TPTP Problem File: SEV676+1.p
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%------------------------------------------------------------------------------
% File : SEV676+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - UrysohnsLemma Un incr
% 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 : UrysohnsLemma.Un.incr.p [Kal26]
% Status : Theorem
% Rating : 0.96 v9.3.0
% Syntax : Number of formulae : 3005 (1094 unt; 0 def)
% Number of atoms : 10054 (2079 equ)
% Maximal formula atoms : 76 ( 3 avg)
% Number of connectives : 7179 ( 130 ~; 293 |;1388 &)
% (1072 <=>;4296 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 6 avg)
% Maximal term depth : 19 ( 1 avg)
% Number of predicates : 592 ( 591 usr; 0 prp; 1-15 aty)
% Number of functors : 1563 (1563 usr; 924 con; 0-18 aty)
% Number of variables : 8836 (8254 !; 582 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.nat$38069',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2438069___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__5 )
| ? [Vvar__0___24Anonymous__38070] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38070)
& Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38070)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2438069___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__38095__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__0___24Anonymous__38070,Vv__CANONICAL__5)) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sig$50774',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( c_24__type__50842___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ? [Vvar__2__x__50783] :
( t(Vvar__2__x__50783,Vv__CANONICAL__0)
& c_24__lam__50517___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vvar__2__x__50783)
& happ(Vv__CANONICAL__2,Vv__CANONICAL__5) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,c_24__lam__50517___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5),Vvar__2__x__50783)
& c_24__case__Coq_2eInit_2eSpecif_2esig_2450774___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vvar__2__x__50783 ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sig$51063',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( c_24__type__51101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ? [Vvar__2__x__51072] :
( t(Vvar__2__x__51072,Vv__CANONICAL__0)
& c_24__lam__50608___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vvar__2__x__51072)
& happ(Vv__CANONICAL__3,Vv__CANONICAL__5) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,c_24__lam__50608___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5),Vvar__2__x__51072)
& c_24__case__Coq_2eInit_2eSpecif_2esig_2451063___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vvar__2__x__51072 ) ) ) ) ) ).
fof('$_case_Topology.TopologicalSpaces.TopologicalSpace$49888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__1)
=> ( c_24__type__49944___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ? [Vvar__0__point__set__49889] :
( cType___24t(Vvar__0__point__set__49889)
& ? [Vvar__1__open__49890] :
( c_24__type__49948___24t(Vv__CANONICAL__1,Vvar__0__point__set__49889,Vvar__1__open__49890)
& ! [Vvar__var__2__F__49894__49898] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__49889,Vvar__var__2__F__49894__49898)
=> ( ! [Vvar__var__3__S__49895__49899] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__49889,Vvar__var__3__S__49895__49899)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__49889),Vvar__var__2__F__49894__49898,Vvar__var__3__S__49895__49899)
=> p(happ(Vvar__1__open__49890,Vvar__var__3__S__49895__49899)) ) )
=> p(happ(Vvar__1__open__49890,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__49889,Vvar__var__2__F__49894__49898))) ) )
& ! [Vvar__var__3__U__49903__49907] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__49889,Vvar__var__3__U__49903__49907)
=> ! [Vvar__var__4__V__49904__49908] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__49889,Vvar__var__4__V__49904__49908)
=> ( p(happ(Vvar__1__open__49890,Vvar__var__3__U__49903__49907))
=> ( p(happ(Vvar__1__open__49890,Vvar__var__4__V__49904__49908))
=> p(happ(Vvar__1__open__49890,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__49889,Vvar__var__3__U__49903__49907,Vvar__var__4__V__49904__49908))) ) ) ) )
& p(happ(Vvar__1__open__49890,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__49889)))
& happ(Vv__CANONICAL__2,Vv__CANONICAL__3) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__49889,Vvar__1__open__49890)
& c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2449888___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vvar__0__point__set__49889 ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_2225',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__2225___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_12388',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__12391] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12391)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12391)
& c_24__let__16__mkpow__12388___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__12392] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12392)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12392)
& c_24__let__16__mkpow__12388___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__12388___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_12389',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__12389___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__12388___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_12390',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__12390___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__12388___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_2_C_41463',axiom,
! [V0__U,V1__D] : c_24__let__2__C__41463___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_41607',axiom,
! [V0__U,V1__D] : c_24__let__2__C__41607___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_41753',axiom,
! [V0__U,V1__D] : c_24__let__2__C__41753___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_41956',axiom,
! [V0__U,V1__D] : c_24__let__2__C__41956___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_42115',axiom,
! [V0__U,V1__D] : c_24__let__2__C__42115___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_42249',axiom,
! [V0__U,V1__D] : c_24__let__2__C__42249___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_41464',axiom,
! [V0__U,V1__D] : c_24__let__3__R__41464___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_41608',axiom,
! [V0__U,V1__D] : c_24__let__3__R__41608___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_41754',axiom,
! [V0__U,V1__D] : c_24__let__3__R__41754___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_41957',axiom,
! [V0__U,V1__D] : c_24__let__3__R__41957___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_42116',axiom,
! [V0__U,V1__D] : c_24__let__3__R__42116___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_42250',axiom,
! [V0__U,V1__D] : c_24__let__3__R__42250___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_5_subF_43860',axiom,
! [V0__A,V1__B,V2__T,V3__f,V4__F,V5__a] : c_24__let__5__subF__43860___24a6(V0__A,V1__B,V2__T,V3__f,V4__F,V5__a) = happ(V4__F,happ(V3__f,V5__a)) ).
fof('$_def_$_let_5_subF_43863',axiom,
! [V0__A,V1__B,V2__T,V3__f,V4__F,V5__a] : c_24__let__5__subF__43863___24a6(V0__A,V1__B,V2__T,V3__f,V4__F,V5__a) = happ(V4__F,happ(V3__f,V5__a)) ).
fof('$_def_$_let_6_lmp_1750',axiom,
! [V2__lpe] : c_24__let__6__lmp__1750___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_var_11_x_11500_11550',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11499] : c_24__let__var__11__x__11500__11550___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11499) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11499) ).
fof('$_def_$_let_var_11_x_11503_11551',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11502] : c_24__let__var__11__x__11503__11551___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11502) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11502) ).
fof('$_def_$_let_var_var_12_x_11458_11461_11531',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455] : c_24__let__var__var__12__x__11458__11461__11531___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455) ).
fof('$_def_$_let_var_var_12_x_11471_11474_11537',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468] : c_24__let__var__var__12__x__11471__11474__11537___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468) ).
fof('$_def_$_let_var_var_12_x_11484_11488_11546',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481] : c_24__let__var__var__12__x__11484__11488__11546___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481) ).
fof('$_def_$_let_var_var_12_x_11508_11512_11558',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505] : c_24__let__var__var__12__x__11508__11512__11558___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505) ).
fof('$_def_$_let_var_var_12_x_11525_11527_11562',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11523] : c_24__let__var__var__12__x__11525__11527__11562___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11523) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11523) ).
fof('$_def_$_let_var_var_13_y_11459_11462_11532',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11456] : c_24__let__var__var__13__y__11459__11462__11532___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11456) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11456) ).
fof('$_def_$_let_var_var_13_y_11472_11475_11538',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11469] : c_24__let__var__var__13__y__11472__11475__11538___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11469) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11469) ).
fof('$_def_$_let_var_var_13_y_11485_11489_11547',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11482] : c_24__let__var__var__13__y__11485__11489__11547___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11482) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11482) ).
fof('$_def_$_let_var_var_13_y_11509_11513_11559',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11506] : c_24__let__var__var__13__y__11509__11513__11559___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11506) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11506) ).
fof('$_def_$_let_var_var_14_s1_11486_11490_11548',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482] : c_24__let__var__var__14__s1__11486__11490__11548___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__11484__11488__11546___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__11485__11489__11547___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11482))) ).
fof('$_def_$_let_var_var_14_s1_11510_11514_11560',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506] : c_24__let__var__var__14__s1__11510__11514__11560___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__11508__11512__11558___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__11509__11513__11559___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11506))) ).
fof('$_def_$_let_var_var_14_s_11460_11463_11533',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456] : c_24__let__var__var__14__s__11460__11463__11533___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__11458__11461__11531___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__11459__11462__11532___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11456))) ).
fof('$_def_$_let_var_var_14_s_11473_11476_11539',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469] : c_24__let__var__var__14__s__11473__11476__11539___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__11471__11474__11537___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__11472__11475__11538___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11469))) ).
fof('$_def_$_let_var_var_15_s2_11487_11491_11549',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482] : c_24__let__var__var__15__s2__11487__11491__11549___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__11485__11489__11547___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11482)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__11484__11488__11546___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481))) ).
fof('$_def_$_let_var_var_15_s2_11511_11515_11561',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506] : c_24__let__var__var__15__s2__11511__11515__11561___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__11508__11512__11558___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__11509__11513__11559___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11506))) ).
fof('$_def_Coq.Arith.Compare.le_or_le_S',axiom,
cCoq_2eArith_2eCompare_2ele__or__le__S = cCoq_2eArith_2eCompare__dec_2ele__le__S__dec ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__4915] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4915)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4915)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4916] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4916)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4916)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__4919] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4919)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4919)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__4916,Vvar__0___24Anonymous__4919) ) ) ) ) ) ) ) ) ).
fof('$_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__1451] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1451)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1451)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1451),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__1451)) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.Even',axiom,
! [V0__n] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V0__n)
<=> ? [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
& V0__n = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__m) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.lt_alt',axiom,
! [V0__n,V1__m] :
( cCoq_2eArith_2ePeanoNat_2eNat_2elt__alt___24a2(V0__n,V1__m)
<=> ? [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
& cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),V0__n) = V1__m ) ) ).
fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__5547] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5547)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5547)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__5547,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Bool.Bvector.Bcons',axiom,
cCoq_2eBool_2eBvector_2eBcons = cCoq_2eVectors_2eVectorDef_2econs___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Bvector.Bvector',axiom,
cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__9031] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__9031)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__9031) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__9032] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__9032)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__9032) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.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__1238] :
( t(Vvar__1___24Anonymous__1238,V0__A)
& ? [Vvar__2___24Anonymous__1239] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1239)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1238,Vvar__2___24Anonymous__1239)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1238,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__1239,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__15181] :
( t(Vvar__2___24Anonymous__15181,V0__A)
& ? [Vvar__3___24Anonymous__15182] :
( t(Vvar__3___24Anonymous__15182,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__15181,Vvar__3___24Anonymous__15182)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__15181 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.id',axiom,
! [V0__A,V1__x] : cCoq_2eInit_2eDatatypes_2eid___24a2(V0__A,V1__x) = V1__x ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__1228] :
( t(Vvar__1___24Anonymous__1228,V0__A)
& ? [Vvar__2___24Anonymous__1229] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1229)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1228,Vvar__2___24Anonymous__1229)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__1229)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rec',axiom,
! [V0__P] : cCoq_2eInit_2eDatatypes_2enat__rec___24a1(V0__P) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V0__P) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__4488___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__4486] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4486)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4486)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__4486),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__4486)) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__1185] :
( t(Vvar__2___24Anonymous__1185,V0__A)
& ? [Vvar__3___24Anonymous__1186] :
( t(Vvar__3___24Anonymous__1186,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__1185,Vvar__3___24Anonymous__1186)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__1186 ) ) ) ) ) ).
fof('$_def_Coq.Init.Decimal.nb_digits',axiom,
! [V1__d] :
( cCoq_2eInit_2eDecimal_2euint___24t(V1__d)
=> ( ( V1__d = cCoq_2eInit_2eDecimal_2eNil
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__64968] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64968)
& V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__64968)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64968)) )
| ? [Vvar__0___24Anonymous__64969] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64969)
& V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__64969)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64969)) )
| ? [Vvar__0___24Anonymous__64970] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64970)
& V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__64970)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64970)) )
| ? [Vvar__0___24Anonymous__64971] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64971)
& V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__64971)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64971)) )
| ? [Vvar__0___24Anonymous__64972] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64972)
& V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__64972)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64972)) )
| ? [Vvar__0___24Anonymous__64973] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64973)
& V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__64973)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64973)) )
| ? [Vvar__0___24Anonymous__64974] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64974)
& V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__64974)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64974)) )
| ? [Vvar__0___24Anonymous__64975] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64975)
& V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__64975)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64975)) )
| ? [Vvar__0___24Anonymous__64976] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64976)
& V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__64976)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64976)) )
| ? [Vvar__0___24Anonymous__64977] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__64977)
& V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__64977)
& cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__64977)) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__358] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__358)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__358)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__358,V2__m)) ) ) ) ).
fof('$_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__1691] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1691)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1691)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1691)
& ( ( Vvar__0___24Anonymous__1691 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__1694] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1694)
& Vvar__0___24Anonymous__1691 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1694)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__1694)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.divmod',axiom,
! [V1__x,V2__y,V3__q,V4__u] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ( ( V1__x = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,V3__q,V4__u) )
| ? [Vvar__0___24Anonymous__1678] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1678)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__u)
=> ( V1__x = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1678)
& ( ( V4__u = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eInit_2eNat_2edivmod___24a4(Vvar__0___24Anonymous__1678,V2__y,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V2__y) )
| ? [Vvar__0___24Anonymous__1681] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1681)
& V4__u = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1681)
& cCoq_2eInit_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eInit_2eNat_2edivmod___24a4(Vvar__0___24Anonymous__1678,V2__y,V3__q,Vvar__0___24Anonymous__1681) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.double',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2edouble___24a1(V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V0__n) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__1673] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1673)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1673)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1673)
& ( ( Vvar__0___24Anonymous__1673 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__1676] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1676)
& Vvar__0___24Anonymous__1673 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1676)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__1676) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.gcd',axiom,
! [V1__a,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
| ? [Vvar__0___24Anonymous__439] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__439)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__439)
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__439)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__439)) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__5322] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5322)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5322)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__5322,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__5325] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5325)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5325)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__5322,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__5325) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.ltb',axiom,
! [V0__n,V1__m] : cCoq_2eInit_2eNat_2eltb___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eleb___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__498] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__498)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__498)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__501] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__501)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__501)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__498,Vvar__0___24Anonymous__501)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__504] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__504)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__504)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__507] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__507)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__507)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__504,Vvar__0___24Anonymous__507)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__9,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.odd',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eNat_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__367] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__367)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__367)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__367)) ) ) ) ).
fof('$_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__437] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__437)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__437)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__437 ) ) ) ).
fof('$_def_Coq.Init.Nat.sqrt',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esqrt___24a1(V0__n) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V0__n,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Coq.Init.Nat.sqrt_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__514] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__514)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__514)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__514,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q)),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q))) )
| ? [Vvar__0___24Anonymous__517] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__517)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__517)
& cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__514,V2__p,V3__q,Vvar__0___24Anonymous__517) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__361] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__361)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__361)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__364] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__364)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__364)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__361,Vvar__0___24Anonymous__364) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.tail_add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__5314] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5314)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5314)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__5314,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__370] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__370)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__370)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__370) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_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('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__32518___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__32512] :
( t(Vvar__2__x__32512,V0__A)
& p(happ(V1__P,Vvar__2__x__32512))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__32512)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__32512 ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Specif.sig_rect',axiom,
! [V0__A,V1__P,V2__P,V3__f,V4__s] :
( cType___24t(V0__A)
=> ( c_24__type__45777___24t(V0__A,V1__P,V2__P,V1__P)
=> ( c_24__type__45785___24t(V0__A,V1__P,V2__P,V2__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
=> ? [Vvar__2__x__45769] :
( t(Vvar__2__x__45769,V0__A)
& p(happ(V1__P,Vvar__2__x__45769))
& V4__s = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__45769)
& cCoq_2eInit_2eSpecif_2esig__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(V3__f,Vvar__2__x__45769) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.seq',axiom,
! [V1__start,V2__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__len)
=> ( ( V2__len = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__1582] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1582)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1582)
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__start,cCoq_2eLists_2eList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),Vvar__0___24Anonymous__1582)) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalDependentChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__529___24t(V0__A,V1__R)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__R,V2__x),V3__y)) ) )
=> ! [V3__x0] :
( t(V3__x0,V0__A)
=> ? [V4__f] :
( c_24__type__1737___24t(V0__A,V4__f)
& happ(V4__f,cCoq_2eInit_2eDatatypes_2eO) = V3__x0
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> p(happ(happ(V1__R,happ(V4__f,V5__n)),happ(V4__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__n)))) ) ) ) ) ) ) ).
fof('$_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__3125] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3125)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3125)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__3128] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3128)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3128)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__3125,Vvar__0___24Anonymous__3128)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__25322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25322)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25322)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25322)
& ( ? [Vvar__0___24Anonymous__25326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25326)
& Vvar__0___24Anonymous__25322 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25326)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25326) )
| ? [Vvar__0___24Anonymous__25327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25327)
& Vvar__0___24Anonymous__25322 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25327)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25327) )
| ( Vvar__0___24Anonymous__25322 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__3167] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3167)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3167)
& ( ( 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__3170] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3170)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3170)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__3167,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__3124] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3124)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3124)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3124)) ) ) ) ).
fof('$_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__3156] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3156)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3156)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__3157] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3157)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3157)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__3160] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3160)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3160)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__3157,Vvar__0___24Anonymous__3160) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__3142] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3142)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3142)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__3145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3145)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3145)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3142,Vvar__0___24Anonymous__3145)) ) ) ) ) ) ) ) ).
fof('$_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__3184] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3184)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3184)
& 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__3184)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__3121] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3121)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3121)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3121)) ) ) ) ).
fof('$_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__8993] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8993)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__8993)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__8993) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__9030] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9030)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9030)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__9030)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__3699] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3699)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3699)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__3699)) )
| ? [Vvar__0___24Anonymous__3700] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3700)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3700)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__3700)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_def_Coq.Reals.AltSeries.positivity_seq',axiom,
! [V0__Un] :
( cCoq_2eReals_2eAltSeries_2epositivity__seq___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V0__Un,V1__n))) ) ) ).
fof('$_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('$_def_Coq.Reals.RIneq.pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> ? [Vvar__0__pos__35551] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__35551)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__35551))
& V0__p = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__35551)
& cCoq_2eReals_2eRIneq_2epos___24a1(V0__p) = Vvar__0__pos__35551 ) ) ).
fof('$_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__45370] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__45370)
& ? [Vvar__1___24Anonymous__45371] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__45371)
& V2__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__45370,Vvar__1___24Anonymous__45371)
& ( cCoq_2eReals_2eRList_2eIn___24a2(V1__x,V2__l)
<=> ( V1__x = Vvar__0___24Anonymous__45370
| cCoq_2eReals_2eRList_2eIn___24a2(V1__x,Vvar__1___24Anonymous__45371) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.Rlength',axiom,
! [V1__l] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2eRlength___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__45377] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__45377)
& ? [Vvar__1___24Anonymous__45378] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__45378)
& V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__45377,Vvar__1___24Anonymous__45378)
& cCoq_2eReals_2eRList_2eRlength___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eReals_2eRList_2eRlength___24a1(Vvar__1___24Anonymous__45378)) ) ) ) ) ).
fof('$_def_Coq.Reals.RList.ordered_Rlist',axiom,
! [V0__l] :
( cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V0__l)
<=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__i,cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eReals_2eRList_2eRlength___24a1(V0__l))))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRList_2epos__Rl___24a2(V0__l,V1__i),cCoq_2eReals_2eRList_2epos__Rl___24a2(V0__l,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__i)))) ) ) ) ).
fof('$_def_Coq.Reals.RList.pos_Rl',axiom,
! [V1__l,V2__i] :
( cCoq_2eReals_2eRList_2eRlist___24t(V1__l)
=> ( ( V1__l = cCoq_2eReals_2eRList_2enil
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__45383] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__45383)
& ? [Vvar__1___24Anonymous__45384] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__45384)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ( V1__l = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__45383,Vvar__1___24Anonymous__45384)
& ( ( V2__i = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = Vvar__0___24Anonymous__45383 )
| ? [Vvar__0___24Anonymous__45390] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45390)
& V2__i = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45390)
& cCoq_2eReals_2eRList_2epos__Rl___24a2(V1__l,V2__i) = cCoq_2eReals_2eRList_2epos__Rl___24a2(Vvar__1___24Anonymous__45384,Vvar__0___24Anonymous__45390) ) ) ) ) ) ) ) ) ).
fof('$_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.fct_cte',axiom,
! [V0__a,V1__x] : cCoq_2eReals_2eRanalysis1_2efct__cte___24a2(V0__a,V1__x) = V0__a ).
fof('$_def_Coq.Reals.Ranalysis1.mult_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2emult__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Ranalysis1.plus_fct',axiom,
! [V0__f1,V1__f2,V2__x] : cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V0__f1,V1__f2,V2__x) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(V0__f1,V2__x),happ(V1__f2,V2__x)) ).
fof('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__1753] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1753)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1753)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1753)
& ( ( Vvar__0___24Anonymous__1753 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__1756] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1756)
& Vvar__0___24Anonymous__1753 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1756)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__1753),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_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__35440___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__35441___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V0__x ) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmin',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__18344___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V0__x )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__18345___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V1__y ) ) ) ) ).
fof('$_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__1779] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1779)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1779)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__1779) )
| ? [Vvar__0___24Anonymous__1780] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1780)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1780)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__1780)) ) ) ) ).
