,
! [V_24Y] :
( c_24__type__32809___24t(V_24Y)
<=> t(V_24Y,c_24__type__32809) ) ).
fof('$tdef_$_type_1780',axiom,
! [V_24Y] :
( c_24__type__1780___24t(V_24Y)
<=> t(V_24Y,c_24__type__1780) ) ).
fof('$tdef_$_type_61974',axiom,
! [V_24Y] :
( c_24__type__61974___24t(V_24Y)
<=> t(V_24Y,c_24__type__61974) ) ).
fof('$tdef_$_type_15506',axiom,
! [V_24Y] :
( c_24__type__15506___24t(V_24Y)
<=> t(V_24Y,c_24__type__15506) ) ).
fof('$tdef_$_type_22210',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__22210___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__22210___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_98690',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__98690___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__98690___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_31639',axiom,
! [V_24Y] :
( c_24__type__31639___24t(V_24Y)
<=> t(V_24Y,c_24__type__31639) ) ).
fof('$tdef_$_type_35624',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35624___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35624___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20093',axiom,
! [V_24Y] :
( c_24__type__20093___24t(V_24Y)
<=> t(V_24Y,c_24__type__20093) ) ).
fof('$tdef_$_type_29893',axiom,
! [V_24Y] :
( c_24__type__29893___24t(V_24Y)
<=> t(V_24Y,c_24__type__29893) ) ).
fof('$tdef_$_type_25023',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__25023___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__25023___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.micromega.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_30528',axiom,
! [V_24Y] :
( c_24__type__30528___24t(V_24Y)
<=> t(V_24Y,c_24__type__30528) ) ).
fof('$tdef_$_type_19808',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19808___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19808___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_20308',axiom,
! [V_24Y] :
( c_24__type__20308___24t(V_24Y)
<=> t(V_24Y,c_24__type__20308) ) ).
fof('$tdef_$_type_31570',axiom,
! [V_24Y] :
( c_24__type__31570___24t(V_24Y)
<=> t(V_24Y,c_24__type__31570) ) ).
fof('$tdef_$_type_98351',axiom,
! [V_24Y] :
( c_24__type__98351___24t(V_24Y)
<=> t(V_24Y,c_24__type__98351) ) ).
fof('$tdef_$_type_935',axiom,
! [V_24Y] :
( c_24__type__935___24t(V_24Y)
<=> t(V_24Y,c_24__type__935) ) ).
fof('$tdef_$_type_263',axiom,
! [V_24Y] :
( c_24__type__263___24t(V_24Y)
<=> t(V_24Y,c_24__type__263) ) ).
fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).
fof('$tdef_$_type_33355',axiom,
! [V_24Y] :
( c_24__type__33355___24t(V_24Y)
<=> t(V_24Y,c_24__type__33355) ) ).
fof('$tdef_$_type_31635',axiom,
! [V_24Y] :
( c_24__type__31635___24t(V_24Y)
<=> t(V_24Y,c_24__type__31635) ) ).
fof('$tdef_$_type_76350',axiom,
! [V_24Y] :
( c_24__type__76350___24t(V_24Y)
<=> t(V_24Y,c_24__type__76350) ) ).
fof('$tdef_$_type_34145',axiom,
! [V_24Y] :
( c_24__type__34145___24t(V_24Y)
<=> t(V_24Y,c_24__type__34145) ) ).
fof('$tdef_$_type_1200',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1200___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1200___24a1(V_24X1)) ) ).
fof('$tdef_$_type_62025',axiom,
! [V_24Y] :
( c_24__type__62025___24t(V_24Y)
<=> t(V_24Y,c_24__type__62025) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_25786',axiom,
! [V_24Y] :
( c_24__type__25786___24t(V_24Y)
<=> t(V_24Y,c_24__type__25786) ) ).
fof('$tdef_$_type_19516',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19516___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19516___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34459',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34459___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34459___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32961',axiom,
! [V_24Y] :
( c_24__type__32961___24t(V_24Y)
<=> t(V_24Y,c_24__type__32961) ) ).