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.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('$_def_Coq.Reals.Rfunctions.infinite_sum',axiom,
! [V0__s,V1__l] :
( cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V0__s,V1__l)
<=> ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V4__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__N)
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__s,V5__n),V1__l),V2__eps)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rfunctions.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__18620] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18620)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18620)
& 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__18620),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18620))) ) ) ) ).
fof('$_def_Coq.Reals.Rfunctions.sum_nat_f_O',axiom,
! [V1__f,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V1__f,V2__n) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__65005] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__65005)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__65005)
& cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V1__f,V2__n) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V1__f,Vvar__0___24Anonymous__65005),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__65005))) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.Nbound',axiom,
! [V0__I] :
( cCoq_2eReals_2eRiemannInt__SF_2eNbound___24a1(V0__I)
<=> ? [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
& ! [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ( p(happ(V0__I,V2__i))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V2__i,V1__n)) ) ) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.co_interval',axiom,
! [V0__a,V1__b,V2__x] :
( cCoq_2eReals_2eRiemannInt__SF_2eco__interval___24a3(V0__a,V1__b,V2__x)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V2__x))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__x,V1__b)) ) ) ).
fof('$_def_Coq.Reals.RiemannInt_SF.fe',axiom,
! [V0__a,V1__b,V2__s] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(V0__a,V1__b,V2__s)
=> ? [Vvar__2__fe__45509] :
( c_24__type__45482___24t(V0__a,V1__b,Vvar__2__fe__45509)
& ? [Vvar__3__pre__45512] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vvar__2__fe__45509,V0__a,V1__b,Vvar__3__pre__45512)
& V2__s = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(V0__a,V1__b,Vvar__2__fe__45509,Vvar__3__pre__45512)
& cCoq_2eReals_2eRiemannInt__SF_2efe___24a3(V0__a,V1__b,V2__s) = Vvar__2__fe__45509 ) ) ) ) ) ).
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.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__2630] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2630)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2630)
& 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__2630)) ) ) ) ).
fof('$_def_Coq.Reals.Rprod.prod_f_R0',axiom,
! [V1__f,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,V2__N) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__65010] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__65010)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__65010)
& cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,V2__N) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRprod_2eprod__f__R0___24a2(V1__f,Vvar__0___24Anonymous__65010),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__65010))) ) ) ) ).
fof('$_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('$_def_Coq.Reals.Rseries.Pser',axiom,
! [V0__An,V1__x,V2__l] :
( cCoq_2eReals_2eRseries_2ePser___24a3(V0__An,V1__x,V2__l)
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(c_24__lam__45144___24a2(V0__An,V1__x),V2__l) ) ).
fof('$_def_Coq.Reals.Rseries.Rmax_N',axiom,
! [V0__Un,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRseries_2eRmax__N___24a2(V0__Un,V2__N) = happ(V0__Un,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__65013] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__65013)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__65013)
& cCoq_2eReals_2eRseries_2eRmax__N___24a2(V0__Un,V2__N) = cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__65013)),cCoq_2eReals_2eRseries_2eRmax__N___24a2(V0__Un,Vvar__0___24Anonymous__65013)) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.Un_cv',axiom,
! [V0__Un,V1__l] :
( cCoq_2eReals_2eRseries_2eUn__cv___24a2(V0__Un,V1__l)
<=> ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V4__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__N)
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(happ(V0__Un,V5__n),V1__l),V2__eps)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rseries.Un_growing',axiom,
! [V0__Un] :
( cCoq_2eReals_2eRseries_2eUn__growing___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,V1__n),happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)))) ) ) ).
fof('$_def_Coq.Reals.SeqProp.Un_decreasing',axiom,
! [V0__Un] :
( cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V0__Un)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V0__Un,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)),happ(V0__Un,V1__n))) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__529___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Sets.Cpo.Conditionally_complete_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eConditionally__complete__rec___24a2(V0__U,V1__D) = c_24__lam__42253___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Conditionally_complete_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a2(V0__U,V1__D) = c_24__generic__case__42158 ).
fof('$_def_Coq.Sets.Cpo.Directed_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eDirected__rec___24a2(V0__U,V1__D) = c_24__lam__41963___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Directed_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eDirected__rect___24a2(V0__U,V1__D) = c_24__generic__case__41821 ).
fof('$_def_Coq.Sets.Cpo.Totally_ordered_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eTotally__ordered__rec___24a2(V0__U,V1__D) = c_24__lam__41614___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Totally_ordered_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a2(V0__U,V1__D) = c_24__generic__case__41512 ).
fof('$_def_Coq.Sets.Ensembles.Add',axiom,
! [V0__U,V1__B,V2__x] : cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__B,V2__x) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__x)) ).
fof('$_def_Coq.Sets.Ensembles.Complement',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eComplement___24a3(V0__U,V1__A,V2__x)
<=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x) ) ).
fof('$_def_Coq.Sets.Ensembles.Ensemble',axiom,
! [V0__U] : cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U) = c_24__type__8715___24a1(V0__U) ).
fof('$_def_Coq.Sets.Ensembles.In',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x)
<=> p(happ(V1__A,V2__x)) ) ).
fof('$_def_Coq.Sets.Ensembles.Included',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Same_set',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__B,V2__C)
<=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__C,V1__B) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Setminus',axiom,
! [V0__U,V1__B,V2__C,V3__x] :
( cCoq_2eSets_2eEnsembles_2eSetminus___24a4(V0__U,V1__B,V2__C,V3__x)
<=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Strict_Included',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__B,V2__C)
<=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
& V1__B != V2__C ) ) ).
fof('$_def_Coq.Sets.Ensembles.Subtract',axiom,
! [V0__U,V1__B,V2__x] : cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__B,V2__x) = cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V1__B,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__x)) ).
fof('$_def_Coq.Sets.Partial_Order.Carrier_of',axiom,
! [V0__U,V1__p] :
( cType___24t(V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ? [Vvar__1__Carrier__of__45210] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,Vvar__1__Carrier__of__45210)
& ? [Vvar__2__Rel__of__45211] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,Vvar__2__Rel__of__45211)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,Vvar__1__Carrier__of__45210)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(V0__U,Vvar__2__Rel__of__45211)
& V1__p = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V0__U,Vvar__1__Carrier__of__45210,Vvar__2__Rel__of__45211)
& cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__p) = Vvar__1__Carrier__of__45210 ) ) ) ) ).
fof('$_def_Coq.Sets.Partial_Order.Rel_of',axiom,
! [V0__U,V1__p] :
( cType___24t(V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ? [Vvar__1__Carrier__of__45225] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,Vvar__1__Carrier__of__45225)
& ? [Vvar__2__Rel__of__45226] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,Vvar__2__Rel__of__45226)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,Vvar__1__Carrier__of__45225)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(V0__U,Vvar__2__Rel__of__45226)
& V1__p = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V0__U,Vvar__1__Carrier__of__45225,Vvar__2__Rel__of__45226)
& cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__p) = Vvar__2__Rel__of__45226 ) ) ) ) ).
fof('$_def_Coq.Sets.Partial_Order.Strict_Rel_of',axiom,
! [V0__U,V1__p,V2__x,V3__y] :
( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V2__x,V3__y)
<=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__p,V2__x,V3__y)
& V2__x != V3__y ) ) ).
fof('$_def_Coq.Sets.Powerset.Power_set_PO',axiom,
! [V0__U,V1__A] : cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a5(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__Inhabited___24a2(V0__U,V1__A),cCoq_2eSets_2ePowerset_2eInclusion__is__an__order___24a1(V0__U)) ).
fof('$_def_Coq.Sets.Relations_1.Antisymmetric',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Sets.Relations_1.Reflexive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__529___24a1(V0__U) ).
fof('$_def_Coq.Sets.Relations_1.Transitive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Sets.Relations_1.contains',axiom,
! [V0__U,V1__R,V2__R_27] :
( cCoq_2eSets_2eRelations__1_2econtains___24a3(V0__U,V1__R,V2__R_27)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__y] :
( t(V4__y,V0__U)
=> ( p(happ(happ(V2__R_27,V3__x),V4__y))
=> p(happ(happ(V1__R,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Strings.String.length',axiom,
! [V1__s] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s)
=> ( ( V1__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2elength___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__2766] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__2766)
& ? [Vvar__1___24Anonymous__2767] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__2767)
& V1__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__2766,Vvar__1___24Anonymous__2767)
& cCoq_2eStrings_2eString_2elength___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eStrings_2eString_2elength___24a1(Vvar__1___24Anonymous__2767)) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.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.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__4355] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4355)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4355)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__4359] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4359)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4359)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4355,Vvar__0___24Anonymous__4359)) )
| ? [Vvar__0___24Anonymous__4360] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4360)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4360)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__4355,Vvar__0___24Anonymous__4360) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4361] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4361)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4361)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__4365] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4365)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4365)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__4365,Vvar__0___24Anonymous__4361) )
| ? [Vvar__0___24Anonymous__4366] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4366)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4366)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4361,Vvar__0___24Anonymous__4366)) ) ) ) ) ) ) ) ).
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__4388] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4388)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4388)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__4389] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4389)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4389)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__4390] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4390)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4390)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__4394] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4394)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4394)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__4390,Vvar__0___24Anonymous__4394) )
| ? [Vvar__0___24Anonymous__4395] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4395)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4395)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__4396] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4396)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4396)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__4400] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4400)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4400)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__4401] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4401)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4401)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__4396,Vvar__0___24Anonymous__4401)) ) ) ) ) ) ) ) ).
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__4375] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4375)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4375)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__4379] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4379)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4379)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4375,Vvar__0___24Anonymous__4379)) )
| ? [Vvar__0___24Anonymous__4380] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4380)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4380)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4375,Vvar__0___24Anonymous__4380)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4381] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4381)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4381)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__4385] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4385)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4385)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4381,Vvar__0___24Anonymous__4385)) )
| ? [Vvar__0___24Anonymous__4386] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4386)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4386)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4381,Vvar__0___24Anonymous__4386)) ) ) ) ) ) ) ) ).
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__4405] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4405)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4405)
& 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__4405)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__4370] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4370)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4370)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4370) )
| ? [Vvar__0___24Anonymous__4371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4371)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4371)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4371) ) ) ) ).
fof('$_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__4411] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4411)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4411)
& ( ( 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__4421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4421)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4411)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4421)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4421)
& ? [Vvar__2___24Anonymous__4429] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__4429)
& ? [Vvar__3___24Anonymous__4430] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__4430)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__4411,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4421)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__4429,Vvar__3___24Anonymous__4430)
& 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__4429),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__4430)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4432)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4411)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4432)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4432)
& ? [Vvar__2___24Anonymous__4440] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__4440)
& ? [Vvar__3___24Anonymous__4441] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__4441)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__4411,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4432)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__4440,Vvar__3___24Anonymous__4441)
& 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__4440)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__4441)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4443] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4443)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4443)
& ( ( 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__4453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4453)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4443)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4453)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4453)
& ? [Vvar__2___24Anonymous__4461] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__4461)
& ? [Vvar__3___24Anonymous__4462] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__4462)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__4443,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4453)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__4461,Vvar__3___24Anonymous__4462)
& 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__4461)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__4462))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4464] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4464)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4443)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4464)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4464)
& ? [Vvar__2___24Anonymous__4472] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__4472)
& ? [Vvar__3___24Anonymous__4473] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__4473)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__4443,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4464)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__4472,Vvar__3___24Anonymous__4473)
& 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__4472),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__4473))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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.micromega.QMicromega.QWitness',axiom,
! [Vvar__18255] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__18255)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__18255) ) ).
fof('$_def_Coq.micromega.RMicromega.RTautoChecker',axiom,
! [V0__f,V1__w] : cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V0__f,V1__w) = cCoq_2emicromega_2eTauto_2etauto__checker___24a11(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit,cCoq_2emicromega_2eRMicromega_2erunsat,cCoq_2emicromega_2eRMicromega_2erdeduce,cCoq_2emicromega_2eRMicromega_2eRnormalise___24a1(cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRMicromega_2eRnegate___24a1(cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRMicromega_2eRWitness,c_24__lam__35677,cCoq_2emicromega_2eTauto_2emap__bformula___24a7(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2emicromega_2eRingMicromega_2emap__Formula___24a3(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2emicromega_2eRMicromega_2eRcst,cCoq_2emicromega_2eRMicromega_2eQ__of__Rcst),V0__f),V1__w) ).
fof('$_def_Coq.micromega.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__49423] :
( t(Vvar__1___24Anonymous__49423,V0__A)
& V3__vm = cCoq_2emicromega_2eVarMap_2eElt___24a2(V0__A,Vvar__1___24Anonymous__49423)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__1___24Anonymous__49423 )
| ? [Vvar__1___24Anonymous__49425] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__1___24Anonymous__49425)
& ? [Vvar__2___24Anonymous__49426] :
( t(Vvar__2___24Anonymous__49426,V0__A)
& ? [Vvar__3___24Anonymous__49427] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__3___24Anonymous__49427)
& ( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> ( V3__vm = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V0__A,Vvar__1___24Anonymous__49425,Vvar__2___24Anonymous__49426,Vvar__3___24Anonymous__49427)
& ( ? [Vvar__0___24Anonymous__49440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__49440)
& V4__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__49440)
& 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__49427,Vvar__0___24Anonymous__49440) )
| ? [Vvar__0___24Anonymous__49441] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__49441)
& V4__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__49441)
& 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__49425,Vvar__0___24Anonymous__49441) )
| ( V4__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__2___24Anonymous__49426 ) ) ) ) ) ) ) ) ) ) ) ).
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__10703] :
( t(Vvar__1___24Anonymous__10703,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__10703)
& 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__10703) )
| ? [Vvar__1___24Anonymous__10705] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10705)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__10705)
& 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__10705,V15__l) )
| ? [Vvar__1___24Anonymous__10707] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10707)
& ? [Vvar__2___24Anonymous__10708] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10708)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__10707,Vvar__2___24Anonymous__10708)
& 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__10707)),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__10708)) ) )
| ? [Vvar__1___24Anonymous__10711] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10711)
& ? [Vvar__2___24Anonymous__10712] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10712)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__10711,Vvar__2___24Anonymous__10712)
& 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__10711)),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__10712)) ) )
| ? [Vvar__1___24Anonymous__10715] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10715)
& ? [Vvar__2___24Anonymous__10716] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10716)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__10715,Vvar__2___24Anonymous__10716)
& 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__10715)),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__10716)) ) )
| ? [Vvar__1___24Anonymous__10719] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10719)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__10719)
& 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__10719)) )
| ? [Vvar__1___24Anonymous__10721] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10721)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__10721)
& 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__10721)) )
| ? [Vvar__1___24Anonymous__10723] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10723)
& ? [Vvar__2___24Anonymous__10724] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__10724)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__10723,Vvar__2___24Anonymous__10724)
& 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__10723)),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__10724)) ) )
| ? [Vvar__1___24Anonymous__10727] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__10727)
& ? [Vvar__2___24Anonymous__10728] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__10728)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__10727,Vvar__2___24Anonymous__10728)
& 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__10727)),happ(V12__Cp__phi,Vvar__2___24Anonymous__10728)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__16057] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__16057)
& ? [Vvar__2___24Anonymous__16058] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__16058)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__16057,Vvar__2___24Anonymous__16058)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__16057),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__16058,V4__m)) ) ) ) ) ) ).
fof('$_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__11451] :
( t(Vvar__1___24Anonymous__11451,V0__C)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V0__C,Vvar__1___24Anonymous__11451)
& 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__11451),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__11453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__11453)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V0__C,Vvar__1___24Anonymous__11453)
& 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__11453),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__11455] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__11455)
& ? [Vvar__2___24Anonymous__11456] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__11456)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V0__C,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456)
& 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__11458__11461__11531___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__11460__11463__11533___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456))),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__11459__11462__11532___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11456)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__11460__11463__11533___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456)))),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__11460__11463__11533___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456)),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__11460__11463__11533___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__11460__11463__11533___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455,Vvar__2___24Anonymous__11456)))),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__11458__11461__11531___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11455)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__11459__11462__11532___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11456)))) ) )
| ? [Vvar__1___24Anonymous__11468] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__11468)
& ? [Vvar__2___24Anonymous__11469] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__11469)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V0__C,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469)
& 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__11471__11474__11537___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__11473__11476__11539___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469))),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__11472__11475__11538___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11469)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__11473__11476__11539___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469)))),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__11473__11476__11539___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469)),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__11473__11476__11539___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__11473__11476__11539___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468,Vvar__2___24Anonymous__11469)))),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__11471__11474__11537___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11468)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__11472__11475__11538___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11469)))) ) )
| ? [Vvar__1___24Anonymous__11481] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__11481)
& ? [Vvar__2___24Anonymous__11482] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__11482)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V0__C,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482)
& 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__11486__11490__11548___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__15__s2__11487__11491__11549___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482))),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__11487__11491__11549___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__11486__11490__11548___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481,Vvar__2___24Anonymous__11482))),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__11484__11488__11546___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11481)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__11485__11489__11547___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11482)))) ) )
| ? [Vvar__1___24Anonymous__11499] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__11499)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V0__C,Vvar__1___24Anonymous__11499)
& 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__11500__11550___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11499))),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__11__x__11500__11550___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11499)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__11500__11550___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11499))) )
| ? [Vvar__1___24Anonymous__11502] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__11502)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V0__C,Vvar__1___24Anonymous__11502)
& 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__11503__11551___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11502)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__11503__11551___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11502)),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__11503__11551___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11502)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__11503__11551___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11502)))) )
| ? [Vvar__1___24Anonymous__11505] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__11505)
& ? [Vvar__2___24Anonymous__11506] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__11506)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V0__C,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506)
& 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__11510__11514__11560___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__15__s2__11511__11515__11561___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506))),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__11511__11515__11561___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__11510__11514__11560___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505,Vvar__2___24Anonymous__11506))),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__11509__11513__11559___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11506)),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__11508__11512__11558___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11505)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__11509__11513__11559___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__11506))))) ) )
| ? [Vvar__1___24Anonymous__11523] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__11523)
& ? [Vvar__2___24Anonymous__11524] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__11524)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V0__C,Vvar__1___24Anonymous__11523,Vvar__2___24Anonymous__11524)
& 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__11525__11527__11562___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11523)),Vvar__2___24Anonymous__11524),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__11525__11527__11562___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11523)),Vvar__2___24Anonymous__11524),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__11525__11527__11562___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__11523))) ) ) ) ) ) ).
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__11024] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__11024)
& ? [Vvar__2___24Anonymous__11025] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__11025)
& ( 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__11025)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__11024,Vvar__2___24Anonymous__11025)
& ( ( Vvar__2___24Anonymous__11025 = 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__11024)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__11036] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__11036)
& ? [Vvar__2___24Anonymous__11037] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__11037)
& Vvar__2___24Anonymous__11025 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__11036,Vvar__2___24Anonymous__11037)
& ( 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__11024)),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__11025) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__11011] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__11011)
& ? [Vvar__2__denum__11012] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__11012)
& ? [Vvar__3__condition__11013] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__11013)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__11011,Vvar__2__denum__11012,Vvar__3__condition__11013)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__11013 ) ) ) ) ) ).
fof('$_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__11002] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__11002)
& ? [Vvar__2__denum__11003] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__11003)
& ? [Vvar__3__condition__11004] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__11004)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__11002,Vvar__2__denum__11003,Vvar__3__condition__11004)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__11003 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__10991] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__10991)
& ? [Vvar__2__denum__10992] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__10992)
& ? [Vvar__3__condition__10993] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__10993)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__10991,Vvar__2__denum__10992,Vvar__3__condition__10993)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__10991 ) ) ) ) ) ).
fof('$_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__11786] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11786)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11786)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__11787] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11787)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11787)
& 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__11787)) ) ) ) ).
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__11813] :
( t(Vvar__1___24Anonymous__11813,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__11813)
& 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__11813) )
| ? [Vvar__1___24Anonymous__11815] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__11815)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__11815)
& 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__11815,V13__l) )
| ? [Vvar__1___24Anonymous__11817] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__11817)
& ? [Vvar__2___24Anonymous__11818] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__11818)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__11817,Vvar__2___24Anonymous__11818)
& 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__11817)),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__11818)) ) )
| ? [Vvar__1___24Anonymous__11821] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__11821)
& ? [Vvar__2___24Anonymous__11822] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__11822)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__11821,Vvar__2___24Anonymous__11822)
& 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__11821)),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__11822)) ) )
| ? [Vvar__1___24Anonymous__11825] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__11825)
& ? [Vvar__2___24Anonymous__11826] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__11826)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__11825,Vvar__2___24Anonymous__11826)
& 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__11825)),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__11826)) ) )
| ? [Vvar__1___24Anonymous__11829] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__11829)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__11829)
& 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__11829)) )
| ? [Vvar__1___24Anonymous__11831] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__11831)
& ? [Vvar__2___24Anonymous__11832] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__11832)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__11831,Vvar__2___24Anonymous__11832)
& 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__11831)),happ(V10__Cp__phi,Vvar__2___24Anonymous__11832)) ) ) ) ) ) ) ) ).