fof('$tdef_$_type_22264',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__22264___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__22264___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34468',axiom,
! [V_24Y] :
( c_24__type__34468___24t(V_24Y)
<=> t(V_24Y,c_24__type__34468) ) ).
fof('$tdef_$_type_19707',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19707___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19707___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Reals.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_20594',axiom,
! [V_24Y] :
( c_24__type__20594___24t(V_24Y)
<=> t(V_24Y,c_24__type__20594) ) ).
fof('$tdef_$_type_249',axiom,
! [V_24Y] :
( c_24__type__249___24t(V_24Y)
<=> t(V_24Y,c_24__type__249) ) ).
fof('$tdef_$_type_22633',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22633___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22633___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_966',axiom,
! [V_24Y] :
( c_24__type__966___24t(V_24Y)
<=> t(V_24Y,c_24__type__966) ) ).
fof('$tdef_$_type_37150',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__37150___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__37150___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_32805',axiom,
! [V_24Y] :
( c_24__type__32805___24t(V_24Y)
<=> t(V_24Y,c_24__type__32805) ) ).
fof('$tdef_$_type_21729',axiom,
! [V_24Y] :
( c_24__type__21729___24t(V_24Y)
<=> t(V_24Y,c_24__type__21729) ) ).
fof('$tdef_$_type_34451',axiom,
! [V_24Y] :
( c_24__type__34451___24t(V_24Y)
<=> t(V_24Y,c_24__type__34451) ) ).
fof('$tdef_$_type_124',axiom,
! [V_24Y] :
( c_24__type__124___24t(V_24Y)
<=> t(V_24Y,c_24__type__124) ) ).
fof('$tdef_$_type_34485',axiom,
! [V_24Y] :
( c_24__type__34485___24t(V_24Y)
<=> t(V_24Y,c_24__type__34485) ) ).
fof('$tdef_$_type_25486',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25486___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25486___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_31244',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31244___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31244___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25977',axiom,
! [V_24Y] :
( c_24__type__25977___24t(V_24Y)
<=> t(V_24Y,c_24__type__25977) ) ).
fof('$tdef_$_type_37191',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__37191___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__37191___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_33387',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33387___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33387___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31776',axiom,
! [V_24Y] :
( c_24__type__31776___24t(V_24Y)
<=> t(V_24Y,c_24__type__31776) ) ).
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_$_type_107',axiom,
! [V_24Y] :
( c_24__type__107___24t(V_24Y)
<=> t(V_24Y,c_24__type__107) ) ).
fof('$tdef_$_type_77217',axiom,
! [V_24Y] :
( c_24__type__77217___24t(V_24Y)
<=> t(V_24Y,c_24__type__77217) ) ).
fof('$tdef_$_type_31617',axiom,
! [V_24Y] :
( c_24__type__31617___24t(V_24Y)
<=> t(V_24Y,c_24__type__31617) ) ).
fof('$tdef_$_type_76465',axiom,
! [V_24Y] :
( c_24__type__76465___24t(V_24Y)
<=> t(V_24Y,c_24__type__76465) ) ).
fof('$tdef_$_type_98342',axiom,
! [V_24Y] :
( c_24__type__98342___24t(V_24Y)
<=> t(V_24Y,c_24__type__98342) ) ).
fof('$tdef_$_type_66320',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__66320___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__66320___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_34148',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34148___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34148___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26003',axiom,
! [V_24Y] :
( c_24__type__26003___24t(V_24Y)
<=> t(V_24Y,c_24__type__26003) ) ).
fof('$tdef_$_type_2040',axiom,
! [V_24Y] :
( c_24__type__2040___24t(V_24Y)
<=> t(V_24Y,c_24__type__2040) ) ).
fof('$tdef_$_type_22327',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__22327___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__22327___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_$_type_101',axiom,
! [V_24Y] :
( c_24__type__101___24t(V_24Y)
<=> t(V_24Y,c_24__type__101) ) ).
fof('$tdef_$_type_31450',axiom,
! [V_24Y] :
( c_24__type__31450___24t(V_24Y)
<=> t(V_24Y,c_24__type__31450) ) ).