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__1835] :
( t(Vvar__1___24Anonymous__1835,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__1835)
& ( ? [Vvar__1___24Anonymous__1845] :
( t(Vvar__1___24Anonymous__1845,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1845)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__1835),Vvar__1___24Anonymous__1845) )
| ? [Vvar__1___24Anonymous__1847] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1847)
& ? [Vvar__2___24Anonymous__1848] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1848)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1847,Vvar__2___24Anonymous__1848)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__1851] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1851)
& ? [Vvar__2___24Anonymous__1852] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1852)
& ? [Vvar__3___24Anonymous__1853] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1853)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1851,Vvar__2___24Anonymous__1852,Vvar__3___24Anonymous__1853)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__1858] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1858)
& ? [Vvar__2___24Anonymous__1859] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1859)
& ( 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__1858,Vvar__2___24Anonymous__1859)
& ( ? [Vvar__1___24Anonymous__1879] :
( t(Vvar__1___24Anonymous__1879,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1879)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__1881] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1881)
& ? [Vvar__2___24Anonymous__1882] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1882)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1858)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1881)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1881,Vvar__2___24Anonymous__1882)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__1858,Vvar__1___24Anonymous__1881) = 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__1859,Vvar__2___24Anonymous__1882) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__1858,Vvar__1___24Anonymous__1881) = 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__1858,Vvar__1___24Anonymous__1881) = 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__1887] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1887)
& ? [Vvar__2___24Anonymous__1888] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1888)
& ? [Vvar__3___24Anonymous__1889] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1889)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1887,Vvar__2___24Anonymous__1888,Vvar__3___24Anonymous__1889)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__1894] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1894)
& ? [Vvar__2___24Anonymous__1895] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1895)
& ? [Vvar__3___24Anonymous__1896] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1896)
& ( 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__1894,Vvar__2___24Anonymous__1895,Vvar__3___24Anonymous__1896)
& ( ? [Vvar__1___24Anonymous__1929] :
( t(Vvar__1___24Anonymous__1929,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1929)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__1931] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1931)
& ? [Vvar__2___24Anonymous__1932] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1932)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1931,Vvar__2___24Anonymous__1932)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__1935] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1935)
& ? [Vvar__2___24Anonymous__1936] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1936)
& ? [Vvar__3___24Anonymous__1937] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1937)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1895)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1936)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1935,Vvar__2___24Anonymous__1936,Vvar__3___24Anonymous__1937)
& ( ( cType___24t(V0__C)
=> ( c_24__type__1950___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1894)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1935)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__1895,Vvar__2___24Anonymous__1936) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__1894,Vvar__1___24Anonymous__1935) = 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__1896,Vvar__3___24Anonymous__1937) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__1894,Vvar__1___24Anonymous__1935) = 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__1895,Vvar__2___24Anonymous__1936) = 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__1895,Vvar__2___24Anonymous__1936) = 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('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__12388___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__12389___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__12390___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
=> ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__2457] :
( 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__2457)
& ? [Vvar__2___24Anonymous__2458] :
( 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__2458)
& ( 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__2457)
=> ( 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__2457,Vvar__2___24Anonymous__2458)
& ? [Vvar__2___24Anonymous__2474] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__2474)
& ? [Vvar__3___24Anonymous__2475] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__2475)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__2434___24t(V0__C,V3__cadd)
=> ( c_24__type__2434___24t(V0__C,V4__cmul)
=> ( c_24__type__2434___24t(V0__C,V5__csub)
=> ( c_24__type__2443___24t(V0__C,V6__copp)
=> ( c_24__type__1950___24t(V0__C,V7__ceqb)
=> ( c_24__type__2451___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__2474)
=> ( Vvar__1___24Anonymous__2457 = 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__2474,Vvar__3___24Anonymous__2475)
& ( ? [Vvar__1___24Anonymous__2483] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__2483)
& 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__2474)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__2483)
& 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__2483,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__2475)),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__2458)) )
| ( 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__2474)) = 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__2458) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__2297___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_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('$_def_Topology.Compactness.compact',axiom,
! [V0__X] :
( cTopology_2eCompactness_2ecompact___24a1(V0__X)
<=> ! [V1__C] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__C)
=> ( ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__C,V2__U)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__U) ) )
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__C) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))
=> ? [V4__C_27] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__C_27)
& cCoq_2eSets_2eFinite__sets_2eFinite___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__C_27)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__C_27,V1__C)
& cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__C_27) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ).
fof('$_def_Topology.Completeness.cauchy',axiom,
! [V0__X,V1__d,V2__x] :
( cTopology_2eCompleteness_2ecauchy___24a3(V0__X,V1__d,V2__x)
<=> ! [V3__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V3__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V5__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__N)
& ! [V6__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__m)
=> ! [V7__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V6__m,V5__N)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V7__n,V5__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(V1__d,happ(V2__x,V6__m)),happ(V2__x,V7__n)),V3__eps)) ) ) ) ) ) ) ) ) ).
fof('$_def_Topology.Completeness.complete',axiom,
! [V0__X,V1__d] :
( cTopology_2eCompleteness_2ecomplete___24a2(V0__X,V1__d)
<=> ! [V3__x] :
( c_24__type__38820___24t(V0__X,V1__d,V3__x)
=> ( cTopology_2eCompleteness_2ecauchy___24a3(V0__X,V1__d,V3__x)
=> ? [V5__x0] :
( t(V5__x0,V0__X)
& cTopology_2eNets_2enet__limit___24a4(cTopology_2eDirectedSets_2enat__DS,cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V3__x,V5__x0) ) ) ) ) ).
fof('$_def_Topology.Connectedness.clopen',axiom,
! [V0__X,V1__S] :
( cTopology_2eConnectedness_2eclopen___24a2(V0__X,V1__S)
<=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__S)
& cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__S) ) ) ).
fof('$_def_Topology.Connectedness.connected',axiom,
! [V0__X] :
( cTopology_2eConnectedness_2econnected___24a1(V0__X)
<=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eConnectedness_2eclopen___24a2(V0__X,V1__S)
=> ( V1__S = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))
| V1__S = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ).
fof('$_def_Topology.Continuity.continuous',axiom,
! [V0__X,V1__Y,V2__f] :
( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
<=> ! [V3__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V3__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V1__Y,V3__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V3__V)) ) ) ) ).
fof('$_def_Topology.Continuity.continuous_at',axiom,
! [V0__X,V1__Y,V2__f,V3__x] :
( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x)
<=> ! [V4__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V4__V)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(V1__Y,V4__V,happ(V2__f,V3__x))
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V4__V),V3__x) ) ) ) ).
fof('$_def_Topology.CountabilityAxioms.Lindelof',axiom,
! [V0__X] :
( cTopology_2eCountabilityAxioms_2eLindelof___24a1(V0__X)
<=> ! [V1__cover] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__cover)
=> ( ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__cover,V2__U)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__U) ) )
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__cover) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))
=> ? [V4__subcover] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__subcover)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__subcover,V1__cover)
& cZornsLemma_2eCountableTypes_2eCountable___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__subcover)
& cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__subcover) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ).
fof('$_def_Topology.CountabilityAxioms.first_countable',axiom,
! [V0__X] :
( cTopology_2eCountabilityAxioms_2efirst__countable___24a1(V0__X)
<=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ? [V2__NBx] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__NBx)
& cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V0__X,V2__NBx,V1__x)
& cZornsLemma_2eCountableTypes_2eCountable___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V2__NBx) ) ) ) ).
fof('$_def_Topology.DirectedSets.DS_ord',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> ? [Vvar__0__DS__set__38348] :
( cType___24t(Vvar__0__DS__set__38348)
& ? [Vvar__1__DS__ord__38349] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__38348,Vvar__1__DS__ord__38349)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__38348,Vvar__1__DS__ord__38349)
& ! [Vvar__var__3__i__38352__38355] :
( t(Vvar__var__3__i__38352__38355,Vvar__0__DS__set__38348)
=> ! [Vvar__var__4__j__38354__38357] :
( t(Vvar__var__4__j__38354__38357,Vvar__0__DS__set__38348)
=> ? [Vvar__var__5__k__38353__38356] :
( t(Vvar__var__5__k__38353__38356,Vvar__0__DS__set__38348)
& p(happ(happ(Vvar__1__DS__ord__38349,Vvar__var__3__i__38352__38355),Vvar__var__5__k__38353__38356))
& p(happ(happ(Vvar__1__DS__ord__38349,Vvar__var__4__j__38354__38357),Vvar__var__5__k__38353__38356)) ) ) )
& V0__d = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__38348,Vvar__1__DS__ord__38349)
& cTopology_2eDirectedSets_2eDS__ord___24a1(V0__d) = Vvar__1__DS__ord__38349 ) ) ) ).
fof('$_def_Topology.DirectedSets.DS_set',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> ? [Vvar__0__DS__set__38318] :
( cType___24t(Vvar__0__DS__set__38318)
& ? [Vvar__1__DS__ord__38319] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__38318,Vvar__1__DS__ord__38319)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__38318,Vvar__1__DS__ord__38319)
& ! [Vvar__var__3__i__38322__38325] :
( t(Vvar__var__3__i__38322__38325,Vvar__0__DS__set__38318)
=> ! [Vvar__var__4__j__38324__38327] :
( t(Vvar__var__4__j__38324__38327,Vvar__0__DS__set__38318)
=> ? [Vvar__var__5__k__38323__38326] :
( t(Vvar__var__5__k__38323__38326,Vvar__0__DS__set__38318)
& p(happ(happ(Vvar__1__DS__ord__38319,Vvar__var__3__i__38322__38325),Vvar__var__5__k__38323__38326))
& p(happ(happ(Vvar__1__DS__ord__38319,Vvar__var__4__j__38324__38327),Vvar__var__5__k__38323__38326)) ) ) )
& V0__d = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__38318,Vvar__1__DS__ord__38319)
& cTopology_2eDirectedSets_2eDS__set___24a1(V0__d) = Vvar__0__DS__set__38318 ) ) ) ).
fof('$_def_Topology.DirectedSets.eventually',axiom,
! [V0__I,V1__P] :
( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V1__P)
<=> ? [V2__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V2__i)
& ! [V3__j] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V3__j)
=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(V0__I,V2__i,V3__j)
=> p(happ(V1__P,V3__j)) ) ) ) ) ).
fof('$_def_Topology.DirectedSets.exists_arbitrarily_large',axiom,
! [V0__I,V1__P] :
( cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,V1__P)
<=> ! [V2__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V2__i)
=> ? [V3__j] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V3__j)
& cTopology_2eDirectedSets_2eDS__ord___24a3(V0__I,V2__i,V3__j)
& p(happ(V1__P,V3__j)) ) ) ) ).
fof('$_def_Topology.DirectedSets.nat_DS',axiom,
cTopology_2eDirectedSets_2enat__DS = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele) ).
fof('$_def_Topology.FilterLimits.filter_cluster_point',axiom,
! [V0__X,V1__F,V2__x0] :
( cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0)
<=> ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F),V3__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V3__S),V2__x0) ) ) ) ).
fof('$_def_Topology.FilterLimits.filter_limit',axiom,
! [V0__X,V1__F,V2__x0] :
( cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V1__F,V2__x0)
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eFilterLimits_2eneighborhood__filter___24a2(V0__X,V2__x0)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ).
fof('$_def_Topology.FilterLimits.neighborhood_filter',axiom,
! [V0__X,V1__x0] : cTopology_2eFilterLimits_2eneighborhood__filter___24a2(V0__X,V1__x0) = cTopology_2eFilters_2eBuild__Filter___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__37632___24a2(V0__X,V1__x0))) ).
fof('$_def_Topology.Filters.Build_Filter_from_basis',axiom,
! [V0__X,V1__B] : cTopology_2eFilters_2eBuild__Filter__from__basis___24a2(V0__X,V1__B) = cTopology_2eFilters_2eBuild__Filter___24a2(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__37771___24a2(V0__X,V1__B))) ).
fof('$_def_Topology.Filters.filter_family',axiom,
! [V0__X,V1__f] :
( cType___24t(V0__X)
=> ( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> ? [Vvar__1__filter__family__37699] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,Vvar__1__filter__family__37699)
& ! [Vvar__var__var__2__S1__37701__37705__37720] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__2__S1__37701__37705__37720)
=> ! [Vvar__var__var__3__S2__37702__37706__37721] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__3__S2__37702__37706__37721)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__37699,Vvar__var__var__2__S1__37701__37705__37720)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__37699,Vvar__var__var__3__S2__37702__37706__37721)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__37699,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,Vvar__var__var__2__S1__37701__37705__37720,Vvar__var__var__3__S2__37702__37706__37721)) ) ) ) )
& ! [Vvar__var__var__3__S1__37710__37714__37724] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__3__S1__37710__37714__37724)
=> ! [Vvar__var__var__4__S2__37711__37715__37725] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,Vvar__var__var__4__S2__37711__37715__37725)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__37699,Vvar__var__var__3__S1__37710__37714__37724)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,Vvar__var__var__3__S1__37710__37714__37724,Vvar__var__var__4__S2__37711__37715__37725)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__37699,Vvar__var__var__4__S2__37711__37715__37725) ) ) ) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__37699,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X))
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),Vvar__1__filter__family__37699,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X))
& V1__f = cTopology_2eFilters_2eBuild__Filter___24a2(V0__X,Vvar__1__filter__family__37699)
& cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f) = Vvar__1__filter__family__37699 ) ) ) ).
fof('$_def_Topology.Filters.ultrafilter',axiom,
! [V0__X,V1__F] :
( cTopology_2eFilters_2eultrafilter___24a2(V0__X,V1__F)
<=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F),V2__S)
| cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F),cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__X,V2__S)) ) ) ) ).
fof('$_def_Topology.FiltersAndNets.filter_to_net',axiom,
! [V0__X,V1__F] : cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F) = cTopology_2eFiltersAndNets_2eftn__x___24a2(V0__X,V1__F) ).
fof('$_def_Topology.FiltersAndNets.ftn_S',axiom,
! [V0__X,V1__F,V2__f] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(V0__X,V1__F,V2__f)
=> ? [Vvar__2__ftn__S__42675] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__ftn__S__42675)
& ? [Vvar__3__ftn__x__42676] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__ftn__x__42676)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F),Vvar__2__ftn__S__42675)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__ftn__S__42675,Vvar__3__ftn__x__42676)
& V2__f = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(V0__X,V1__F,Vvar__2__ftn__S__42675,Vvar__3__ftn__x__42676)
& cTopology_2eFiltersAndNets_2eftn__S___24a3(V0__X,V1__F,V2__f) = Vvar__2__ftn__S__42675 ) ) ) ) ) ).
fof('$_def_Topology.FiltersAndNets.ftn_x',axiom,
! [V0__X,V1__F,V2__f] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(V0__X,V1__F,V2__f)
=> ? [Vvar__2__ftn__S__42694] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__ftn__S__42694)
& ? [Vvar__3__ftn__x__42695] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__ftn__x__42695)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F),Vvar__2__ftn__S__42694)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__ftn__S__42694,Vvar__3__ftn__x__42695)
& V2__f = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(V0__X,V1__F,Vvar__2__ftn__S__42694,Vvar__3__ftn__x__42695)
& cTopology_2eFiltersAndNets_2eftn__x___24a3(V0__X,V1__F,V2__f) = Vvar__3__ftn__x__42695 ) ) ) ) ) ).
fof('$_def_Topology.FiltersAndNets.net_tail',axiom,
! [V0__X,V1__J,V2__x,V3__j] : cTopology_2eFiltersAndNets_2enet__tail___24a4(V0__X,V1__J,V2__x,V3__j) = cCoq_2eSets_2eImage_2eIm___24a4(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J),c_24__lam__42592___24a3(V0__X,V1__J,V3__j)),V2__x) ).
fof('$_def_Topology.FiltersAndNets.tail_filter_basis',axiom,
! [V0__X,V1__J,V2__x] : cTopology_2eFiltersAndNets_2etail__filter__basis___24a3(V0__X,V1__J,V2__x) = cCoq_2eSets_2eImage_2eIm___24a4(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J),cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J)),cTopology_2eFiltersAndNets_2enet__tail___24a3(V0__X,V1__J,V2__x)) ).
fof('$_def_Topology.Homeomorphisms.open_map',axiom,
! [V0__X,V1__Y,V2__f] :
( cTopology_2eHomeomorphisms_2eopen__map___24a3(V0__X,V1__Y,V2__f)
<=> ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V1__Y,cCoq_2eSets_2eImage_2eIm___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V3__U,V2__f)) ) ) ) ).
fof('$_def_Topology.Homeomorphisms.topological_property',axiom,
! [V0__P] :
( cTopology_2eHomeomorphisms_2etopological__property___24a1(V0__P)
<=> ! [V1__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__X)
=> ! [V2__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V2__Y)
=> ! [V3__f] :
( c_24__type__38915___24t(V1__X,V2__Y,V3__f)
=> ( cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V1__X,V2__Y,V3__f)
=> ( p(happ(V0__P,V1__X))
=> p(happ(V0__P,V2__Y)) ) ) ) ) ) ) ).
fof('$_def_Topology.InteriorsClosures.Build_TopologicalSpace_from_closure_operator',axiom,
! [V0__X,V1__cl] : cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__closure__operator___24a2(V0__X,V1__cl) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace__from__closed__sets___24a2(V0__X,c_24__lam__43888___24a2(V0__X,V1__cl)) ).
fof('$_def_Topology.InteriorsClosures.closure',axiom,
! [V0__X,V1__S] : cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__37373___24a2(V0__X,V1__S))) ).
fof('$_def_Topology.InteriorsClosures.dense',axiom,
! [V0__X,V1__S] :
( cTopology_2eInteriorsClosures_2edense___24a2(V0__X,V1__S)
<=> cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ).
fof('$_def_Topology.InteriorsClosures.idempotent',axiom,
! [V0__T,V1__f] :
( cTopology_2eInteriorsClosures_2eidempotent___24a2(V0__T,V1__f)
<=> ! [V2__x] :
( t(V2__x,V0__T)
=> happ(V1__f,happ(V1__f,V2__x)) = happ(V1__f,V2__x) ) ) ).
fof('$_def_Topology.InteriorsClosures.interior',axiom,
! [V0__X,V1__S] : cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__39032___24a2(V0__X,V1__S))) ).
fof('$_def_Topology.MetricSpaces.dist_to_set',axiom,
! [V0__X,V1__d,V3__S,V5__x] : cTopology_2eMetricSpaces_2edist__to__set___24a4(V0__X,V1__d,V3__S,V5__x) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__38507___24a4(V0__X,V1__d,V3__S,V5__x),cTopology_2eSupInf_2einf___24a1(cCoq_2eSets_2eImage_2eIm___24a4(V0__X,cCoq_2eReals_2eRdefinitions_2eR,V3__S,happ(V1__d,V5__x)))) ).
fof('$_def_Topology.MetricSpaces.metrizes',axiom,
! [V0__X,V1__d] :
( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
<=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d,V2__x),V2__x) ) ) ).
fof('$_def_Topology.MetricSpaces.open_ball',axiom,
! [V0__X,V1__d,V2__x0,V3__r] : cTopology_2eMetricSpaces_2eopen__ball___24a4(V0__X,V1__d,V2__x0,V3__r) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__39150___24a4(V0__X,V1__d,V2__x0,V3__r)) ).
fof('$_def_Topology.Neighborhoods.neighborhood',axiom,
! [V0__X,V1__N,V2__x] :
( cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V1__N,V2__x)
<=> ? [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V3__U,V2__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V1__N) ) ) ).
fof('$_def_Topology.Neighborhoods.open_neighborhood',axiom,
! [V0__X,V1__U,V2__x] :
( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V1__U,V2__x)
<=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U,V2__x) ) ) ).
fof('$_def_Topology.Nets.Net',axiom,
! [V0__I,V1__X] : cTopology_2eNets_2eNet___24a2(V0__I,V1__X) = c_24__type__38578___24a2(V0__I,V1__X) ).
fof('$_def_Topology.Nets.cluster_point_subnet',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V5__iU] : cTopology_2eNets_2ecluster__point__subnet___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU) = happ(V2__x,cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU)) ).
fof('$_def_Topology.Nets.cluster_point_subnet_DS',axiom,
! [V0__X,V1__I,V2__x,V3__x0] : cTopology_2eNets_2ecluster__point__subnet__DS___24a4(V0__X,V1__I,V2__x,V3__x0) = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(cTopology_2eNets_2ecluster__point__subnet__DS__set___24a4(V0__X,V1__I,V2__x,V3__x0),cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a4(V0__X,V1__I,V2__x,V3__x0)) ).
fof('$_def_Topology.Nets.cluster_point_subnet_DS_ord',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V4__iU1,V5__iU2] :
( cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a6(V0__X,V1__I,V2__x,V3__x0,V4__iU1,V5__iU2)
<=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(V1__I,cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V4__iU1),cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU2))
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V5__iU2),cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__iU1)) ) ) ).
fof('$_def_Topology.Nets.cps_U',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V4__c] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> ? [Vvar__4__cps__i__39527] :
( cTopology_2eDirectedSets_2eDS__set___24t(V1__I,Vvar__4__cps__i__39527)
& ? [Vvar__5__cps__U__39528] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__39528)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,Vvar__5__cps__U__39528,V3__x0)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__39528,happ(V2__x,Vvar__4__cps__i__39527))
& V4__c = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(V0__X,V1__I,V2__x,V3__x0,Vvar__4__cps__i__39527,Vvar__5__cps__U__39528)
& cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c) = Vvar__5__cps__U__39528 ) ) ) ) ) ) ) ).
fof('$_def_Topology.Nets.cps_i',axiom,
! [V0__X,V1__I,V2__x,V3__x0,V4__c] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> ? [Vvar__4__cps__i__39489] :
( cTopology_2eDirectedSets_2eDS__set___24t(V1__I,Vvar__4__cps__i__39489)
& ? [Vvar__5__cps__U__39490] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__39490)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,Vvar__5__cps__U__39490,V3__x0)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__5__cps__U__39490,happ(V2__x,Vvar__4__cps__i__39489))
& V4__c = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(V0__X,V1__I,V2__x,V3__x0,Vvar__4__cps__i__39489,Vvar__5__cps__U__39490)
& cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c) = Vvar__4__cps__i__39489 ) ) ) ) ) ) ) ).
fof('$_def_Topology.Nets.neighborhood_net',axiom,
! [V0__X,V1__x,V2__x] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V2__x)
=> ? [Vvar__2__U__38731] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38731)
& ? [Vvar__3__y__38732] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__38732)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,Vvar__2__U__38731)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38731,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38731,Vvar__3__y__38732)
& V2__x = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,Vvar__2__U__38731,Vvar__3__y__38732)
& cTopology_2eNets_2eneighborhood__net___24a3(V0__X,V1__x,V2__x) = Vvar__3__y__38732 ) ) ) ) ) ).
fof('$_def_Topology.Nets.neighborhood_net_DS',axiom,
! [V0__X,V1__x] : cTopology_2eNets_2eneighborhood__net__DS___24a2(V0__X,V1__x) = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(cTopology_2eNets_2eneighborhood__net__DS__set___24a2(V0__X,V1__x),cTopology_2eNets_2eneighborhood__net__DS__ord___24a2(V0__X,V1__x)) ).