fof('$tdef_$_type_31768',axiom,
! [V_24Y] :
( c_24__type__31768___24t(V_24Y)
<=> t(V_24Y,c_24__type__31768) ) ).
fof('$tdef_$_type_22690',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22690___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22690___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_20127',axiom,
! [V_24Y] :
( c_24__type__20127___24t(V_24Y)
<=> t(V_24Y,c_24__type__20127) ) ).
fof('$tdef_$_type_31622',axiom,
! [V_24Y] :
( c_24__type__31622___24t(V_24Y)
<=> t(V_24Y,c_24__type__31622) ) ).
fof('$tdef_$_type_179',axiom,
! [V_24Y] :
( c_24__type__179___24t(V_24Y)
<=> t(V_24Y,c_24__type__179) ) ).
fof('$tdef_$_type_71814',axiom,
! [V_24Y] :
( c_24__type__71814___24t(V_24Y)
<=> t(V_24Y,c_24__type__71814) ) ).
fof('$tdef_$_type_67840',axiom,
! [V_24Y] :
( c_24__type__67840___24t(V_24Y)
<=> t(V_24Y,c_24__type__67840) ) ).
fof('$tdef_$_type_20432',axiom,
! [V_24Y] :
( c_24__type__20432___24t(V_24Y)
<=> t(V_24Y,c_24__type__20432) ) ).
fof('$tdef_$_type_71311',axiom,
! [V_24Y] :
( c_24__type__71311___24t(V_24Y)
<=> t(V_24Y,c_24__type__71311) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_30650',axiom,
! [V_24Y] :
( c_24__type__30650___24t(V_24Y)
<=> t(V_24Y,c_24__type__30650) ) ).
fof('$tdef_$_type_25972',axiom,
! [V_24Y] :
( c_24__type__25972___24t(V_24Y)
<=> t(V_24Y,c_24__type__25972) ) ).
fof('$tdef_$_type_26021',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26021___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26021___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_18961',axiom,
! [V_24X1,V_24Y] :
( c_24__type__18961___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__18961___24a1(V_24X1)) ) ).
fof('$tdef_$_type_25965',axiom,
! [V_24Y] :
( c_24__type__25965___24t(V_24Y)
<=> t(V_24Y,c_24__type__25965) ) ).
fof('$tdef_$_type_30976',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__30976___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__30976___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.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_25829',axiom,
! [V_24Y] :
( c_24__type__25829___24t(V_24Y)
<=> t(V_24Y,c_24__type__25829) ) ).
fof('$tdef_$_type_22084',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__22084___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__22084___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_48957',axiom,
! [V_24Y] :
( c_24__type__48957___24t(V_24Y)
<=> t(V_24Y,c_24__type__48957) ) ).
fof('$tdef_$_type_20303',axiom,
! [V_24Y] :
( c_24__type__20303___24t(V_24Y)
<=> t(V_24Y,c_24__type__20303) ) ).
fof('$tdef_$_type_65305',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__65305___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__65305___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_899',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__899___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__899___24a2(V_24X1,V_24X2)) ) ).
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_$_type_72',axiom,
! [V_24Y] :
( c_24__type__72___24t(V_24Y)
<=> t(V_24Y,c_24__type__72) ) ).
fof('$tdef_$_type_18953',axiom,
! [V_24Y] :
( c_24__type__18953___24t(V_24Y)
<=> t(V_24Y,c_24__type__18953) ) ).
fof('$tdef_$_type_74873',axiom,
! [V_24Y] :
( c_24__type__74873___24t(V_24Y)
<=> t(V_24Y,c_24__type__74873) ) ).
fof('$tdef_$_type_29915',axiom,
! [V_24Y] :
( c_24__type__29915___24t(V_24Y)
<=> t(V_24Y,c_24__type__29915) ) ).
fof('$tdef_$_type_20131',axiom,
! [V_24Y] :
( c_24__type__20131___24t(V_24Y)
<=> t(V_24Y,c_24__type__20131) ) ).
fof('$tdef_Coq.Reals.RList.Rlist',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRList_2eRlist___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRList_2eRlist) ) ).
fof('$tdef_$_type_610',axiom,
! [V_24Y] :
( c_24__type__610___24t(V_24Y)
<=> t(V_24Y,c_24__type__610) ) ).
fof('$tdef_$_type_15768',axiom,
! [V_24Y] :
( c_24__type__15768___24t(V_24Y)
<=> t(V_24Y,c_24__type__15768) ) ).
fof('$tdef_$_type_71937',axiom,
! [V_24Y] :
( c_24__type__71937___24t(V_24Y)
<=> t(V_24Y,c_24__type__71937) ) ).
fof('$tdef_$_type_26617',axiom,
! [V_24Y] :
( c_24__type__26617___24t(V_24Y)
<=> t(V_24Y,c_24__type__26617) ) ).
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_$_type_32447',axiom,
! [V_24Y] :
( c_24__type__32447___24t(V_24Y)
<=> t(V_24Y,c_24__type__32447) ) ).
fof('$tdef_$_type_18966',axiom,
! [V_24Y] :
( c_24__type__18966___24t(V_24Y)
<=> t(V_24Y,c_24__type__18966) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_34819',axiom,
! [V_24Y] :
( c_24__type__34819___24t(V_24Y)
<=> t(V_24Y,c_24__type__34819) ) ).
fof('$tdef_$_type_877',axiom,
! [V_24Y] :
( c_24__type__877___24t(V_24Y)
<=> t(V_24Y,c_24__type__877) ) ).
fof('$tdef_$_type_76398',axiom,
! [V_24Y] :
( c_24__type__76398___24t(V_24Y)
<=> t(V_24Y,c_24__type__76398) ) ).
fof('$tdef_$_type_71884',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__71884___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__71884___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_25406',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__25406___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__25406___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_19617',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19617___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19617___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_70096',axiom,
! [V_24Y] :
( c_24__type__70096___24t(V_24Y)
<=> t(V_24Y,c_24__type__70096) ) ).
fof('$tdef_$_type_20118',axiom,
! [V_24Y] :
( c_24__type__20118___24t(V_24Y)
<=> t(V_24Y,c_24__type__20118) ) ).
fof('$tdef_$_type_23568',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__23568___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__23568___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_51705',axiom,
! [V_24Y] :
( c_24__type__51705___24t(V_24Y)
<=> t(V_24Y,c_24__type__51705) ) ).
fof('$tdef_$_type_33406',axiom,
! [V_24Y] :
( c_24__type__33406___24t(V_24Y)
<=> t(V_24Y,c_24__type__33406) ) ).
fof('$tdef_$_type_30595',axiom,
! [V_24Y] :
( c_24__type__30595___24t(V_24Y)
<=> t(V_24Y,c_24__type__30595) ) ).
fof('$tdef_$_type_23763',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__23763___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__23763___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_34344',axiom,
! [V_24Y] :
( c_24__type__34344___24t(V_24Y)
<=> t(V_24Y,c_24__type__34344) ) ).
fof('$tdef_$_type_2600',axiom,
! [V_24Y] :
( c_24__type__2600___24t(V_24Y)
<=> t(V_24Y,c_24__type__2600) ) ).
fof('$tdef_$_type_98673',axiom,
! [V_24Y] :
( c_24__type__98673___24t(V_24Y)
<=> t(V_24Y,c_24__type__98673) ) ).
fof('$tdef_$_type_25942',axiom,
! [V_24Y] :
( c_24__type__25942___24t(V_24Y)
<=> t(V_24Y,c_24__type__25942) ) ).
fof('$tdef_$_type_18930',axiom,
! [V_24Y] :
( c_24__type__18930___24t(V_24Y)
<=> t(V_24Y,c_24__type__18930) ) ).
fof('$tdef_$_type_25771',axiom,
! [V_24Y] :
( c_24__type__25771___24t(V_24Y)
<=> t(V_24Y,c_24__type__25771) ) ).
fof('$tdef_$_type_31521',axiom,
! [V_24Y] :
( c_24__type__31521___24t(V_24Y)
<=> t(V_24Y,c_24__type__31521) ) ).