fof('$_def_Topology.Nets.neighborhood_net_DS_ord',axiom,
! [V0__X,V1__x,V2__Uy,V3__Vz] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V2__Uy)
=> ? [Vvar__2__U__38650] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38650)
& ? [Vvar__3__y__38651] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__38651)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,Vvar__2__U__38650)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38650,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38650,Vvar__3__y__38651)
& ( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V3__Vz)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38650)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__38651)
=> ( V2__Uy = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,Vvar__2__U__38650,Vvar__3__y__38651)
& ? [Vvar__2__U__38699] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38699)
& ? [Vvar__3__y__38700] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__38700)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,Vvar__2__U__38699)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38699,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38699,Vvar__3__y__38700)
& V3__Vz = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,Vvar__2__U__38699,Vvar__3__y__38700)
& ( cTopology_2eNets_2eneighborhood__net__DS__ord___24a4(V0__X,V1__x,V2__Uy,V3__Vz)
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__38699,Vvar__2__U__38650) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Topology.Nets.neighborhood_net_DS_set_rec',axiom,
! [V0__X,V1__x,V2__P] : cTopology_2eNets_2eneighborhood__net__DS__set__rec___24a3(V0__X,V1__x,V2__P) = cTopology_2eNets_2eneighborhood__net__DS__set__rect___24a3(V0__X,V1__x,V2__P) ).
fof('$_def_Topology.Nets.neighborhood_net_DS_set_rect',axiom,
! [V0__X,V1__x,V2__P,V3__f,V4__n] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ( c_24__type__44608___24t(V0__X,V1__x,V2__P,V2__P)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V4__n)
=> ? [Vvar__2__U__44598] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__44598)
& ? [Vvar__3__y__44599] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,Vvar__3__y__44599)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,Vvar__2__U__44598)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__44598,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),Vvar__2__U__44598,Vvar__3__y__44599)
& V4__n = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,Vvar__2__U__44598,Vvar__3__y__44599)
& cTopology_2eNets_2eneighborhood__net__DS__set__rect___24a5(V0__X,V1__x,V2__P,V3__f,V4__n) = happ(happ(V3__f,Vvar__2__U__44598),Vvar__3__y__44599) ) ) ) ) ) ) ).
fof('$_def_Topology.Nets.net_cluster_point',axiom,
! [V0__I,V1__X,V2__x,V3__x0] :
( cTopology_2eNets_2enet__cluster__point___24a4(V0__I,V1__X,V2__x,V3__x0)
<=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V1__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U,V3__x0)
=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,c_24__lam__38587___24a4(V0__I,V1__X,V2__x,V4__U)) ) ) ) ) ).
fof('$_def_Topology.Nets.net_limit',axiom,
! [V0__I,V1__X,V2__x,V3__x0] :
( cTopology_2eNets_2enet__limit___24a4(V0__I,V1__X,V2__x,V3__x0)
<=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V1__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V4__U,V3__x0)
=> cTopology_2eDirectedSets_2eeventually___24a2(V0__I,c_24__lam__38587___24a4(V0__I,V1__X,V2__x,V4__U)) ) ) ) ) ).
fof('$_def_Topology.OpenBases.open_basis_cond',axiom,
! [V0__X,V1__B] :
( cTopology_2eOpenBases_2eopen__basis__cond___24a2(V0__X,V1__B)
<=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__U)
=> ! [V3__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,V3__V)
=> ! [V6__x] :
( t(V6__x,V0__X)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__U,V3__V),V6__x)
=> ? [V8__W] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V8__W)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,V8__W)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,V8__W,V6__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V8__W,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__U,V3__V)) ) ) ) ) ) ) ) ) ).
fof('$_def_Topology.OpenBases.open_basis_cover_cond',axiom,
! [V0__X,V1__B] :
( cTopology_2eOpenBases_2eopen__basis__cover__cond___24a2(V0__X,V1__B)
<=> ! [V2__x] :
( t(V2__x,V0__X)
=> ? [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,V3__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,V3__U,V2__x) ) ) ) ).
fof('$_def_Topology.RTopology.RTop',axiom,
cTopology_2eRTopology_2eRTop = cTopology_2eOrderTopology_2eOrderTopology___24a2(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_def_Topology.SeparatednessAxioms.Hausdorff',axiom,
! [V0__X] :
( cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X)
<=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ! [V2__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__y)
=> ( V1__x != V2__y
=> ? [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
& ? [V5__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__V)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V5__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__V,V2__y)
& cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V5__V) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ) ).
fof('$_def_Topology.SeparatednessAxioms.T0_sep',axiom,
! [V0__X] :
( cTopology_2eSeparatednessAxioms_2eT0__sep___24a1(V0__X)
<=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ! [V2__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__y)
=> ( V1__x != V2__y
=> ( ? [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V1__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V2__y) )
| ? [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V1__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V2__y) ) ) ) ) ) ) ).
fof('$_def_Topology.SeparatednessAxioms.T1_sep',axiom,
! [V0__X] :
( cTopology_2eSeparatednessAxioms_2eT1__sep___24a1(V0__X)
<=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__x)) ) ) ).
fof('$_def_Topology.SeparatednessAxioms.T3_sep',axiom,
! [V0__X] :
( cTopology_2eSeparatednessAxioms_2eT3__sep___24a1(V0__X)
<=> ( cTopology_2eSeparatednessAxioms_2eT1__sep___24a1(V0__X)
& ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ! [V2__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__F)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F,V1__x)
=> ? [V5__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__U)
& ? [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V5__U)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V6__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__U,V1__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F,V6__V)
& cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__U,V6__V) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ) ) ) ).
fof('$_def_Topology.SeparatednessAxioms.normal_sep',axiom,
! [V0__X] :
( cTopology_2eSeparatednessAxioms_2enormal__sep___24a1(V0__X)
<=> ( cTopology_2eSeparatednessAxioms_2eT1__sep___24a1(V0__X)
& ! [V1__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__G)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__G)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F,V2__G) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))
=> ? [V6__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__U)
& ? [V7__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V6__U)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V7__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F,V6__U)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__G,V7__V)
& cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__U,V7__V) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Topology.Subbases.Build_TopologicalSpace_from_subbasis',axiom,
! [V0__X,V1__S] : cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis___24a2(V0__X,V1__S) = cTopology_2eOpenBases_2eBuild__TopologicalSpace__from__open__basis___24a2(V0__X,cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S)) ).
fof('$_def_Topology.SubspaceTopology.SubspaceTopology',axiom,
! [V0__X,V1__A] : cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V0__X,V1__A) = cTopology_2eWeakTopology_2eWeakTopology1___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),c_24__lam__39712___24a2(V0__X,V1__A)),V0__X,cCoq_2eInit_2eSpecif_2eproj1__sig___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),c_24__lam__39712___24a2(V0__X,V1__A))) ).
fof('$_def_Topology.SubspaceTopology.subspace_inc',axiom,
! [V0__X,V1__A] : cTopology_2eSubspaceTopology_2esubspace__inc___24a2(V0__X,V1__A) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),c_24__lam__39712___24a2(V0__X,V1__A)) ).
fof('$_def_Topology.SupInf.is_glb',axiom,
! [V0__E,V1__m] :
( cTopology_2eSupInf_2eis__glb___24a2(V0__E,V1__m)
<=> ( cTopology_2eSupInf_2eis__lower__bound___24a2(V0__E,V1__m)
& ! [V2__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__b)
=> ( cTopology_2eSupInf_2eis__lower__bound___24a2(V0__E,V2__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__b,V1__m)) ) ) ) ) ).
fof('$_def_Topology.SupInf.is_lower_bound',axiom,
! [V0__E,V1__m] :
( cTopology_2eSupInf_2eis__lower__bound___24a2(V0__E,V1__m)
<=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(happ(V0__E,V2__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V2__x,V1__m)) ) ) ) ).
fof('$_def_Topology.TopologicalSpaces.closed',axiom,
! [V0__X,V1__F] :
( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
<=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ).
fof('$_def_Topology.TopologicalSpaces.open',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ? [Vvar__0__point__set__37526] :
( cType___24t(Vvar__0__point__set__37526)
& ? [Vvar__1__open__37527] :
( c_24__type__37437___24t(Vvar__0__point__set__37526,Vvar__1__open__37527)
& ! [Vvar__var__2__F__37531__37535] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__37526,Vvar__var__2__F__37531__37535)
=> ( ! [Vvar__var__3__S__37532__37536] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37526,Vvar__var__3__S__37532__37536)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__37526),Vvar__var__2__F__37531__37535,Vvar__var__3__S__37532__37536)
=> p(happ(Vvar__1__open__37527,Vvar__var__3__S__37532__37536)) ) )
=> p(happ(Vvar__1__open__37527,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__37526,Vvar__var__2__F__37531__37535))) ) )
& ! [Vvar__var__3__U__37540__37544] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37526,Vvar__var__3__U__37540__37544)
=> ! [Vvar__var__4__V__37541__37545] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37526,Vvar__var__4__V__37541__37545)
=> ( p(happ(Vvar__1__open__37527,Vvar__var__3__U__37540__37544))
=> ( p(happ(Vvar__1__open__37527,Vvar__var__4__V__37541__37545))
=> p(happ(Vvar__1__open__37527,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__37526,Vvar__var__3__U__37540__37544,Vvar__var__4__V__37541__37545))) ) ) ) )
& p(happ(Vvar__1__open__37527,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__37526)))
& V0__t = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__37526,Vvar__1__open__37527)
& cTopology_2eTopologicalSpaces_2eopen___24a1(V0__t) = Vvar__1__open__37527 ) ) ) ).
fof('$_def_Topology.TopologicalSpaces.point_set',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ? [Vvar__0__point__set__37459] :
( cType___24t(Vvar__0__point__set__37459)
& ? [Vvar__1__open__37460] :
( c_24__type__37437___24t(Vvar__0__point__set__37459,Vvar__1__open__37460)
& ! [Vvar__var__2__F__37464__37468] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__37459,Vvar__var__2__F__37464__37468)
=> ( ! [Vvar__var__3__S__37465__37469] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37459,Vvar__var__3__S__37465__37469)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__37459),Vvar__var__2__F__37464__37468,Vvar__var__3__S__37465__37469)
=> p(happ(Vvar__1__open__37460,Vvar__var__3__S__37465__37469)) ) )
=> p(happ(Vvar__1__open__37460,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__37459,Vvar__var__2__F__37464__37468))) ) )
& ! [Vvar__var__3__U__37473__37477] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37459,Vvar__var__3__U__37473__37477)
=> ! [Vvar__var__4__V__37474__37478] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37459,Vvar__var__4__V__37474__37478)
=> ( p(happ(Vvar__1__open__37460,Vvar__var__3__U__37473__37477))
=> ( p(happ(Vvar__1__open__37460,Vvar__var__4__V__37474__37478))
=> p(happ(Vvar__1__open__37460,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__37459,Vvar__var__3__U__37473__37477,Vvar__var__4__V__37474__37478))) ) ) ) )
& p(happ(Vvar__1__open__37460,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__37459)))
& V0__t = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__37459,Vvar__1__open__37460)
& cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t) = Vvar__0__point__set__37459 ) ) ) ).
fof('$_def_Topology.WeakTopology.WeakTopology',axiom,
! [V0__X,V1__A,V2__Y,V3__f] : cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f) = cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis___24a2(V0__X,cTopology_2eWeakTopology_2eweak__topology__subbasis___24a4(V0__X,V1__A,V2__Y,V3__f)) ).
fof('$_def_Topology.WeakTopology.WeakTopology1',axiom,
! [V0__X,V1__Y,V2__f] : cTopology_2eWeakTopology_2eWeakTopology1___24a3(V0__X,V1__Y,V2__f) = cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,c_24True,c_24__lam__50156___24a2(V0__X,V1__Y),cCoq_2eInit_2eLogic_2eTrue__rect___24a2(c_24__type__39840___24a2(V0__X,V1__Y),V2__f)) ).
fof('$_def_UrysohnsLemma.Urysohns_Lemma_construction.Un',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(V0__n) = cU0 )
| ? [Vvar__0___24Anonymous__51809] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__51809)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__51809)
=> ( V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__51809)
& ( ( Vvar__0___24Anonymous__51809 = cCoq_2eInit_2eDatatypes_2eO
& cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(V0__n) = cU1 )
| ? [Vvar__0___24Anonymous__51812] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__51812)
& Vvar__0___24Anonymous__51809 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__51812)
& cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(V0__n) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX)) ) ) ) ) ) ) ) ).
fof('$_def_ZornsLemma.CountableTypes.Countable',axiom,
! [V0__X,V1__S] :
( cZornsLemma_2eCountableTypes_2eCountable___24a2(V0__X,V1__S)
<=> cZornsLemma_2eCountableTypes_2eCountableT___24a1(cCoq_2eInit_2eSpecif_2esig___24a2(V0__X,c_24__lam__38269___24a2(V0__X,V1__S))) ) ).
fof('$_def_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
! [V0__X,V1__P] : cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,V1__P) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P) ).
fof('$_def_ZornsLemma.Families.Family',axiom,
! [V0__T] : cZornsLemma_2eFamilies_2eFamily___24a1(V0__T) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T)) ).
fof('$_def_ZornsLemma.FunctionProperties.injective',axiom,
! [V0__X,V1__Y,V2__f] :
( cZornsLemma_2eFunctionProperties_2einjective___24a3(V0__X,V1__Y,V2__f)
<=> ! [V3__x1] :
( t(V3__x1,V0__X)
=> ! [V4__x2] :
( t(V4__x2,V0__X)
=> ( happ(V2__f,V3__x1) = happ(V2__f,V4__x2)
=> V3__x1 = V4__x2 ) ) ) ) ).
fof('$_def_ZornsLemma.FunctionProperties.surjective',axiom,
! [V0__X,V1__Y,V2__f] :
( cZornsLemma_2eFunctionProperties_2esurjective___24a3(V0__X,V1__Y,V2__f)
<=> ! [V3__y] :
( t(V3__y,V1__Y)
=> ? [V4__x] :
( t(V4__x,V0__X)
& happ(V2__f,V4__x) = V3__y ) ) ) ).
fof('$_def_ZornsLemma.IndexedFamilies.ImageFamily',axiom,
! [V0__T,V1__A,V2__F] : cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V0__T,V1__A,V2__F) = cCoq_2eSets_2eImage_2eIm___24a4(V1__A,cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V1__A),V2__F) ).
fof('$_def_ZornsLemma.IndexedFamilies.IndexedFamily',axiom,
! [V0__A,V1__T] : cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24a2(V0__A,V1__T) = c_24__type__39022___24a2(V0__A,V1__T) ).
fof('$_def_ZornsLemma.InverseImage.inverse_image',axiom,
! [V0__X,V1__Y,V2__f,V3__T] : cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__39043___24a4(V0__X,V1__Y,V2__f,V3__T)) ).
fof('$_def_ZornsLemma.Quotients.quotient',axiom,
! [V0__A,V1__R] : cZornsLemma_2eQuotients_2equotient___24a2(V0__A,V1__R) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__A),c_24__lam__45314___24a2(V0__A,V1__R)) ).
fof('$_def_ZornsLemma.ZornsLemma.chain',axiom,
! [V0__T,V1__R,V2__S] :
( cZornsLemma_2eZornsLemma_2echain___24a3(V0__T,V1__R,V2__S)
<=> ! [V3__x] :
( t(V3__x,V0__T)
=> ! [V4__y] :
( t(V4__y,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V2__S,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V2__S,V4__y)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
| p(happ(happ(V1__R,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('$_def_ZornsLemma.ZornsLemma.chains',axiom,
! [V0__T,V1__R] : cZornsLemma_2eZornsLemma_2echains___24a2(V0__T,V1__R) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),c_24__lam__51609___24a2(V0__T,V1__R)) ).
fof('$_def_ZornsLemma.ZornsLemma.chains_ord',axiom,
! [V0__T,V1__R,V2__S1,V3__S2] :
( cZornsLemma_2eZornsLemma_2echains__ord___24a4(V0__T,V1__R,V2__S1,V3__S2)
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__T,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),c_24__lam__51609___24a2(V0__T,V1__R),V2__S1),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),c_24__lam__51609___24a2(V0__T,V1__R),V3__S2)) ) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__3] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1149,Vvar__1___24Anonymous__1150,Vvar__0__A__1151] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1149,Vvar__1___24Anonymous__1150) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1151) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__4511,Vvar__1__B__4512,Vvar__2___24Anonymous__4513,Vvar__0__A__4514,Vvar__1__B__4515,Vvar__2___24Anonymous__4516] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4511,Vvar__1__B__4512,Vvar__2___24Anonymous__4513) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4514,Vvar__1__B__4515,Vvar__2___24Anonymous__4516) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__1199,Vvar__0__A__1200,Vvar__1___24Anonymous__1201,Vvar__2___24Anonymous__1202] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1199) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1200,Vvar__1___24Anonymous__1201,Vvar__2___24Anonymous__1202) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2730,Vvar__1__B__2731,Vvar__2___24Anonymous__2732,Vvar__0__A__2733,Vvar__1__B__2734,Vvar__2___24Anonymous__2735] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2730,Vvar__1__B__2731,Vvar__2___24Anonymous__2732) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2733,Vvar__1__B__2734) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2646,Vvar__1__B__2647,Vvar__2___24Anonymous__2648,Vvar__0__A__2649,Vvar__1__B__2650,Vvar__2___24Anonymous__2651] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2646,Vvar__1__B__2647) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2649,Vvar__1__B__2650) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__720] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__720) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__731] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__731) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__704,Vvar__0___24Anonymous__705] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__704) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__705) ).
fof('$_discrim_Coq.Reals.RList.nil$Coq.Reals.RList.cons',axiom,
! [Vvar__0___24Anonymous__45321,Vvar__1___24Anonymous__45322] : cCoq_2eReals_2eRList_2enil != cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__45321,Vvar__1___24Anonymous__45322) ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__5289,Vvar__0__n__5290,Vvar__1___24Anonymous__5291] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__5289) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__5290,Vvar__1___24Anonymous__5291) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__2892,Vvar__0__A__2893,Vvar__1__h__2894,Vvar__2__n__2895,Vvar__3___24Anonymous__2896] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2892) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2893,Vvar__1__h__2894,Vvar__2__n__2895,Vvar__3___24Anonymous__2896) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__4806,Vvar__1___24Anonymous__4807,Vvar__0__C__4808,Vvar__1___24Anonymous__4809] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__4806,Vvar__1___24Anonymous__4807) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__4808,Vvar__1___24Anonymous__4809) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__4870,Vvar__1___24Anonymous__4871,Vvar__0__C__4872,Vvar__1___24Anonymous__4873,Vvar__2___24Anonymous__4874] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4870,Vvar__1___24Anonymous__4871) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4872,Vvar__1___24Anonymous__4873,Vvar__2___24Anonymous__4874) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__5901,Vvar__1___24Anonymous__5902,Vvar__0__C__5903,Vvar__1___24Anonymous__5904] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__5901,Vvar__1___24Anonymous__5902) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__5903,Vvar__1___24Anonymous__5904) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__27879,Vvar__1__TX__27880,Vvar__2__AA__27881,Vvar__3__AF__27882,Vvar__0__TA__27883,Vvar__1__TX__27884,Vvar__2__AA__27885,Vvar__3__AF__27886] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__27879,Vvar__1__TX__27880,Vvar__2__AA__27881,Vvar__3__AF__27882) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__27883,Vvar__1__TX__27884,Vvar__2__AA__27885,Vvar__3__AF__27886) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__27993,Vvar__0__A__27994,Vvar__1___24Anonymous__27995] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__27993) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__27994,Vvar__1___24Anonymous__27995) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__5204,Vvar__0__C__5205] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__5204) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__5205) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2167,Vvar__0__C__2168] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2167) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2168) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1809,Vvar__1___24Anonymous__1810,Vvar__0__C__1811,Vvar__1___24Anonymous__1812,Vvar__2___24Anonymous__1813] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1809,Vvar__1___24Anonymous__1810) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1811,Vvar__1___24Anonymous__1812,Vvar__2___24Anonymous__1813) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__1977,Vvar__1___24Anonymous__1978] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1977,Vvar__1___24Anonymous__1978) ).
fof('$_fix_38095_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__38095__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__0___24Anonymous__38096] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38096)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38096)
& c_24__fix__38095__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__38095__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__0___24Anonymous__38096,Vv__CANONICAL__3)) ) ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1156,Vvar__0__A__1157] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1156) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1157)
=> Vvar__0__A__1156 = Vvar__0__A__1157 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__4,Vvar__0___24Anonymous__5] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5)
=> Vvar__0___24Anonymous__4 = Vvar__0___24Anonymous__5 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__1152,Vvar__0__A__1153,Vvar__1___24Anonymous__1154,Vvar__1___24Anonymous__1155] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1152,Vvar__1___24Anonymous__1154) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1153,Vvar__1___24Anonymous__1155)
=> ( Vvar__1___24Anonymous__1154 = Vvar__1___24Anonymous__1155
& Vvar__0__A__1152 = Vvar__0__A__1153 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__1205,Vvar__0__A__1206,Vvar__1___24Anonymous__1207,Vvar__1___24Anonymous__1208,Vvar__2___24Anonymous__1209,Vvar__2___24Anonymous__1210] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1205,Vvar__1___24Anonymous__1207,Vvar__2___24Anonymous__1209) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1206,Vvar__1___24Anonymous__1208,Vvar__2___24Anonymous__1210)
=> ( Vvar__2___24Anonymous__1209 = Vvar__2___24Anonymous__1210
& Vvar__1___24Anonymous__1207 = Vvar__1___24Anonymous__1208
& Vvar__0__A__1205 = Vvar__0__A__1206 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__4517,Vvar__0__A__4518,Vvar__1__B__4519,Vvar__1__B__4520,Vvar__2___24Anonymous__4521,Vvar__2___24Anonymous__4522] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4517,Vvar__1__B__4519,Vvar__2___24Anonymous__4521) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4518,Vvar__1__B__4520,Vvar__2___24Anonymous__4522)
=> ( Vvar__2___24Anonymous__4521 = Vvar__2___24Anonymous__4522
& Vvar__1__B__4519 = Vvar__1__B__4520
& Vvar__0__A__4517 = Vvar__0__A__4518 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__4523,Vvar__0__A__4524,Vvar__1__B__4525,Vvar__1__B__4526,Vvar__2___24Anonymous__4527,Vvar__2___24Anonymous__4528] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4523,Vvar__1__B__4525,Vvar__2___24Anonymous__4527) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4524,Vvar__1__B__4526,Vvar__2___24Anonymous__4528)
=> ( Vvar__2___24Anonymous__4527 = Vvar__2___24Anonymous__4528
& Vvar__1__B__4525 = Vvar__1__B__4526
& Vvar__0__A__4523 = Vvar__0__A__4524 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__1203,Vvar__0__A__1204] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1203) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1204)
=> Vvar__0__A__1203 = Vvar__0__A__1204 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__1173,Vvar__0__A__1174,Vvar__1__B__1175,Vvar__1__B__1176,Vvar__2___24Anonymous__1177,Vvar__2___24Anonymous__1178,Vvar__3___24Anonymous__1179,Vvar__3___24Anonymous__1180] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1173,Vvar__1__B__1175,Vvar__2___24Anonymous__1177,Vvar__3___24Anonymous__1179) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1174,Vvar__1__B__1176,Vvar__2___24Anonymous__1178,Vvar__3___24Anonymous__1180)
=> ( Vvar__3___24Anonymous__1179 = Vvar__3___24Anonymous__1180
& Vvar__2___24Anonymous__1177 = Vvar__2___24Anonymous__1178
& Vvar__1__B__1175 = Vvar__1__B__1176
& Vvar__0__A__1173 = Vvar__0__A__1174 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__8717,Vvar__0__A__8718,Vvar__1__P__8719,Vvar__1__P__8720,Vvar__2__x__8721,Vvar__2__x__8722,Vvar__3___24Anonymous__8723,Vvar__3___24Anonymous__8724] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__8717,Vvar__1__P__8719,Vvar__2__x__8721) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__8718,Vvar__1__P__8720,Vvar__2__x__8722)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__8721 = Vvar__2__x__8722
& Vvar__1__P__8719 = Vvar__1__P__8720
& Vvar__0__A__8717 = Vvar__0__A__8718 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__24665,Vvar__0__A__24666,Vvar__1__P__24667,Vvar__1__P__24668,Vvar__2__x__24669,Vvar__2__x__24670,Vvar__3___24Anonymous__24671,Vvar__3___24Anonymous__24672] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__24665,Vvar__1__P__24667,Vvar__2__x__24669,Vvar__3___24Anonymous__24671) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__24666,Vvar__1__P__24668,Vvar__2__x__24670,Vvar__3___24Anonymous__24672)
=> ( Vvar__3___24Anonymous__24671 = Vvar__3___24Anonymous__24672
& Vvar__2__x__24669 = Vvar__2__x__24670
& Vvar__1__P__24667 = Vvar__1__P__24668
& Vvar__0__A__24665 = Vvar__0__A__24666 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__2736,Vvar__0__A__2737,Vvar__1__B__2738,Vvar__1__B__2739,Vvar__2___24Anonymous__2740,Vvar__2___24Anonymous__2741] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2736,Vvar__1__B__2738,Vvar__2___24Anonymous__2740) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2737,Vvar__1__B__2739,Vvar__2___24Anonymous__2741)
=> ( Vvar__2___24Anonymous__2740 = Vvar__2___24Anonymous__2741
& Vvar__1__B__2738 = Vvar__1__B__2739
& Vvar__0__A__2736 = Vvar__0__A__2737 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2742,Vvar__0__A__2743,Vvar__1__B__2744,Vvar__1__B__2745,Vvar__2___24Anonymous__2746,Vvar__2___24Anonymous__2747] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2742,Vvar__1__B__2744) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2743,Vvar__1__B__2745)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2744 = Vvar__1__B__2745
& Vvar__0__A__2742 = Vvar__0__A__2743 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__2652,Vvar__0__A__2653,Vvar__1__B__2654,Vvar__1__B__2655,Vvar__2___24Anonymous__2656,Vvar__2___24Anonymous__2657] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2652,Vvar__1__B__2654) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2653,Vvar__1__B__2655)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2654 = Vvar__1__B__2655
& Vvar__0__A__2652 = Vvar__0__A__2653 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2658,Vvar__0__A__2659,Vvar__1__B__2660,Vvar__1__B__2661,Vvar__2___24Anonymous__2662,Vvar__2___24Anonymous__2663] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2658,Vvar__1__B__2660) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2659,Vvar__1__B__2661)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2660 = Vvar__1__B__2661
& Vvar__0__A__2658 = Vvar__0__A__2659 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__721,Vvar__0___24Anonymous__722] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__721) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__722)
=> Vvar__0___24Anonymous__721 = Vvar__0___24Anonymous__722 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__734,Vvar__0___24Anonymous__735] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__734) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__735)
=> Vvar__0___24Anonymous__734 = Vvar__0___24Anonymous__735 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__732,Vvar__0___24Anonymous__733] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__732) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__733)
=> Vvar__0___24Anonymous__732 = Vvar__0___24Anonymous__733 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__706,Vvar__0___24Anonymous__707] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__706) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__707)
=> Vvar__0___24Anonymous__706 = Vvar__0___24Anonymous__707 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__708,Vvar__0___24Anonymous__709] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__708) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__709)
=> Vvar__0___24Anonymous__708 = Vvar__0___24Anonymous__709 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__5552,Vvar__0__Qnum__5553,Vvar__1__Qden__5554,Vvar__1__Qden__5555] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__5552,Vvar__1__Qden__5554) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__5553,Vvar__1__Qden__5555)
=> ( Vvar__1__Qden__5554 = Vvar__1__Qden__5555
& Vvar__0__Qnum__5552 = Vvar__0__Qnum__5553 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__28226,Vvar__0__pos__28227,Vvar__1__cond__pos__28228,Vvar__1__cond__pos__28229] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__28226) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__28227)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__28226 = Vvar__0__pos__28227 ) ) ).
fof('$_inj_Coq.Reals.RList.cons',axiom,
! [Vvar__0___24Anonymous__45323,Vvar__0___24Anonymous__45324,Vvar__1___24Anonymous__45325,Vvar__1___24Anonymous__45326] :
( cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__45323,Vvar__1___24Anonymous__45325) = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__45324,Vvar__1___24Anonymous__45326)
=> ( Vvar__1___24Anonymous__45325 = Vvar__1___24Anonymous__45326
& Vvar__0___24Anonymous__45323 = Vvar__0___24Anonymous__45324 ) ) ).
fof('$_inj_Coq.Reals.RiemannInt_SF.mkStepFun',axiom,
! [Vvar__0__a__45487,Vvar__0__a__45488,Vvar__1__b__45489,Vvar__1__b__45490,Vvar__2__fe__45491,Vvar__2__fe__45492,Vvar__3__pre__45493,Vvar__3__pre__45494] :
( cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(Vvar__0__a__45487,Vvar__1__b__45489,Vvar__2__fe__45491,Vvar__3__pre__45493) = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(Vvar__0__a__45488,Vvar__1__b__45490,Vvar__2__fe__45492,Vvar__3__pre__45494)
=> ( Vvar__3__pre__45493 = Vvar__3__pre__45494
& Vvar__2__fe__45491 = Vvar__2__fe__45492
& Vvar__1__b__45489 = Vvar__1__b__45490
& Vvar__0__a__45487 = Vvar__0__a__45488 ) ) ).
fof('$_inj_Coq.Sets.Partial_Order.Definition_of_PO',axiom,
! [Vvar__0__U__45186,Vvar__0__U__45187,Vvar__1__Carrier__of__45188,Vvar__1__Carrier__of__45189,Vvar__2__Rel__of__45190,Vvar__2__Rel__of__45191,Vvar__3__PO__cond1__45192,Vvar__3__PO__cond1__45193,Vvar__4__PO__cond2__45194,Vvar__4__PO__cond2__45195] :
( cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__45186,Vvar__1__Carrier__of__45188,Vvar__2__Rel__of__45190) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__45187,Vvar__1__Carrier__of__45189,Vvar__2__Rel__of__45191)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__Rel__of__45190 = Vvar__2__Rel__of__45191
& Vvar__1__Carrier__of__45188 = Vvar__1__Carrier__of__45189
& Vvar__0__U__45186 = Vvar__0__U__45187 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__613,Vvar__0___24Anonymous__614,Vvar__1___24Anonymous__615,Vvar__1___24Anonymous__616,Vvar__2___24Anonymous__617,Vvar__2___24Anonymous__618,Vvar__3___24Anonymous__619,Vvar__3___24Anonymous__620,Vvar__4___24Anonymous__621,Vvar__4___24Anonymous__622,Vvar__5___24Anonymous__623,Vvar__5___24Anonymous__624,Vvar__6___24Anonymous__625,Vvar__6___24Anonymous__626,Vvar__7___24Anonymous__627,Vvar__7___24Anonymous__628] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__613,Vvar__1___24Anonymous__615,Vvar__2___24Anonymous__617,Vvar__3___24Anonymous__619,Vvar__4___24Anonymous__621,Vvar__5___24Anonymous__623,Vvar__6___24Anonymous__625,Vvar__7___24Anonymous__627) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__614,Vvar__1___24Anonymous__616,Vvar__2___24Anonymous__618,Vvar__3___24Anonymous__620,Vvar__4___24Anonymous__622,Vvar__5___24Anonymous__624,Vvar__6___24Anonymous__626,Vvar__7___24Anonymous__628)
=> ( Vvar__7___24Anonymous__627 = Vvar__7___24Anonymous__628
& Vvar__6___24Anonymous__625 = Vvar__6___24Anonymous__626
& Vvar__5___24Anonymous__623 = Vvar__5___24Anonymous__624
& Vvar__4___24Anonymous__621 = Vvar__4___24Anonymous__622
& Vvar__3___24Anonymous__619 = Vvar__3___24Anonymous__620
& Vvar__2___24Anonymous__617 = Vvar__2___24Anonymous__618
& Vvar__1___24Anonymous__615 = Vvar__1___24Anonymous__616
& Vvar__0___24Anonymous__613 = Vvar__0___24Anonymous__614 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__5292,Vvar__0__n__5293] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__5292) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__5293)
=> Vvar__0__n__5292 = Vvar__0__n__5293 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__5294,Vvar__0__n__5295,Vvar__1___24Anonymous__5296,Vvar__1___24Anonymous__5297] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__5294,Vvar__1___24Anonymous__5296) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__5295,Vvar__1___24Anonymous__5297)
=> ( Vvar__1___24Anonymous__5296 = Vvar__1___24Anonymous__5297
& Vvar__0__n__5294 = Vvar__0__n__5295 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__2899,Vvar__0__A__2900,Vvar__1__h__2901,Vvar__1__h__2902,Vvar__2__n__2903,Vvar__2__n__2904,Vvar__3___24Anonymous__2905,Vvar__3___24Anonymous__2906] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2899,Vvar__1__h__2901,Vvar__2__n__2903,Vvar__3___24Anonymous__2905) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2900,Vvar__1__h__2902,Vvar__2__n__2904,Vvar__3___24Anonymous__2906)
=> ( Vvar__3___24Anonymous__2905 = Vvar__3___24Anonymous__2906
& Vvar__2__n__2903 = Vvar__2__n__2904
& Vvar__1__h__2901 = Vvar__1__h__2902
& Vvar__0__A__2899 = Vvar__0__A__2900 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__2897,Vvar__0__A__2898] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2897) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2898)
=> Vvar__0__A__2897 = Vvar__0__A__2898 ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__4814,Vvar__0__C__4815,Vvar__1___24Anonymous__4816,Vvar__1___24Anonymous__4817] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__4814,Vvar__1___24Anonymous__4816) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__4815,Vvar__1___24Anonymous__4817)
=> ( Vvar__1___24Anonymous__4816 = Vvar__1___24Anonymous__4817
& Vvar__0__C__4814 = Vvar__0__C__4815 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__4818,Vvar__0__C__4819,Vvar__1___24Anonymous__4820,Vvar__1___24Anonymous__4821,Vvar__2___24Anonymous__4822,Vvar__2___24Anonymous__4823] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__4818,Vvar__1___24Anonymous__4820,Vvar__2___24Anonymous__4822) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__4819,Vvar__1___24Anonymous__4821,Vvar__2___24Anonymous__4823)
=> ( Vvar__2___24Anonymous__4822 = Vvar__2___24Anonymous__4823
& Vvar__1___24Anonymous__4820 = Vvar__1___24Anonymous__4821
& Vvar__0__C__4818 = Vvar__0__C__4819 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__4810,Vvar__0__C__4811,Vvar__1___24Anonymous__4812,Vvar__1___24Anonymous__4813] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__4810,Vvar__1___24Anonymous__4812) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__4811,Vvar__1___24Anonymous__4813)
=> ( Vvar__1___24Anonymous__4812 = Vvar__1___24Anonymous__4813
& Vvar__0__C__4810 = Vvar__0__C__4811 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__4830,Vvar__0__C__4831,Vvar__1___24Anonymous__4832,Vvar__1___24Anonymous__4833,Vvar__2___24Anonymous__4834,Vvar__2___24Anonymous__4835] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__4830,Vvar__1___24Anonymous__4832,Vvar__2___24Anonymous__4834) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__4831,Vvar__1___24Anonymous__4833,Vvar__2___24Anonymous__4835)
=> ( Vvar__2___24Anonymous__4834 = Vvar__2___24Anonymous__4835
& Vvar__1___24Anonymous__4832 = Vvar__1___24Anonymous__4833
& Vvar__0__C__4830 = Vvar__0__C__4831 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__4836,Vvar__0__C__4837,Vvar__1___24Anonymous__4838,Vvar__1___24Anonymous__4839] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__4836,Vvar__1___24Anonymous__4838) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__4837,Vvar__1___24Anonymous__4839)
=> ( Vvar__1___24Anonymous__4838 = Vvar__1___24Anonymous__4839
& Vvar__0__C__4836 = Vvar__0__C__4837 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__4840,Vvar__0__C__4841,Vvar__1___24Anonymous__4842,Vvar__1___24Anonymous__4843,Vvar__2___24Anonymous__4844,Vvar__2___24Anonymous__4845] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__4840,Vvar__1___24Anonymous__4842,Vvar__2___24Anonymous__4844) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__4841,Vvar__1___24Anonymous__4843,Vvar__2___24Anonymous__4845)
=> ( Vvar__2___24Anonymous__4844 = Vvar__2___24Anonymous__4845
& Vvar__1___24Anonymous__4842 = Vvar__1___24Anonymous__4843
& Vvar__0__C__4840 = Vvar__0__C__4841 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__4824,Vvar__0__C__4825,Vvar__1___24Anonymous__4826,Vvar__1___24Anonymous__4827,Vvar__2___24Anonymous__4828,Vvar__2___24Anonymous__4829] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__4824,Vvar__1___24Anonymous__4826,Vvar__2___24Anonymous__4828) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__4825,Vvar__1___24Anonymous__4827,Vvar__2___24Anonymous__4829)
=> ( Vvar__2___24Anonymous__4828 = Vvar__2___24Anonymous__4829
& Vvar__1___24Anonymous__4826 = Vvar__1___24Anonymous__4827
& Vvar__0__C__4824 = Vvar__0__C__4825 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__4885,Vvar__0__C__4886,Vvar__1___24Anonymous__4887,Vvar__1___24Anonymous__4888,Vvar__2___24Anonymous__4889,Vvar__2___24Anonymous__4890,Vvar__3___24Anonymous__4891,Vvar__3___24Anonymous__4892] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4885,Vvar__1___24Anonymous__4887,Vvar__2___24Anonymous__4889,Vvar__3___24Anonymous__4891) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4886,Vvar__1___24Anonymous__4888,Vvar__2___24Anonymous__4890,Vvar__3___24Anonymous__4892)
=> ( Vvar__3___24Anonymous__4891 = Vvar__3___24Anonymous__4892
& Vvar__2___24Anonymous__4889 = Vvar__2___24Anonymous__4890
& Vvar__1___24Anonymous__4887 = Vvar__1___24Anonymous__4888
& Vvar__0__C__4885 = Vvar__0__C__4886 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__4875,Vvar__0__C__4876,Vvar__1___24Anonymous__4877,Vvar__1___24Anonymous__4878] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4875,Vvar__1___24Anonymous__4877) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4876,Vvar__1___24Anonymous__4878)
=> ( Vvar__1___24Anonymous__4877 = Vvar__1___24Anonymous__4878
& Vvar__0__C__4875 = Vvar__0__C__4876 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__4879,Vvar__0__C__4880,Vvar__1___24Anonymous__4881,Vvar__1___24Anonymous__4882,Vvar__2___24Anonymous__4883,Vvar__2___24Anonymous__4884] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4879,Vvar__1___24Anonymous__4881,Vvar__2___24Anonymous__4883) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4880,Vvar__1___24Anonymous__4882,Vvar__2___24Anonymous__4884)
=> ( Vvar__2___24Anonymous__4883 = Vvar__2___24Anonymous__4884
& Vvar__1___24Anonymous__4881 = Vvar__1___24Anonymous__4882
& Vvar__0__C__4879 = Vvar__0__C__4880 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__5697,Vvar__0__r__5698] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__5697) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__5698)
=> Vvar__0__r__5697 = Vvar__0__r__5698 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__5685,Vvar__0__r1__5686,Vvar__1__r2__5687,Vvar__1__r2__5688] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__5685,Vvar__1__r2__5687) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__5686,Vvar__1__r2__5688)
=> ( Vvar__1__r2__5687 = Vvar__1__r2__5688
& Vvar__0__r1__5685 = Vvar__0__r1__5686 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__5689,Vvar__0__r1__5690,Vvar__1__r2__5691,Vvar__1__r2__5692] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__5689,Vvar__1__r2__5691) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__5690,Vvar__1__r2__5692)
=> ( Vvar__1__r2__5691 = Vvar__1__r2__5692
& Vvar__0__r1__5689 = Vvar__0__r1__5690 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__5699,Vvar__0__r__5700] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__5699) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__5700)
=> Vvar__0__r__5699 = Vvar__0__r__5700 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__5681,Vvar__0__r1__5682,Vvar__1__r2__5683,Vvar__1__r2__5684] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__5681,Vvar__1__r2__5683) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__5682,Vvar__1__r2__5684)
=> ( Vvar__1__r2__5683 = Vvar__1__r2__5684
& Vvar__0__r1__5681 = Vvar__0__r1__5682 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__5693,Vvar__0__r1__5694,Vvar__1__z__5695,Vvar__1__z__5696] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__5693,Vvar__1__z__5695) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__5694,Vvar__1__z__5696)
=> ( Vvar__1__z__5695 = Vvar__1__z__5696
& Vvar__0__r1__5693 = Vvar__0__r1__5694 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__5677,Vvar__0__r__5678] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__5677) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__5678)
=> Vvar__0__r__5677 = Vvar__0__r__5678 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__5679,Vvar__0__r__5680] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__5679) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__5680)
=> Vvar__0__r__5679 = Vvar__0__r__5680 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__24171,Vvar__0__T__24172,Vvar__1__Flhs__24173,Vvar__1__Flhs__24174,Vvar__2__Fop__24175,Vvar__2__Fop__24176,Vvar__3__Frhs__24177,Vvar__3__Frhs__24178] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__24171,Vvar__1__Flhs__24173,Vvar__2__Fop__24175,Vvar__3__Frhs__24177) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__24172,Vvar__1__Flhs__24174,Vvar__2__Fop__24176,Vvar__3__Frhs__24178)
=> ( Vvar__3__Frhs__24177 = Vvar__3__Frhs__24178
& Vvar__2__Fop__24175 = Vvar__2__Fop__24176
& Vvar__1__Flhs__24173 = Vvar__1__Flhs__24174
& Vvar__0__T__24171 = Vvar__0__T__24172 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__5925,Vvar__0__C__5926,Vvar__1___24Anonymous__5927,Vvar__1___24Anonymous__5928,Vvar__2___24Anonymous__5929,Vvar__2___24Anonymous__5930] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__5925,Vvar__1___24Anonymous__5927,Vvar__2___24Anonymous__5929) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__5926,Vvar__1___24Anonymous__5928,Vvar__2___24Anonymous__5930)
=> ( Vvar__2___24Anonymous__5929 = Vvar__2___24Anonymous__5930
& Vvar__1___24Anonymous__5927 = Vvar__1___24Anonymous__5928
& Vvar__0__C__5925 = Vvar__0__C__5926 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__5931,Vvar__0__C__5932,Vvar__1___24Anonymous__5933,Vvar__1___24Anonymous__5934] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__5931,Vvar__1___24Anonymous__5933) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__5932,Vvar__1___24Anonymous__5934)