fof('$tdef_$_type_32437',axiom,
! [V_24Y] :
( c_24__type__32437___24t(V_24Y)
<=> t(V_24Y,c_24__type__32437) ) ).
fof('$tdef_$_type_26014',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26014___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26014___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_26554',axiom,
! [V_24Y] :
( c_24__type__26554___24t(V_24Y)
<=> t(V_24Y,c_24__type__26554) ) ).
fof('$tdef_$_type_30673',axiom,
! [V_24Y] :
( c_24__type__30673___24t(V_24Y)
<=> t(V_24Y,c_24__type__30673) ) ).
fof('$tdef_$_type_20306',axiom,
! [V_24Y] :
( c_24__type__20306___24t(V_24Y)
<=> t(V_24Y,c_24__type__20306) ) ).
fof('$tdef_$_type_31633',axiom,
! [V_24Y] :
( c_24__type__31633___24t(V_24Y)
<=> t(V_24Y,c_24__type__31633) ) ).
fof('$tdef_$_type_21254',axiom,
! [V_24Y] :
( c_24__type__21254___24t(V_24Y)
<=> t(V_24Y,c_24__type__21254) ) ).
fof('$tdef_$_type_71172',axiom,
! [V_24Y] :
( c_24__type__71172___24t(V_24Y)
<=> t(V_24Y,c_24__type__71172) ) ).
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_$_type_882',axiom,
! [V_24X1,V_24Y] :
( c_24__type__882___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__882___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20326',axiom,
! [V_24Y] :
( c_24__type__20326___24t(V_24Y)
<=> t(V_24Y,c_24__type__20326) ) ).
fof('$tdef_$_type_20312',axiom,
! [V_24Y] :
( c_24__type__20312___24t(V_24Y)
<=> t(V_24Y,c_24__type__20312) ) ).
fof('$tdef_$_type_20437',axiom,
! [V_24Y] :
( c_24__type__20437___24t(V_24Y)
<=> t(V_24Y,c_24__type__20437) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30513',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30513___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30513___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34401',axiom,
! [V_24Y] :
( c_24__type__34401___24t(V_24Y)
<=> t(V_24Y,c_24__type__34401) ) ).
fof('$tdef_$_type_21186',axiom,
! [V_24Y] :
( c_24__type__21186___24t(V_24Y)
<=> t(V_24Y,c_24__type__21186) ) ).
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_$_type_22717',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22717___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22717___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32425',axiom,
! [V_24Y] :
( c_24__type__32425___24t(V_24Y)
<=> t(V_24Y,c_24__type__32425) ) ).
fof('$tdef_$_type_31151',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__31151___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__31151___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_62',axiom,
! [V_24Y] :
( c_24__type__62___24t(V_24Y)
<=> t(V_24Y,c_24__type__62) ) ).
fof('$tdef_$_type_72005',axiom,
! [V_24Y] :
( c_24__type__72005___24t(V_24Y)
<=> t(V_24Y,c_24__type__72005) ) ).
fof('$tdef_$_type_21220',axiom,
! [V_24Y] :
( c_24__type__21220___24t(V_24Y)
<=> t(V_24Y,c_24__type__21220) ) ).
fof('$tdef_$_type_75033',axiom,
! [V_24Y] :
( c_24__type__75033___24t(V_24Y)
<=> t(V_24Y,c_24__type__75033) ) ).
fof('$tdef_$_type_26648',axiom,
! [V_24Y] :
( c_24__type__26648___24t(V_24Y)
<=> t(V_24Y,c_24__type__26648) ) ).
fof('$tdef_$_type_35030',axiom,
! [V_24Y] :
( c_24__type__35030___24t(V_24Y)
<=> t(V_24Y,c_24__type__35030) ) ).
fof('$tdef_$_type_268',axiom,
! [V_24Y] :
( c_24__type__268___24t(V_24Y)
<=> t(V_24Y,c_24__type__268) ) ).
fof('$tdef_$_type_32152',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32152___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32152___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_22579',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22579___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22579___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_76347',axiom,
! [V_24X1,V_24Y] :
( c_24__type__76347___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__76347___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30501',axiom,
! [V_24Y] :
( c_24__type__30501___24t(V_24Y)
<=> t(V_24Y,c_24__type__30501) ) ).