=> ( Vvar__1___24Anonymous__5933 = Vvar__1___24Anonymous__5934
& Vvar__0__C__5931 = Vvar__0__C__5932 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__5905,Vvar__0__C__5906,Vvar__1___24Anonymous__5907,Vvar__1___24Anonymous__5908] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__5905,Vvar__1___24Anonymous__5907) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__5906,Vvar__1___24Anonymous__5908)
=> ( Vvar__1___24Anonymous__5907 = Vvar__1___24Anonymous__5908
& Vvar__0__C__5905 = Vvar__0__C__5906 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__5913,Vvar__0__C__5914,Vvar__1___24Anonymous__5915,Vvar__1___24Anonymous__5916,Vvar__2___24Anonymous__5917,Vvar__2___24Anonymous__5918] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__5913,Vvar__1___24Anonymous__5915,Vvar__2___24Anonymous__5917) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__5914,Vvar__1___24Anonymous__5916,Vvar__2___24Anonymous__5918)
=> ( Vvar__2___24Anonymous__5917 = Vvar__2___24Anonymous__5918
& Vvar__1___24Anonymous__5915 = Vvar__1___24Anonymous__5916
& Vvar__0__C__5913 = Vvar__0__C__5914 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__5919,Vvar__0__C__5920,Vvar__1___24Anonymous__5921,Vvar__1___24Anonymous__5922,Vvar__2___24Anonymous__5923,Vvar__2___24Anonymous__5924] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__5919,Vvar__1___24Anonymous__5921,Vvar__2___24Anonymous__5923) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__5920,Vvar__1___24Anonymous__5922,Vvar__2___24Anonymous__5924)
=> ( Vvar__2___24Anonymous__5923 = Vvar__2___24Anonymous__5924
& Vvar__1___24Anonymous__5921 = Vvar__1___24Anonymous__5922
& Vvar__0__C__5919 = Vvar__0__C__5920 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__5909,Vvar__0__C__5910,Vvar__1___24Anonymous__5911,Vvar__1___24Anonymous__5912] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__5909,Vvar__1___24Anonymous__5911) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__5910,Vvar__1___24Anonymous__5912)
=> ( Vvar__1___24Anonymous__5911 = Vvar__1___24Anonymous__5912
& Vvar__0__C__5909 = Vvar__0__C__5910 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__5935,Vvar__0__C__5936] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__5935) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__5936)
=> Vvar__0__C__5935 = Vvar__0__C__5936 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__27913,Vvar__0__TA__27914,Vvar__1__TX__27915,Vvar__1__TX__27916,Vvar__2__AA__27917,Vvar__2__AA__27918,Vvar__3__AF__27919,Vvar__3__AF__27920,Vvar__4___24Anonymous__27921,Vvar__4___24Anonymous__27922,Vvar__5___24Anonymous__27923,Vvar__5___24Anonymous__27924] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__27913,Vvar__1__TX__27915,Vvar__2__AA__27917,Vvar__3__AF__27919,Vvar__4___24Anonymous__27921,Vvar__5___24Anonymous__27923) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__27914,Vvar__1__TX__27916,Vvar__2__AA__27918,Vvar__3__AF__27920,Vvar__4___24Anonymous__27922,Vvar__5___24Anonymous__27924)
=> ( Vvar__5___24Anonymous__27923 = Vvar__5___24Anonymous__27924
& Vvar__4___24Anonymous__27921 = Vvar__4___24Anonymous__27922
& Vvar__3__AF__27919 = Vvar__3__AF__27920
& Vvar__2__AA__27917 = Vvar__2__AA__27918
& Vvar__1__TX__27915 = Vvar__1__TX__27916
& Vvar__0__TA__27913 = Vvar__0__TA__27914 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__27925,Vvar__0__TA__27926,Vvar__1__TX__27927,Vvar__1__TX__27928,Vvar__2__AA__27929,Vvar__2__AA__27930,Vvar__3__AF__27931,Vvar__3__AF__27932,Vvar__4___24Anonymous__27933,Vvar__4___24Anonymous__27934,Vvar__5___24Anonymous__27935,Vvar__5___24Anonymous__27936] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__27925,Vvar__1__TX__27927,Vvar__2__AA__27929,Vvar__3__AF__27931,Vvar__4___24Anonymous__27933,Vvar__5___24Anonymous__27935) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__27926,Vvar__1__TX__27928,Vvar__2__AA__27930,Vvar__3__AF__27932,Vvar__4___24Anonymous__27934,Vvar__5___24Anonymous__27936)
=> ( Vvar__5___24Anonymous__27935 = Vvar__5___24Anonymous__27936
& Vvar__4___24Anonymous__27933 = Vvar__4___24Anonymous__27934
& Vvar__3__AF__27931 = Vvar__3__AF__27932
& Vvar__2__AA__27929 = Vvar__2__AA__27930
& Vvar__1__TX__27927 = Vvar__1__TX__27928
& Vvar__0__TA__27925 = Vvar__0__TA__27926 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__27937,Vvar__0__TA__27938,Vvar__1__TX__27939,Vvar__1__TX__27940,Vvar__2__AA__27941,Vvar__2__AA__27942,Vvar__3__AF__27943,Vvar__3__AF__27944,Vvar__4___24Anonymous__27945,Vvar__4___24Anonymous__27946,Vvar__5___24Anonymous__27947,Vvar__5___24Anonymous__27948] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__27937,Vvar__1__TX__27939,Vvar__2__AA__27941,Vvar__3__AF__27943,Vvar__4___24Anonymous__27945,Vvar__5___24Anonymous__27947) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__27938,Vvar__1__TX__27940,Vvar__2__AA__27942,Vvar__3__AF__27944,Vvar__4___24Anonymous__27946,Vvar__5___24Anonymous__27948)
=> ( Vvar__5___24Anonymous__27947 = Vvar__5___24Anonymous__27948
& Vvar__4___24Anonymous__27945 = Vvar__4___24Anonymous__27946
& Vvar__3__AF__27943 = Vvar__3__AF__27944
& Vvar__2__AA__27941 = Vvar__2__AA__27942
& Vvar__1__TX__27939 = Vvar__1__TX__27940
& Vvar__0__TA__27937 = Vvar__0__TA__27938 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__27895,Vvar__0__TA__27896,Vvar__1__TX__27897,Vvar__1__TX__27898,Vvar__2__AA__27899,Vvar__2__AA__27900,Vvar__3__AF__27901,Vvar__3__AF__27902] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__27895,Vvar__1__TX__27897,Vvar__2__AA__27899,Vvar__3__AF__27901) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__27896,Vvar__1__TX__27898,Vvar__2__AA__27900,Vvar__3__AF__27902)
=> ( Vvar__3__AF__27901 = Vvar__3__AF__27902
& Vvar__2__AA__27899 = Vvar__2__AA__27900
& Vvar__1__TX__27897 = Vvar__1__TX__27898
& Vvar__0__TA__27895 = Vvar__0__TA__27896 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__27959,Vvar__0__TA__27960,Vvar__1__TX__27961,Vvar__1__TX__27962,Vvar__2__AA__27963,Vvar__2__AA__27964,Vvar__3__AF__27965,Vvar__3__AF__27966,Vvar__4___24Anonymous__27967,Vvar__4___24Anonymous__27968,Vvar__5___24Anonymous__27969,Vvar__5___24Anonymous__27970,Vvar__6___24Anonymous__27971,Vvar__6___24Anonymous__27972] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__27959,Vvar__1__TX__27961,Vvar__2__AA__27963,Vvar__3__AF__27965,Vvar__4___24Anonymous__27967,Vvar__5___24Anonymous__27969,Vvar__6___24Anonymous__27971) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__27960,Vvar__1__TX__27962,Vvar__2__AA__27964,Vvar__3__AF__27966,Vvar__4___24Anonymous__27968,Vvar__5___24Anonymous__27970,Vvar__6___24Anonymous__27972)
=> ( Vvar__6___24Anonymous__27971 = Vvar__6___24Anonymous__27972
& Vvar__5___24Anonymous__27969 = Vvar__5___24Anonymous__27970
& Vvar__4___24Anonymous__27967 = Vvar__4___24Anonymous__27968
& Vvar__3__AF__27965 = Vvar__3__AF__27966
& Vvar__2__AA__27963 = Vvar__2__AA__27964
& Vvar__1__TX__27961 = Vvar__1__TX__27962
& Vvar__0__TA__27959 = Vvar__0__TA__27960 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__27949,Vvar__0__TA__27950,Vvar__1__TX__27951,Vvar__1__TX__27952,Vvar__2__AA__27953,Vvar__2__AA__27954,Vvar__3__AF__27955,Vvar__3__AF__27956,Vvar__4___24Anonymous__27957,Vvar__4___24Anonymous__27958] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__27949,Vvar__1__TX__27951,Vvar__2__AA__27953,Vvar__3__AF__27955,Vvar__4___24Anonymous__27957) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__27950,Vvar__1__TX__27952,Vvar__2__AA__27954,Vvar__3__AF__27956,Vvar__4___24Anonymous__27958)
=> ( Vvar__4___24Anonymous__27957 = Vvar__4___24Anonymous__27958
& Vvar__3__AF__27955 = Vvar__3__AF__27956
& Vvar__2__AA__27953 = Vvar__2__AA__27954
& Vvar__1__TX__27951 = Vvar__1__TX__27952
& Vvar__0__TA__27949 = Vvar__0__TA__27950 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__27887,Vvar__0__TA__27888,Vvar__1__TX__27889,Vvar__1__TX__27890,Vvar__2__AA__27891,Vvar__2__AA__27892,Vvar__3__AF__27893,Vvar__3__AF__27894] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__27887,Vvar__1__TX__27889,Vvar__2__AA__27891,Vvar__3__AF__27893) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__27888,Vvar__1__TX__27890,Vvar__2__AA__27892,Vvar__3__AF__27894)
=> ( Vvar__3__AF__27893 = Vvar__3__AF__27894
& Vvar__2__AA__27891 = Vvar__2__AA__27892
& Vvar__1__TX__27889 = Vvar__1__TX__27890
& Vvar__0__TA__27887 = Vvar__0__TA__27888 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__27903,Vvar__0__TA__27904,Vvar__1__TX__27905,Vvar__1__TX__27906,Vvar__2__AA__27907,Vvar__2__AA__27908,Vvar__3__AF__27909,Vvar__3__AF__27910,Vvar__4___24Anonymous__27911,Vvar__4___24Anonymous__27912] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__27903,Vvar__1__TX__27905,Vvar__2__AA__27907,Vvar__3__AF__27909,Vvar__4___24Anonymous__27911) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__27904,Vvar__1__TX__27906,Vvar__2__AA__27908,Vvar__3__AF__27910,Vvar__4___24Anonymous__27912)
=> ( Vvar__4___24Anonymous__27911 = Vvar__4___24Anonymous__27912
& Vvar__3__AF__27909 = Vvar__3__AF__27910
& Vvar__2__AA__27907 = Vvar__2__AA__27908
& Vvar__1__TX__27905 = Vvar__1__TX__27906
& Vvar__0__TA__27903 = Vvar__0__TA__27904 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__28002,Vvar__0__A__28003,Vvar__1___24Anonymous__28004,Vvar__1___24Anonymous__28005,Vvar__2___24Anonymous__28006,Vvar__2___24Anonymous__28007,Vvar__3___24Anonymous__28008,Vvar__3___24Anonymous__28009] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__28002,Vvar__1___24Anonymous__28004,Vvar__2___24Anonymous__28006,Vvar__3___24Anonymous__28008) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__28003,Vvar__1___24Anonymous__28005,Vvar__2___24Anonymous__28007,Vvar__3___24Anonymous__28009)
=> ( Vvar__3___24Anonymous__28008 = Vvar__3___24Anonymous__28009
& Vvar__2___24Anonymous__28006 = Vvar__2___24Anonymous__28007
& Vvar__1___24Anonymous__28004 = Vvar__1___24Anonymous__28005
& Vvar__0__A__28002 = Vvar__0__A__28003 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__27998,Vvar__0__A__27999,Vvar__1___24Anonymous__28000,Vvar__1___24Anonymous__28001] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__27998,Vvar__1___24Anonymous__28000) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__27999,Vvar__1___24Anonymous__28001)
=> ( Vvar__1___24Anonymous__28000 = Vvar__1___24Anonymous__28001
& Vvar__0__A__27998 = Vvar__0__A__27999 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__27996,Vvar__0__A__27997] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__27996) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__27997)
=> Vvar__0__A__27996 = Vvar__0__A__27997 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__5208,Vvar__0__C__5209] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__5208) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__5209)
=> Vvar__0__C__5208 = Vvar__0__C__5209 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__5206,Vvar__0__C__5207] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__5206) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__5207)
=> Vvar__0__C__5206 = Vvar__0__C__5207 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__5214,Vvar__0__C__5215,Vvar__1___24Anonymous__5216,Vvar__1___24Anonymous__5217] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__5214,Vvar__1___24Anonymous__5216) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__5215,Vvar__1___24Anonymous__5217)
=> ( Vvar__1___24Anonymous__5216 = Vvar__1___24Anonymous__5217
& Vvar__0__C__5214 = Vvar__0__C__5215 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__5218,Vvar__0__C__5219,Vvar__1___24Anonymous__5220,Vvar__1___24Anonymous__5221,Vvar__2___24Anonymous__5222,Vvar__2___24Anonymous__5223] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__5218,Vvar__1___24Anonymous__5220,Vvar__2___24Anonymous__5222) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__5219,Vvar__1___24Anonymous__5221,Vvar__2___24Anonymous__5223)
=> ( Vvar__2___24Anonymous__5222 = Vvar__2___24Anonymous__5223
& Vvar__1___24Anonymous__5220 = Vvar__1___24Anonymous__5221
& Vvar__0__C__5218 = Vvar__0__C__5219 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__5210,Vvar__0__C__5211,Vvar__1___24Anonymous__5212,Vvar__1___24Anonymous__5213] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__5210,Vvar__1___24Anonymous__5212) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__5211,Vvar__1___24Anonymous__5213)
=> ( Vvar__1___24Anonymous__5212 = Vvar__1___24Anonymous__5213
& Vvar__0__C__5210 = Vvar__0__C__5211 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__5244,Vvar__0__C__5245,Vvar__1___24Anonymous__5246,Vvar__1___24Anonymous__5247,Vvar__2___24Anonymous__5248,Vvar__2___24Anonymous__5249] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__5244,Vvar__1___24Anonymous__5246,Vvar__2___24Anonymous__5248) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__5245,Vvar__1___24Anonymous__5247,Vvar__2___24Anonymous__5249)
=> ( Vvar__2___24Anonymous__5248 = Vvar__2___24Anonymous__5249
& Vvar__1___24Anonymous__5246 = Vvar__1___24Anonymous__5247
& Vvar__0__C__5244 = Vvar__0__C__5245 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__5240,Vvar__0__C__5241,Vvar__1___24Anonymous__5242,Vvar__1___24Anonymous__5243] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__5240,Vvar__1___24Anonymous__5242) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__5241,Vvar__1___24Anonymous__5243)
=> ( Vvar__1___24Anonymous__5242 = Vvar__1___24Anonymous__5243
& Vvar__0__C__5240 = Vvar__0__C__5241 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__5230,Vvar__0__C__5231,Vvar__1___24Anonymous__5232,Vvar__1___24Anonymous__5233,Vvar__2___24Anonymous__5234,Vvar__2___24Anonymous__5235] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__5230,Vvar__1___24Anonymous__5232,Vvar__2___24Anonymous__5234) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__5231,Vvar__1___24Anonymous__5233,Vvar__2___24Anonymous__5235)
=> ( Vvar__2___24Anonymous__5234 = Vvar__2___24Anonymous__5235
& Vvar__1___24Anonymous__5232 = Vvar__1___24Anonymous__5233
& Vvar__0__C__5230 = Vvar__0__C__5231 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__5236,Vvar__0__C__5237,Vvar__1___24Anonymous__5238,Vvar__1___24Anonymous__5239] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__5236,Vvar__1___24Anonymous__5238) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__5237,Vvar__1___24Anonymous__5239)
=> ( Vvar__1___24Anonymous__5238 = Vvar__1___24Anonymous__5239
& Vvar__0__C__5236 = Vvar__0__C__5237 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__5250,Vvar__0__C__5251,Vvar__1___24Anonymous__5252,Vvar__1___24Anonymous__5253,Vvar__2___24Anonymous__5254,Vvar__2___24Anonymous__5255] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__5250,Vvar__1___24Anonymous__5252,Vvar__2___24Anonymous__5254) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__5251,Vvar__1___24Anonymous__5253,Vvar__2___24Anonymous__5255)
=> ( Vvar__2___24Anonymous__5254 = Vvar__2___24Anonymous__5255
& Vvar__1___24Anonymous__5252 = Vvar__1___24Anonymous__5253
& Vvar__0__C__5250 = Vvar__0__C__5251 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__5224,Vvar__0__C__5225,Vvar__1___24Anonymous__5226,Vvar__1___24Anonymous__5227,Vvar__2___24Anonymous__5228,Vvar__2___24Anonymous__5229] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__5224,Vvar__1___24Anonymous__5226,Vvar__2___24Anonymous__5228) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__5225,Vvar__1___24Anonymous__5227,Vvar__2___24Anonymous__5229)
=> ( Vvar__2___24Anonymous__5228 = Vvar__2___24Anonymous__5229
& Vvar__1___24Anonymous__5226 = Vvar__1___24Anonymous__5227
& Vvar__0__C__5224 = Vvar__0__C__5225 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__5262,Vvar__0__C__5263,Vvar__1__num__5264,Vvar__1__num__5265,Vvar__2__denum__5266,Vvar__2__denum__5267,Vvar__3__condition__5268,Vvar__3__condition__5269] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__5262,Vvar__1__num__5264,Vvar__2__denum__5266,Vvar__3__condition__5268) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__5263,Vvar__1__num__5265,Vvar__2__denum__5267,Vvar__3__condition__5269)
=> ( Vvar__3__condition__5268 = Vvar__3__condition__5269
& Vvar__2__denum__5266 = Vvar__2__denum__5267
& Vvar__1__num__5264 = Vvar__1__num__5265
& Vvar__0__C__5262 = Vvar__0__C__5263 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__2171,Vvar__0__C__2172] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2171) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__2172)
=> Vvar__0__C__2171 = Vvar__0__C__2172 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__2169,Vvar__0__C__2170] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2169) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__2170)
=> Vvar__0__C__2169 = Vvar__0__C__2170 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__2177,Vvar__0__C__2178,Vvar__1___24Anonymous__2179,Vvar__1___24Anonymous__2180] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2177,Vvar__1___24Anonymous__2179) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__2178,Vvar__1___24Anonymous__2180)
=> ( Vvar__1___24Anonymous__2179 = Vvar__1___24Anonymous__2180
& Vvar__0__C__2177 = Vvar__0__C__2178 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__2181,Vvar__0__C__2182,Vvar__1___24Anonymous__2183,Vvar__1___24Anonymous__2184,Vvar__2___24Anonymous__2185,Vvar__2___24Anonymous__2186] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2181,Vvar__1___24Anonymous__2183,Vvar__2___24Anonymous__2185) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__2182,Vvar__1___24Anonymous__2184,Vvar__2___24Anonymous__2186)
=> ( Vvar__2___24Anonymous__2185 = Vvar__2___24Anonymous__2186
& Vvar__1___24Anonymous__2183 = Vvar__1___24Anonymous__2184
& Vvar__0__C__2181 = Vvar__0__C__2182 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__2173,Vvar__0__C__2174,Vvar__1___24Anonymous__2175,Vvar__1___24Anonymous__2176] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2173,Vvar__1___24Anonymous__2175) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__2174,Vvar__1___24Anonymous__2176)
=> ( Vvar__1___24Anonymous__2175 = Vvar__1___24Anonymous__2176
& Vvar__0__C__2173 = Vvar__0__C__2174 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__2193,Vvar__0__C__2194,Vvar__1___24Anonymous__2195,Vvar__1___24Anonymous__2196,Vvar__2___24Anonymous__2197,Vvar__2___24Anonymous__2198] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2193,Vvar__1___24Anonymous__2195,Vvar__2___24Anonymous__2197) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__2194,Vvar__1___24Anonymous__2196,Vvar__2___24Anonymous__2198)
=> ( Vvar__2___24Anonymous__2197 = Vvar__2___24Anonymous__2198
& Vvar__1___24Anonymous__2195 = Vvar__1___24Anonymous__2196
& Vvar__0__C__2193 = Vvar__0__C__2194 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__2199,Vvar__0__C__2200,Vvar__1___24Anonymous__2201,Vvar__1___24Anonymous__2202] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2199,Vvar__1___24Anonymous__2201) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__2200,Vvar__1___24Anonymous__2202)
=> ( Vvar__1___24Anonymous__2201 = Vvar__1___24Anonymous__2202
& Vvar__0__C__2199 = Vvar__0__C__2200 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__2203,Vvar__0__C__2204,Vvar__1___24Anonymous__2205,Vvar__1___24Anonymous__2206,Vvar__2___24Anonymous__2207,Vvar__2___24Anonymous__2208] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2203,Vvar__1___24Anonymous__2205,Vvar__2___24Anonymous__2207) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__2204,Vvar__1___24Anonymous__2206,Vvar__2___24Anonymous__2208)
=> ( Vvar__2___24Anonymous__2207 = Vvar__2___24Anonymous__2208
& Vvar__1___24Anonymous__2205 = Vvar__1___24Anonymous__2206
& Vvar__0__C__2203 = Vvar__0__C__2204 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__2187,Vvar__0__C__2188,Vvar__1___24Anonymous__2189,Vvar__1___24Anonymous__2190,Vvar__2___24Anonymous__2191,Vvar__2___24Anonymous__2192] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2187,Vvar__1___24Anonymous__2189,Vvar__2___24Anonymous__2191) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__2188,Vvar__1___24Anonymous__2190,Vvar__2___24Anonymous__2192)
=> ( Vvar__2___24Anonymous__2191 = Vvar__2___24Anonymous__2192
& Vvar__1___24Anonymous__2189 = Vvar__1___24Anonymous__2190
& Vvar__0__C__2187 = Vvar__0__C__2188 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__1824,Vvar__0__C__1825,Vvar__1___24Anonymous__1826,Vvar__1___24Anonymous__1827,Vvar__2___24Anonymous__1828,Vvar__2___24Anonymous__1829,Vvar__3___24Anonymous__1830,Vvar__3___24Anonymous__1831] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1824,Vvar__1___24Anonymous__1826,Vvar__2___24Anonymous__1828,Vvar__3___24Anonymous__1830) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1825,Vvar__1___24Anonymous__1827,Vvar__2___24Anonymous__1829,Vvar__3___24Anonymous__1831)
=> ( Vvar__3___24Anonymous__1830 = Vvar__3___24Anonymous__1831
& Vvar__2___24Anonymous__1828 = Vvar__2___24Anonymous__1829
& Vvar__1___24Anonymous__1826 = Vvar__1___24Anonymous__1827
& Vvar__0__C__1824 = Vvar__0__C__1825 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__1814,Vvar__0__C__1815,Vvar__1___24Anonymous__1816,Vvar__1___24Anonymous__1817] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1814,Vvar__1___24Anonymous__1816) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1815,Vvar__1___24Anonymous__1817)
=> ( Vvar__1___24Anonymous__1816 = Vvar__1___24Anonymous__1817
& Vvar__0__C__1814 = Vvar__0__C__1815 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__1818,Vvar__0__C__1819,Vvar__1___24Anonymous__1820,Vvar__1___24Anonymous__1821,Vvar__2___24Anonymous__1822,Vvar__2___24Anonymous__1823] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1818,Vvar__1___24Anonymous__1820,Vvar__2___24Anonymous__1822) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1819,Vvar__1___24Anonymous__1821,Vvar__2___24Anonymous__1823)
=> ( Vvar__2___24Anonymous__1822 = Vvar__2___24Anonymous__1823
& Vvar__1___24Anonymous__1820 = Vvar__1___24Anonymous__1821
& Vvar__0__C__1818 = Vvar__0__C__1819 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__1983,Vvar__0___24Anonymous__1984,Vvar__1___24Anonymous__1985,Vvar__1___24Anonymous__1986] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1983,Vvar__1___24Anonymous__1985) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1984,Vvar__1___24Anonymous__1986)
=> ( Vvar__1___24Anonymous__1985 = Vvar__1___24Anonymous__1986
& Vvar__0___24Anonymous__1983 = Vvar__0___24Anonymous__1984 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__1979,Vvar__0___24Anonymous__1980,Vvar__1___24Anonymous__1981,Vvar__1___24Anonymous__1982] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1979,Vvar__1___24Anonymous__1981) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1980,Vvar__1___24Anonymous__1982)
=> ( Vvar__1___24Anonymous__1981 = Vvar__1___24Anonymous__1982
& Vvar__0___24Anonymous__1979 = Vvar__0___24Anonymous__1980 ) ) ).
fof('$_inj_Topology.DirectedSets.Build_DirectedSet',axiom,
! [Vvar__0__DS__set__38287,Vvar__0__DS__set__38288,Vvar__1__DS__ord__38289,Vvar__1__DS__ord__38290,Vvar__2__DS__ord__cond__38291,Vvar__2__DS__ord__cond__38292,Vvar__3__DS__join__cond__38293,Vvar__3__DS__join__cond__38294] :
( cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__38287,Vvar__1__DS__ord__38289) = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__38288,Vvar__1__DS__ord__38290)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__DS__ord__38289 = Vvar__1__DS__ord__38290
& Vvar__0__DS__set__38287 = Vvar__0__DS__set__38288 ) ) ).
fof('$_inj_Topology.Filters.Build_Filter',axiom,
! [Vvar__0__X__37685,Vvar__0__X__37686,Vvar__1__filter__family__37687,Vvar__1__filter__family__37688,Vvar__2__filter__intersection__37689,Vvar__2__filter__intersection__37690,Vvar__3__filter__upward__closed__37691,Vvar__3__filter__upward__closed__37692,Vvar__4__filter__full__37693,Vvar__4__filter__full__37694,Vvar__5__filter__empty__37695,Vvar__5__filter__empty__37696] :
( cTopology_2eFilters_2eBuild__Filter___24a2(Vvar__0__X__37685,Vvar__1__filter__family__37687) = cTopology_2eFilters_2eBuild__Filter___24a2(Vvar__0__X__37686,Vvar__1__filter__family__37688)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__filter__family__37687 = Vvar__1__filter__family__37688
& Vvar__0__X__37685 = Vvar__0__X__37686 ) ) ).
fof('$_inj_Topology.FiltersAndNets.Build_filter_to_net_DS_set',axiom,
! [Vvar__0__X__42642,Vvar__0__X__42643,Vvar__1__F__42644,Vvar__1__F__42645,Vvar__2__ftn__S__42646,Vvar__2__ftn__S__42647,Vvar__3__ftn__x__42648,Vvar__3__ftn__x__42649,Vvar__4__ftn__S__in__F__42650,Vvar__4__ftn__S__in__F__42651,Vvar__5__ftn__x__in__S__42652,Vvar__5__ftn__x__in__S__42653] :
( cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(Vvar__0__X__42642,Vvar__1__F__42644,Vvar__2__ftn__S__42646,Vvar__3__ftn__x__42648) = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(Vvar__0__X__42643,Vvar__1__F__42645,Vvar__2__ftn__S__42647,Vvar__3__ftn__x__42649)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__ftn__x__42648 = Vvar__3__ftn__x__42649
& Vvar__2__ftn__S__42646 = Vvar__2__ftn__S__42647
& Vvar__1__F__42644 = Vvar__1__F__42645
& Vvar__0__X__42642 = Vvar__0__X__42643 ) ) ).
fof('$_inj_Topology.Nets.Build_cluster_point_subnet_DS_set',axiom,
! [Vvar__0__X__39435,Vvar__0__X__39436,Vvar__1__I__39437,Vvar__1__I__39438,Vvar__2__x__39439,Vvar__2__x__39440,Vvar__3__x0__39441,Vvar__3__x0__39442,Vvar__4__cps__i__39443,Vvar__4__cps__i__39444,Vvar__5__cps__U__39445,Vvar__5__cps__U__39446,Vvar__6__cps__U__open__neigh__39447,Vvar__6__cps__U__open__neigh__39448,Vvar__7__cps__xi__in__U__39449,Vvar__7__cps__xi__in__U__39450] :
( cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(Vvar__0__X__39435,Vvar__1__I__39437,Vvar__2__x__39439,Vvar__3__x0__39441,Vvar__4__cps__i__39443,Vvar__5__cps__U__39445) = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(Vvar__0__X__39436,Vvar__1__I__39438,Vvar__2__x__39440,Vvar__3__x0__39442,Vvar__4__cps__i__39444,Vvar__5__cps__U__39446)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__5__cps__U__39445 = Vvar__5__cps__U__39446
& Vvar__4__cps__i__39443 = Vvar__4__cps__i__39444
& Vvar__3__x0__39441 = Vvar__3__x0__39442
& Vvar__2__x__39439 = Vvar__2__x__39440
& Vvar__1__I__39437 = Vvar__1__I__39438
& Vvar__0__X__39435 = Vvar__0__X__39436 ) ) ).
fof('$_inj_Topology.Nets.intro_neighborhood_net_DS',axiom,
! [Vvar__0__X__38609,Vvar__0__X__38610,Vvar__1__x__38611,Vvar__1__x__38612,Vvar__2__U__38613,Vvar__2__U__38614,Vvar__3__y__38615,Vvar__3__y__38616,Vvar__4___24Anonymous__38617,Vvar__4___24Anonymous__38618,Vvar__5___24Anonymous__38619,Vvar__5___24Anonymous__38620,Vvar__6___24Anonymous__38621,Vvar__6___24Anonymous__38622] :
( cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(Vvar__0__X__38609,Vvar__1__x__38611,Vvar__2__U__38613,Vvar__3__y__38615) = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(Vvar__0__X__38610,Vvar__1__x__38612,Vvar__2__U__38614,Vvar__3__y__38616)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__y__38615 = Vvar__3__y__38616
& Vvar__2__U__38613 = Vvar__2__U__38614
& Vvar__1__x__38611 = Vvar__1__x__38612
& Vvar__0__X__38609 = Vvar__0__X__38610 ) ) ).
fof('$_inj_Topology.TopologicalSpaces.Build_TopologicalSpace',axiom,
! [Vvar__0__point__set__37449,Vvar__0__point__set__37450,Vvar__1__open__37451,Vvar__1__open__37452,Vvar__2__open__family__union__37453,Vvar__2__open__family__union__37454,Vvar__3__open__intersection2__37455,Vvar__3__open__intersection2__37456,Vvar__4__open__full__37457,Vvar__4__open__full__37458] :
( cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__37449,Vvar__1__open__37451) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__37450,Vvar__1__open__37452)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__open__37451 = Vvar__1__open__37452
& Vvar__0__point__set__37449 = Vvar__0__point__set__37450 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__641,Vvar__1__Q__643,Vvar__2__init__646,Vvar__3___24Anonymous__647,Vvar__4___24Anonymous__648] :
( c_24__type__674___24t(Vvar__0__P__641,Vvar__1__Q__643,Vvar__2__init__646,Vvar__3___24Anonymous__647,Vvar__4___24Anonymous__648,Vvar__0__P__641)
=> ( c_24__type__682___24t(Vvar__0__P__641,Vvar__1__Q__643,Vvar__2__init__646,Vvar__3___24Anonymous__647,Vvar__4___24Anonymous__648,Vvar__1__Q__643)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__646)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__647)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__648)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__641,Vvar__1__Q__643,Vvar__2__init__646,Vvar__3___24Anonymous__647,Vvar__4___24Anonymous__648)
=> ( ( Vvar__4___24Anonymous__648 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__647 = Vvar__2__init__646 )
| ? [Vvar__3__k__662] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__662)
& ? [Vvar__4__l__663] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__663)
& ? [Vvar__5__n__664] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__664)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__641,Vvar__1__Q__643,Vvar__2__init__646,Vvar__3__k__662,Vvar__5__n__664)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__641,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__662),Vvar__4__l__663)
& p(happ(Vvar__1__Q__643,Vvar__4__l__663))
& Vvar__4___24Anonymous__648 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__664)
& Vvar__3___24Anonymous__647 = Vvar__4__l__663 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__393,Vvar__1__k__395,Vvar__2___24Anonymous__396] :
( c_24__type__410___24t(Vvar__0__P__393,Vvar__1__k__395,Vvar__2___24Anonymous__396,Vvar__0__P__393)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__395)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__396)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__393,Vvar__1__k__395,Vvar__2___24Anonymous__396)
=> ( Vvar__2___24Anonymous__396 = Vvar__1__k__395
| ? [Vvar__2__l__404] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__404)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__393,Vvar__1__k__395,Vvar__2__l__404)
& p(happ(Vvar__0__P__393,Vvar__2__l__404))
& Vvar__2___24Anonymous__396 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__404) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__468,Vvar__1__k__470,Vvar__2___24Anonymous__471] :
( c_24__type__487___24t(Vvar__0__Q__468,Vvar__1__k__470,Vvar__2___24Anonymous__471,Vvar__0__Q__468)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__470)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__471)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__468,Vvar__1__k__470,Vvar__2___24Anonymous__471)
=> ( ? [Vvar__2__l__476] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__476)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__468,Vvar__1__k__470,Vvar__2__l__476)
& Vvar__2___24Anonymous__471 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__476) )
| ? [Vvar__2__l__481] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__481)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__470,Vvar__2__l__481))
& p(happ(Vvar__0__Q__468,Vvar__2__l__481))
& Vvar__2___24Anonymous__471 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__481) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__4921] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4921)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__4921)
=> ( Vvar__0___24Anonymous__4921 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__4923] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4923)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__4923)
& Vvar__0___24Anonymous__4921 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__4923) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__4925] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4925)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__4925)
=> ? [Vvar__0__n__4927] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4927)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__4927)
& Vvar__0___24Anonymous__4925 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__4927) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX356] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX356)
=> ( VX356 = cCoq_2eInit_2eDatatypes_2etrue
| VX356 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX419] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX419)
=> ( VX419 = cCoq_2eInit_2eDatatypes_2eEq
| VX419 = cCoq_2eInit_2eDatatypes_2eLt
| VX419 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__1193,VX1194] :
( cType___24t(Vvar__0__A__1193)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1193,VX1194)
=> ( VX1194 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1193)
| ? [Vvar__1___24Anonymous__1197] :
( t(Vvar__1___24Anonymous__1197,Vvar__0__A__1193)
& ? [Vvar__2___24Anonymous__1198] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1193,Vvar__2___24Anonymous__1198)
& VX1194 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1193,Vvar__1___24Anonymous__1197,Vvar__2___24Anonymous__1198) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__1144,VX1145] :
( cType___24t(Vvar__0__A__1144)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__1144,VX1145)
=> ( ? [Vvar__1___24Anonymous__1147] :
( t(Vvar__1___24Anonymous__1147,Vvar__0__A__1144)
& VX1145 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1144,Vvar__1___24Anonymous__1147) )
| VX1145 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1144) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__1163,Vvar__1__B__1164,VX1165] :
( cType___24t(Vvar__0__A__1163)
=> ( cType___24t(Vvar__1__B__1164)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__1163,Vvar__1__B__1164,VX1165)
=> ? [Vvar__2___24Anonymous__1168] :
( t(Vvar__2___24Anonymous__1168,Vvar__0__A__1163)
& ? [Vvar__3___24Anonymous__1169] :
( t(Vvar__3___24Anonymous__1169,Vvar__1__B__1164)
& VX1165 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1163,Vvar__1__B__1164,Vvar__2___24Anonymous__1168,Vvar__3___24Anonymous__1169) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__4501,Vvar__1__B__4502,VX4503] :
( cType___24t(Vvar__0__A__4501)
=> ( cType___24t(Vvar__1__B__4502)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__4501,Vvar__1__B__4502,VX4503)
=> ( ? [Vvar__2___24Anonymous__4506] :
( t(Vvar__2___24Anonymous__4506,Vvar__0__A__4501)
& VX4503 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4501,Vvar__1__B__4502,Vvar__2___24Anonymous__4506) )
| ? [Vvar__2___24Anonymous__4509] :
( t(Vvar__2___24Anonymous__4509,Vvar__1__B__4502)
& VX4503 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4501,Vvar__1__B__4502,Vvar__2___24Anonymous__4509) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX355] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX355)
=> VX355 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__377,Vvar__1___24Anonymous__378] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__377)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__378)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__377,Vvar__1___24Anonymous__378))
=> ( Vvar__1___24Anonymous__378 = Vvar__0__n__377
| ? [Vvar__1__m__382] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__382)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__377,Vvar__1__m__382))
& Vvar__1___24Anonymous__378 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__382) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__8694,Vvar__1__P__8695,VX8698] :
( cType___24t(Vvar__0__A__8694)
=> ( c_24__type__8708___24t(Vvar__0__A__8694,Vvar__1__P__8695,Vvar__1__P__8695)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__8694,Vvar__1__P__8695,VX8698)
=> ? [Vvar__2__x__8703] :
( t(Vvar__2__x__8703,Vvar__0__A__8694)
& p(happ(Vvar__1__P__8695,Vvar__2__x__8703))
& VX8698 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__8694,Vvar__1__P__8695,Vvar__2__x__8703) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__24644,Vvar__1__P__24645,VX24648] :
( cType___24t(Vvar__0__A__24644)
=> ( c_24__type__24658___24t(Vvar__0__A__24644,Vvar__1__P__24645,Vvar__1__P__24645)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__24644,Vvar__1__P__24645,VX24648)
=> ? [Vvar__2__x__24653] :
( t(Vvar__2__x__24653,Vvar__0__A__24644)
& ? [Vvar__3___24Anonymous__24654] :
( t(Vvar__3___24Anonymous__24654,happ(Vvar__1__P__24645,Vvar__2__x__24653))
& VX24648 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__24644,Vvar__1__P__24645,Vvar__2__x__24653,Vvar__3___24Anonymous__24654) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__2634,Vvar__1__B__2635,VX2636] :
( cProp___24t(Vvar__0__A__2634)
=> ( cProp___24t(Vvar__1__B__2635)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__2634,Vvar__1__B__2635,VX2636)
=> ( ( p(Vvar__0__A__2634)
& VX2636 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2634,Vvar__1__B__2635) )
| ( p(Vvar__1__B__2635)
& VX2636 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2634,Vvar__1__B__2635) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__2718,Vvar__1__B__2719,VX2720] :
( cType___24t(Vvar__0__A__2718)
=> ( cProp___24t(Vvar__1__B__2719)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__2718,Vvar__1__B__2719,VX2720)
=> ( ? [Vvar__2___24Anonymous__2723] :
( t(Vvar__2___24Anonymous__2723,Vvar__0__A__2718)
& VX2720 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2718,Vvar__1__B__2719,Vvar__2___24Anonymous__2723) )
| ( p(Vvar__1__B__2719)
& VX2720 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2718,Vvar__1__B__2719) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX718] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX718)
=> ( VX718 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__719)
& VX718 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__719) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX725] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX725)
=> ( VX725 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__726] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__726)
& VX725 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__726) )
| ? [Vvar__0___24Anonymous__727] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__727)
& VX725 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__727) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX699] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX699)
=> ( ? [Vvar__0___24Anonymous__700] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__700)
& VX699 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__700) )
| ? [Vvar__0___24Anonymous__701] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__701)
& VX699 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__701) )
| VX699 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX5549] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX5549)
=> ? [Vvar__0__Qnum__5550] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__5550)
& ? [Vvar__1__Qden__5551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__5551)
& VX5549 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__5550,Vvar__1__Qden__5551) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX28223] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX28223)
=> ? [Vvar__0__pos__28224] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__28224)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__28224))
& VX28223 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__28224) ) ) ).
fof('$_inversion_Coq.Reals.RList.Rlist',axiom,
! [VX45318] :
( cCoq_2eReals_2eRList_2eRlist___24t(VX45318)
=> ( VX45318 = cCoq_2eReals_2eRList_2enil
| ? [Vvar__0___24Anonymous__45319] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0___24Anonymous__45319)
& ? [Vvar__1___24Anonymous__45320] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vvar__1___24Anonymous__45320)
& VX45318 = cCoq_2eReals_2eRList_2econs___24a2(Vvar__0___24Anonymous__45319,Vvar__1___24Anonymous__45320) ) ) ) ) ).