fof('$tdef_$_type_20395',axiom,
! [V_24Y] :
( c_24__type__20395___24t(V_24Y)
<=> t(V_24Y,c_24__type__20395) ) ).
fof('$tdef_$_type_66966',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__66966___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__66966___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_71618',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__71618___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__71618___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30533',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30533___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30533___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18516',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18516___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18516___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_21191',axiom,
! [V_24Y] :
( c_24__type__21191___24t(V_24Y)
<=> t(V_24Y,c_24__type__21191) ) ).
fof('$tdef_$_type_98636',axiom,
! [V_24Y] :
( c_24__type__98636___24t(V_24Y)
<=> t(V_24Y,c_24__type__98636) ) ).
fof('$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_6',axiom,
! [V_24Y] :
( c_24__type__6___24t(V_24Y)
<=> t(V_24Y,c_24__type__6) ) ).
fof('$tdef_$_type_20156',axiom,
! [V_24Y] :
( c_24__type__20156___24t(V_24Y)
<=> t(V_24Y,c_24__type__20156) ) ).
fof('$tdef_$_type_66643',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__66643___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__66643___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_75963',axiom,
! [V_24Y] :
( c_24__type__75963___24t(V_24Y)
<=> t(V_24Y,c_24__type__75963) ) ).
fof('$tdef_$_type_29966',axiom,
! [V_24Y] :
( c_24__type__29966___24t(V_24Y)
<=> t(V_24Y,c_24__type__29966) ) ).
fof('$tdef_$_type_32971',axiom,
! [V_24Y] :
( c_24__type__32971___24t(V_24Y)
<=> t(V_24Y,c_24__type__32971) ) ).
fof('$tdef_$_type_31797',axiom,
! [V_24Y] :
( c_24__type__31797___24t(V_24Y)
<=> t(V_24Y,c_24__type__31797) ) ).
fof('$tdef_$_type_30573',axiom,
! [V_24Y] :
( c_24__type__30573___24t(V_24Y)
<=> t(V_24Y,c_24__type__30573) ) ).
fof('$tdef_$_type_32385',axiom,
! [V_24Y] :
( c_24__type__32385___24t(V_24Y)
<=> t(V_24Y,c_24__type__32385) ) ).
fof('$tdef_$_type_74836',axiom,
! [V_24Y] :
( c_24__type__74836___24t(V_24Y)
<=> t(V_24Y,c_24__type__74836) ) ).
fof('$tdef_$_type_29918',axiom,
! [V_24Y] :
( c_24__type__29918___24t(V_24Y)
<=> t(V_24Y,c_24__type__29918) ) ).
fof('$tdef_$_type_15577',axiom,
! [V_24Y] :
( c_24__type__15577___24t(V_24Y)
<=> t(V_24Y,c_24__type__15577) ) ).
fof('$tdef_$_type_30883',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__30883___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__30883___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34455',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34455___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34455___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23976',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__23976___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__23976___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_38426',axiom,
! [V_24Y] :
( c_24__type__38426___24t(V_24Y)
<=> t(V_24Y,c_24__type__38426) ) ).
fof('$tdef_$_type_1453',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1453___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1453___24a1(V_24X1)) ) ).
fof('$tdef_$_type_72588',axiom,
! [V_24Y] :
( c_24__type__72588___24t(V_24Y)
<=> t(V_24Y,c_24__type__72588) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32206',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__32206___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__32206___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_24615',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__24615___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__24615___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_31628',axiom,
! [V_24Y] :
( c_24__type__31628___24t(V_24Y)
<=> t(V_24Y,c_24__type__31628) ) ).
fof('$tdef_$_type_20329',axiom,
! [V_24Y] :
( c_24__type__20329___24t(V_24Y)
<=> t(V_24Y,c_24__type__20329) ) ).
fof('$tdef_$_type_1598',axiom,
! [V_24Y] :
( c_24__type__1598___24t(V_24Y)
<=> t(V_24Y,c_24__type__1598) ) ).
fof('$tdef_$_type_1415',axiom,
! [V_24Y] :
( c_24__type__1415___24t(V_24Y)
<=> t(V_24Y,c_24__type__1415) ) ).
fof('$tdef_$_type_2445',axiom,
! [V_24Y] :
( c_24__type__2445___24t(V_24Y)
<=> t(V_24Y,c_24__type__2445) ) ).
fof('$tdef_$_type_23142',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__23142___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__23142___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_98171',axiom,
! [V_24Y] :
( c_24__type__98171___24t(V_24Y)
<=> t(V_24Y,c_24__type__98171) ) ).
fof('$tdef_$_type_26150',axiom,
! [V_24Y] :
( c_24__type__26150___24t(V_24Y)
<=> t(V_24Y,c_24__type__26150) ) ).
fof('$tdef_$_type_1185',axiom,
! [V_24Y] :
( c_24__type__1185___24t(V_24Y)
<=> t(V_24Y,c_24__type__1185) ) ).
fof('$tdef_$_type_16921',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16921___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16921___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_146',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__146___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__146___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Reals.PSeries_reg.CVN_r',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2ePSeries__reg_2eCVN__r___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2ePSeries__reg_2eCVN__r___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33411',axiom,
! [V_24Y] :
( c_24__type__33411___24t(V_24Y)
<=> t(V_24Y,c_24__type__33411) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_21830',axiom,
! [V_24Y] :
( c_24__type__21830___24t(V_24Y)
<=> t(V_24Y,c_24__type__21830) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_92',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__92___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__92___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32439',axiom,
! [V_24Y] :
( c_24__type__32439___24t(V_24Y)
<=> t(V_24Y,c_24__type__32439) ) ).
fof('$tdef_$_type_76883',axiom,
! [V_24Y] :
( c_24__type__76883___24t(V_24Y)
<=> t(V_24Y,c_24__type__76883) ) ).
fof('$tdef_$_type_25218',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__25218___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__25218___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_32765',axiom,
! [V_24Y] :
( c_24__type__32765___24t(V_24Y)
<=> t(V_24Y,c_24__type__32765) ) ).
fof('$tdef_$_type_1601',axiom,
! [V_24Y] :
( c_24__type__1601___24t(V_24Y)
<=> t(V_24Y,c_24__type__1601) ) ).
fof('$tdef_$_type_63575',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__63575___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__63575___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_30526',axiom,
! [V_24Y] :
( c_24__type__30526___24t(V_24Y)
<=> t(V_24Y,c_24__type__30526) ) ).
fof('$tdef_$_type_24189',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__24189___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__24189___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_78162',axiom,
! [V_24Y] :
( c_24__type__78162___24t(V_24Y)
<=> t(V_24Y,c_24__type__78162) ) ).
fof('$tdef_$_type_25665',axiom,
! [V_24X1,V_24Y] :
( c_24__type__25665___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__25665___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2',axiom,
! [V_24Y] :
( c_24__type__2___24t(V_24Y)
<=> t(V_24Y,c_24__type__2) ) ).
fof('$tdef_$_type_62002',axiom,
! [V_24Y] :
( c_24__type__62002___24t(V_24Y)
<=> t(V_24Y,c_24__type__62002) ) ).
fof('$tdef_Coq.Reals.RiemannInt.Riemann_integrable',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt_2eRiemann__integrable___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29845',axiom,
! [V_24Y] :
( c_24__type__29845___24t(V_24Y)
<=> t(V_24Y,c_24__type__29845) ) ).
fof('$tdef_$_type_904',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__904___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__904___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_16914',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16914___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16914___24a2(V_24X1,V_24X2)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( cPythagorean_2eis__ucp___24a1(cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,V0__x,V1__y))
=> ? [V3__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r)
& cFermat4_2eArithCompl_2eis__rat___24a1(V3__r)
& p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V3__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V3__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
& V0__x = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cPythagorean_2ep2___24a1(V3__r))
& V1__y = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cPythagorean_2ep2___24a1(V3__r)) ) ) ) ) ).
%------------------------------------------------------------------------------