fof('$_inversion_Coq.Reals.RiemannInt_SF.StepFun',axiom,
! [Vvar__0__a__45471,Vvar__1__b__45472,VX45473] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__a__45471)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__1__b__45472)
=> ( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vvar__0__a__45471,Vvar__1__b__45472,VX45473)
=> ? [Vvar__2__fe__45476] :
( c_24__type__45482___24t(Vvar__0__a__45471,Vvar__1__b__45472,Vvar__2__fe__45476)
& ? [Vvar__3__pre__45479] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(Vvar__2__fe__45476,Vvar__0__a__45471,Vvar__1__b__45472,Vvar__3__pre__45479)
& VX45473 = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(Vvar__0__a__45471,Vvar__1__b__45472,Vvar__2__fe__45476,Vvar__3__pre__45479) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__31385,Vvar__1__R__31386] :
( cType___24t(Vvar__0__A__31385)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__31385,Vvar__1__R__31386)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__31385,Vvar__1__R__31386)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__31385,Vvar__1__R__31386)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__31385,Vvar__1__R__31386)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__31385,Vvar__1__R__31386)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__31378,Vvar__1__R__31379] :
( cType___24t(Vvar__0__A__31378)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__31378,Vvar__1__R__31379)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__31378,Vvar__1__R__31379)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__31378,Vvar__1__R__31379)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__31378,Vvar__1__R__31379)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Conditionally_complete',axiom,
! [Vvar__0__U__42035,Vvar__1__D__42036] :
( cType___24t(Vvar__0__U__42035)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__42035,Vvar__1__D__42036)
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(Vvar__0__U__42035,Vvar__1__D__42036)
=> ( ! [Vvar__var__var__var__2__X__42041__42046__42051__42056] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__42035,Vvar__var__var__var__2__X__42041__42046__42051__42056)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__42035,Vvar__var__var__var__2__X__42041__42046__42051__42056,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__42035,Vvar__1__D__42036))
=> ( ? [Vvar__var__var__var__4__maj__42042__42047__42052__42057] :
( t(Vvar__var__var__var__4__maj__42042__42047__42052__42057,Vvar__0__U__42035)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__42035,Vvar__1__D__42036,Vvar__var__var__var__2__X__42041__42046__42051__42056,Vvar__var__var__var__4__maj__42042__42047__42052__42057) )
=> ? [Vvar__var__var__var__5__bsup__42043__42048__42053__42058] :
( t(Vvar__var__var__var__5__bsup__42043__42048__42053__42058,Vvar__0__U__42035)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__42035,Vvar__1__D__42036,Vvar__var__var__var__2__X__42041__42046__42051__42056,Vvar__var__var__var__5__bsup__42043__42048__42053__42058) ) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Directed',axiom,
! [Vvar__0__U__41665,Vvar__1__D__41666,Vvar__2__X__41667] :
( cType___24t(Vvar__0__U__41665)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__41665,Vvar__1__D__41666)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__41665,Vvar__2__X__41667)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(Vvar__0__U__41665,Vvar__1__D__41666,Vvar__2__X__41667)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__41665,Vvar__2__X__41667,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__41665,Vvar__1__D__41666))
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__41665,Vvar__2__X__41667)
& ! [Vvar__var__var__var__var__5__x1__41675__41679__41683__41687__41691] :
( t(Vvar__var__var__var__var__5__x1__41675__41679__41683__41687__41691,Vvar__0__U__41665)
=> ! [Vvar__var__var__var__var__6__x2__41676__41680__41684__41688__41692] :
( t(Vvar__var__var__var__var__6__x2__41676__41680__41684__41688__41692,Vvar__0__U__41665)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__41665,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__41665,Vvar__var__var__var__var__5__x1__41675__41679__41683__41687__41691,Vvar__var__var__var__var__6__x2__41676__41680__41684__41688__41692),Vvar__2__X__41667)
=> ? [Vvar__var__var__var__var__8__x3__41677__41681__41685__41689__41693] :
( t(Vvar__var__var__var__var__8__x3__41677__41681__41685__41689__41693,Vvar__0__U__41665)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__41665,Vvar__2__X__41667,Vvar__var__var__var__var__8__x3__41677__41681__41685__41689__41693)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__41665,Vvar__1__D__41666,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__41665,Vvar__var__var__var__var__5__x1__41675__41679__41683__41687__41691,Vvar__var__var__var__var__6__x2__41676__41680__41684__41688__41692),Vvar__var__var__var__var__8__x3__41677__41681__41685__41689__41693) ) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Glb',axiom,
! [Vvar__0__U__41358,Vvar__1__D__41359,Vvar__2__B__41360,Vvar__3__x__41361] :
( cType___24t(Vvar__0__U__41358)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__41358,Vvar__1__D__41359)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__41358,Vvar__2__B__41360)
=> ( t(Vvar__3__x__41361,Vvar__0__U__41358)
=> ( cCoq_2eSets_2eCpo_2eGlb___24a4(Vvar__0__U__41358,Vvar__1__D__41359,Vvar__2__B__41360,Vvar__3__x__41361)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__41358,Vvar__1__D__41359,Vvar__2__B__41360,Vvar__3__x__41361)
& ! [Vvar__var__var__var__var__var__5__y__41369__41371__41373__41375__41377__41379] :
( t(Vvar__var__var__var__var__var__5__y__41369__41371__41373__41375__41377__41379,Vvar__0__U__41358)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__41358,Vvar__1__D__41359,Vvar__2__B__41360,Vvar__var__var__var__var__var__5__y__41369__41371__41373__41375__41377__41379)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__41358,Vvar__1__D__41359,Vvar__var__var__var__var__var__5__y__41369__41371__41373__41375__41377__41379,Vvar__3__x__41361) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Lower_Bound',axiom,
! [Vvar__0__U__41298,Vvar__1__D__41299,Vvar__2__B__41300,Vvar__3__x__41301] :
( cType___24t(Vvar__0__U__41298)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__41298,Vvar__1__D__41299)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__41298,Vvar__2__B__41300)
=> ( t(Vvar__3__x__41301,Vvar__0__U__41298)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__41298,Vvar__1__D__41299,Vvar__2__B__41300,Vvar__3__x__41301)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__41298,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__41298,Vvar__1__D__41299),Vvar__3__x__41301)
& ! [Vvar__var__var__var__var__var__5__y__41309__41311__41313__41315__41317__41319] :
( t(Vvar__var__var__var__var__var__5__y__41309__41311__41313__41315__41317__41319,Vvar__0__U__41298)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__41298,Vvar__2__B__41300,Vvar__var__var__var__var__var__5__y__41309__41311__41313__41315__41317__41319)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__41298,Vvar__1__D__41299,Vvar__3__x__41301,Vvar__var__var__var__var__var__5__y__41309__41311__41313__41315__41317__41319) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Lub',axiom,
! [Vvar__0__U__41331,Vvar__1__D__41332,Vvar__2__B__41333,Vvar__3__x__41334] :
( cType___24t(Vvar__0__U__41331)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__41331,Vvar__1__D__41332)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__41331,Vvar__2__B__41333)
=> ( t(Vvar__3__x__41334,Vvar__0__U__41331)
=> ( cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__41331,Vvar__1__D__41332,Vvar__2__B__41333,Vvar__3__x__41334)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__41331,Vvar__1__D__41332,Vvar__2__B__41333,Vvar__3__x__41334)
& ! [Vvar__var__var__var__var__var__5__y__41342__41344__41346__41348__41350__41352] :
( t(Vvar__var__var__var__var__var__5__y__41342__41344__41346__41348__41350__41352,Vvar__0__U__41331)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__41331,Vvar__1__D__41332,Vvar__2__B__41333,Vvar__var__var__var__var__var__5__y__41342__41344__41346__41348__41350__41352)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__41331,Vvar__1__D__41332,Vvar__3__x__41334,Vvar__var__var__var__var__var__5__y__41342__41344__41346__41348__41350__41352) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Totally_ordered',axiom,
! [Vvar__0__U__41385,Vvar__1__D__41386,Vvar__2__B__41387] :
( cType___24t(Vvar__0__U__41385)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__41385,Vvar__1__D__41386)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__41385,Vvar__2__B__41387)
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(Vvar__0__U__41385,Vvar__1__D__41386,Vvar__2__B__41387)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__41385,Vvar__2__B__41387,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__41385,Vvar__1__D__41386))
=> ! [Vvar__var__var__var__var__4__x__41393__41397__41401__41405__41409] :
( t(Vvar__var__var__var__var__4__x__41393__41397__41401__41405__41409,Vvar__0__U__41385)
=> ! [Vvar__var__var__var__var__5__y__41394__41398__41402__41406__41410] :
( t(Vvar__var__var__var__var__5__y__41394__41398__41402__41406__41410,Vvar__0__U__41385)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__41385,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__41385,Vvar__var__var__var__var__4__x__41393__41397__41401__41405__41409,Vvar__var__var__var__var__5__y__41394__41398__41402__41406__41410),Vvar__2__B__41387)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__41385,Vvar__1__D__41386,Vvar__var__var__var__var__4__x__41393__41397__41401__41405__41409,Vvar__var__var__var__var__5__y__41394__41398__41402__41406__41410)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__41385,Vvar__1__D__41386,Vvar__var__var__var__var__5__y__41394__41398__41402__41406__41410,Vvar__var__var__var__var__4__x__41393__41397__41401__41405__41409) ) ) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Upper_Bound',axiom,
! [Vvar__0__U__41265,Vvar__1__D__41266,Vvar__2__B__41267,Vvar__3__x__41268] :
( cType___24t(Vvar__0__U__41265)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__41265,Vvar__1__D__41266)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__41265,Vvar__2__B__41267)
=> ( t(Vvar__3__x__41268,Vvar__0__U__41265)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__41265,Vvar__1__D__41266,Vvar__2__B__41267,Vvar__3__x__41268)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__41265,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__41265,Vvar__1__D__41266),Vvar__3__x__41268)
& ! [Vvar__var__var__var__var__var__5__y__41276__41278__41280__41282__41284__41286] :
( t(Vvar__var__var__var__var__var__5__y__41276__41278__41280__41282__41284__41286,Vvar__0__U__41265)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__41265,Vvar__2__B__41267,Vvar__var__var__var__var__var__5__y__41276__41278__41280__41282__41284__41286)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__41265,Vvar__1__D__41266,Vvar__var__var__var__var__var__5__y__41276__41278__41280__41282__41284__41286,Vvar__3__x__41268) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Couple',axiom,
! [Vvar__0__U__42350,Vvar__1__x__42351,Vvar__2__y__42352,Vvar__1___24Anonymous__42353] :
( cType___24t(Vvar__0__U__42350)
=> ( t(Vvar__1__x__42351,Vvar__0__U__42350)
=> ( t(Vvar__2__y__42352,Vvar__0__U__42350)
=> ( t(Vvar__1___24Anonymous__42353,Vvar__0__U__42350)
=> ( cCoq_2eSets_2eEnsembles_2eCouple___24a4(Vvar__0__U__42350,Vvar__1__x__42351,Vvar__2__y__42352,Vvar__1___24Anonymous__42353)
=> ( Vvar__1___24Anonymous__42353 = Vvar__1__x__42351
| Vvar__1___24Anonymous__42353 = Vvar__2__y__42352 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Full_set',axiom,
! [Vvar__0__U__37619,Vvar__1___24Anonymous__37620] :
( cType___24t(Vvar__0__U__37619)
=> ( t(Vvar__1___24Anonymous__37620,Vvar__0__U__37619)
=> ( cCoq_2eSets_2eEnsembles_2eFull__set___24a2(Vvar__0__U__37619,Vvar__1___24Anonymous__37620)
=> ? [Vvar__1__x__37623] :
( t(Vvar__1__x__37623,Vvar__0__U__37619)
& Vvar__1___24Anonymous__37620 = Vvar__1__x__37623 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Inhabited',axiom,
! [Vvar__0__U__37301,Vvar__1__B__37302] :
( cType___24t(Vvar__0__U__37301)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__37301,Vvar__1__B__37302)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__37301,Vvar__1__B__37302)
=> ? [Vvar__2__x__37306] :
( t(Vvar__2__x__37306,Vvar__0__U__37301)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__37301,Vvar__1__B__37302,Vvar__2__x__37306)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Intersection',axiom,
! [Vvar__0__U__37287,Vvar__1__B__37288,Vvar__2__C__37289,Vvar__1___24Anonymous__37290] :
( cType___24t(Vvar__0__U__37287)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__37287,Vvar__1__B__37288)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__37287,Vvar__2__C__37289)
=> ( t(Vvar__1___24Anonymous__37290,Vvar__0__U__37287)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(Vvar__0__U__37287,Vvar__1__B__37288,Vvar__2__C__37289,Vvar__1___24Anonymous__37290)
=> ? [Vvar__3__x__37295] :
( t(Vvar__3__x__37295,Vvar__0__U__37287)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__37287,Vvar__1__B__37288,Vvar__3__x__37295)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__37287,Vvar__2__C__37289,Vvar__3__x__37295)
& Vvar__1___24Anonymous__37290 = Vvar__3__x__37295 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Singleton',axiom,
! [Vvar__0__U__37624,Vvar__1__x__37625,Vvar__1___24Anonymous__37626] :
( cType___24t(Vvar__0__U__37624)
=> ( t(Vvar__1__x__37625,Vvar__0__U__37624)
=> ( t(Vvar__1___24Anonymous__37626,Vvar__0__U__37624)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(Vvar__0__U__37624,Vvar__1__x__37625,Vvar__1___24Anonymous__37626)
=> Vvar__1___24Anonymous__37626 = Vvar__1__x__37625 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Union',axiom,
! [Vvar__0__U__38919,Vvar__1__B__38920,Vvar__2__C__38921,Vvar__1___24Anonymous__38922] :
( cType___24t(Vvar__0__U__38919)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__38919,Vvar__1__B__38920)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__38919,Vvar__2__C__38921)
=> ( t(Vvar__1___24Anonymous__38922,Vvar__0__U__38919)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(Vvar__0__U__38919,Vvar__1__B__38920,Vvar__2__C__38921,Vvar__1___24Anonymous__38922)
=> ( ? [Vvar__3__x__38927] :
( t(Vvar__3__x__38927,Vvar__0__U__38919)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__38919,Vvar__1__B__38920,Vvar__3__x__38927)
& Vvar__1___24Anonymous__38922 = Vvar__3__x__38927 )
| ? [Vvar__3__x__38932] :
( t(Vvar__3__x__38932,Vvar__0__U__38919)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__38919,Vvar__2__C__38921,Vvar__3__x__38932)
& Vvar__1___24Anonymous__38922 = Vvar__3__x__38932 ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Finite_sets.Finite',axiom,
! [Vvar__0__U__39009,Vvar__1___24Anonymous__39010] :
( cType___24t(Vvar__0__U__39009)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__39009,Vvar__1___24Anonymous__39010)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(Vvar__0__U__39009,Vvar__1___24Anonymous__39010)
=> ( Vvar__1___24Anonymous__39010 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__U__39009)
| ? [Vvar__1__A__39014] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__39009,Vvar__1__A__39014)
& cCoq_2eSets_2eFinite__sets_2eFinite___24a2(Vvar__0__U__39009,Vvar__1__A__39014)
& ? [Vvar__3__x__39016] :
( t(Vvar__3__x__39016,Vvar__0__U__39009)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__39009,Vvar__1__A__39014,Vvar__3__x__39016)
& Vvar__1___24Anonymous__39010 = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vvar__0__U__39009,Vvar__1__A__39014,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(Vvar__0__U__39009,Vvar__3__x__39016)) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Finite_sets.cardinal',axiom,
! [Vvar__0__U__42882,Vvar__1___24Anonymous__42883,Vvar__2___24Anonymous__42884] :
( cType___24t(Vvar__0__U__42882)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__42882,Vvar__1___24Anonymous__42883)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__42884)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__42882,Vvar__1___24Anonymous__42883,Vvar__2___24Anonymous__42884)
=> ( ( Vvar__2___24Anonymous__42884 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__42883 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__U__42882) )
| ? [Vvar__1__A__42888] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__42882,Vvar__1__A__42888)
& ? [Vvar__2__n__42889] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__42889)
& cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__42882,Vvar__1__A__42888,Vvar__2__n__42889)
& ? [Vvar__4__x__42891] :
( t(Vvar__4__x__42891,Vvar__0__U__42882)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__42882,Vvar__1__A__42888,Vvar__4__x__42891)
& Vvar__2___24Anonymous__42884 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__42889)
& Vvar__1___24Anonymous__42883 = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vvar__0__U__42882,Vvar__1__A__42888,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(Vvar__0__U__42882,Vvar__4__x__42891)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Image.Im',axiom,
! [Vvar__0__U__38149,Vvar__1__V__38150,Vvar__2__X__38151,Vvar__3__f__38152,Vvar__1___24Anonymous__38155] :
( cType___24t(Vvar__0__U__38149)
=> ( cType___24t(Vvar__1__V__38150)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__38149,Vvar__2__X__38151)
=> ( c_24__type__38175___24t(Vvar__0__U__38149,Vvar__1__V__38150,Vvar__2__X__38151,Vvar__3__f__38152,Vvar__1___24Anonymous__38155,Vvar__3__f__38152)
=> ( t(Vvar__1___24Anonymous__38155,Vvar__1__V__38150)
=> ( cCoq_2eSets_2eImage_2eIm___24a5(Vvar__0__U__38149,Vvar__1__V__38150,Vvar__2__X__38151,Vvar__3__f__38152,Vvar__1___24Anonymous__38155)
=> ? [Vvar__4__x__38163] :
( t(Vvar__4__x__38163,Vvar__0__U__38149)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__38149,Vvar__2__X__38151,Vvar__4__x__38163)
& ? [Vvar__6__y__38165] :
( t(Vvar__6__y__38165,Vvar__1__V__38150)
& Vvar__6__y__38165 = happ(Vvar__3__f__38152,Vvar__4__x__38163)
& Vvar__1___24Anonymous__38155 = Vvar__6__y__38165 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.PO',axiom,
! [Vvar__0__U__45179,VX45180] :
( cType___24t(Vvar__0__U__45179)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__45179,VX45180)
=> ? [Vvar__1__Carrier__of__45182] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__45179,Vvar__1__Carrier__of__45182)
& ? [Vvar__2__Rel__of__45183] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__45179,Vvar__2__Rel__of__45183)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__45179,Vvar__1__Carrier__of__45182)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__45179,Vvar__2__Rel__of__45183)
& VX45180 = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__45179,Vvar__1__Carrier__of__45182,Vvar__2__Rel__of__45183) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.covers',axiom,
! [Vvar__0__U__45241,Vvar__1__p__45242,Vvar__2__y__45243,Vvar__3__x__45244] :
( cType___24t(Vvar__0__U__45241)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__45241,Vvar__1__p__45242)
=> ( t(Vvar__2__y__45243,Vvar__0__U__45241)
=> ( t(Vvar__3__x__45244,Vvar__0__U__45241)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(Vvar__0__U__45241,Vvar__1__p__45242,Vvar__2__y__45243,Vvar__3__x__45244)
=> ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__45241,Vvar__1__p__45242,Vvar__3__x__45244,Vvar__2__y__45243)
& ~ ? [Vvar__var__var__var__var__var__5__z__45252__45253__45254__45255__45256__45257] :
( t(Vvar__var__var__var__var__var__5__z__45252__45253__45254__45255__45256__45257,Vvar__0__U__45241)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__45241,Vvar__1__p__45242,Vvar__3__x__45244,Vvar__var__var__var__var__var__5__z__45252__45253__45254__45255__45256__45257)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__45241,Vvar__1__p__45242,Vvar__var__var__var__var__var__5__z__45252__45253__45254__45255__45256__45257,Vvar__2__y__45243) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Powerset.Power_set',axiom,
! [Vvar__0__U__45263,Vvar__1__A__45264,Vvar__1___24Anonymous__45265] :
( cType___24t(Vvar__0__U__45263)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__45263,Vvar__1__A__45264)
=> ( c_24__type__45278___24t(Vvar__0__U__45263,Vvar__1__A__45264,Vvar__1___24Anonymous__45265,Vvar__1___24Anonymous__45265)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(Vvar__0__U__45263,Vvar__1__A__45264,Vvar__1___24Anonymous__45265)
=> ? [Vvar__2__X__45271] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__45263,Vvar__2__X__45271)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__45263,Vvar__2__X__45271,Vvar__1__A__45264)
& Vvar__1___24Anonymous__45265 = Vvar__2__X__45271 ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Order',axiom,
! [Vvar__0__U__31856,Vvar__1__R__31857] :
( cType___24t(Vvar__0__U__31856)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__31856,Vvar__1__R__31857)
=> ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__31856,Vvar__1__R__31857)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__31856,Vvar__1__R__31857)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__31856,Vvar__1__R__31857)
& cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(Vvar__0__U__31856,Vvar__1__R__31857)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX604] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX604)
=> ? [Vvar__0___24Anonymous__605] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__605)
& ? [Vvar__1___24Anonymous__606] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__606)
& ? [Vvar__2___24Anonymous__607] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__607)
& ? [Vvar__3___24Anonymous__608] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__608)
& ? [Vvar__4___24Anonymous__609] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__609)
& ? [Vvar__5___24Anonymous__610] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__610)
& ? [Vvar__6___24Anonymous__611] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__611)
& ? [Vvar__7___24Anonymous__612] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__612)
& VX604 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__605,Vvar__1___24Anonymous__606,Vvar__2___24Anonymous__607,Vvar__3___24Anonymous__608,Vvar__4___24Anonymous__609,Vvar__5___24Anonymous__610,Vvar__6___24Anonymous__611,Vvar__7___24Anonymous__612) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__5284,VX5285] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5284)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__5284,VX5285)
=> ( ? [Vvar__0__n__5286] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__5286)
& Vvar__0___24Anonymous__5284 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__5286)
& VX5285 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__5286) )
| ? [Vvar__0__n__5287] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__5287)
& ? [Vvar__1___24Anonymous__5288] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__5287,Vvar__1___24Anonymous__5288)
& Vvar__0___24Anonymous__5284 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__5287)
& VX5285 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__5287,Vvar__1___24Anonymous__5288) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__2881,Vvar__1___24Anonymous__2882,VX2883] :
( cType___24t(Vvar__0__A__2881)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2882)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__2881,Vvar__1___24Anonymous__2882,VX2883)
=> ( ( Vvar__1___24Anonymous__2882 = cCoq_2eInit_2eDatatypes_2eO
& VX2883 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2881) )
| ? [Vvar__1__h__2886] :
( t(Vvar__1__h__2886,Vvar__0__A__2881)
& ? [Vvar__2__n__2887] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__2887)
& ? [Vvar__3___24Anonymous__2888] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__2881,Vvar__2__n__2887,Vvar__3___24Anonymous__2888)
& Vvar__1___24Anonymous__2882 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__2887)
& VX2883 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2881,Vvar__1__h__2886,Vvar__2__n__2887,Vvar__3___24Anonymous__2888) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__4682,VX4683] :
( cType___24t(Vvar__0__C__4682)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,VX4683)
=> ( ? [Vvar__1___24Anonymous__4685] :
( t(Vvar__1___24Anonymous__4685,Vvar__0__C__4682)
& VX4683 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__4682,Vvar__1___24Anonymous__4685) )
| ? [Vvar__1___24Anonymous__4687] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4687)
& VX4683 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__4682,Vvar__1___24Anonymous__4687) )
| ? [Vvar__1___24Anonymous__4689] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__1___24Anonymous__4689)
& ? [Vvar__2___24Anonymous__4690] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__2___24Anonymous__4690)
& VX4683 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__4682,Vvar__1___24Anonymous__4689,Vvar__2___24Anonymous__4690) ) )
| ? [Vvar__1___24Anonymous__4692] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__1___24Anonymous__4692)
& ? [Vvar__2___24Anonymous__4693] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__2___24Anonymous__4693)
& VX4683 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__4682,Vvar__1___24Anonymous__4692,Vvar__2___24Anonymous__4693) ) )
| ? [Vvar__1___24Anonymous__4695] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__1___24Anonymous__4695)
& ? [Vvar__2___24Anonymous__4696] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__2___24Anonymous__4696)
& VX4683 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__4682,Vvar__1___24Anonymous__4695,Vvar__2___24Anonymous__4696) ) )
| ? [Vvar__1___24Anonymous__4698] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__1___24Anonymous__4698)
& VX4683 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__4682,Vvar__1___24Anonymous__4698) )
| ? [Vvar__1___24Anonymous__4700] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__4682,Vvar__1___24Anonymous__4700)
& ? [Vvar__2___24Anonymous__4701] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__4701)
& VX4683 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__4682,Vvar__1___24Anonymous__4700,Vvar__2___24Anonymous__4701) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__4846,VX4847] :
( cType___24t(Vvar__0__C__4846)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4846,VX4847)
=> ( ? [Vvar__1___24Anonymous__4849] :
( t(Vvar__1___24Anonymous__4849,Vvar__0__C__4846)
& VX4847 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4846,Vvar__1___24Anonymous__4849) )
| ? [Vvar__1___24Anonymous__4851] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4851)
& ? [Vvar__2___24Anonymous__4852] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4846,Vvar__2___24Anonymous__4852)
& VX4847 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4846,Vvar__1___24Anonymous__4851,Vvar__2___24Anonymous__4852) ) )
| ? [Vvar__1___24Anonymous__4854] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4846,Vvar__1___24Anonymous__4854)
& ? [Vvar__2___24Anonymous__4855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__4855)
& ? [Vvar__3___24Anonymous__4856] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4846,Vvar__3___24Anonymous__4856)
& VX4847 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4846,Vvar__1___24Anonymous__4854,Vvar__2___24Anonymous__4855,Vvar__3___24Anonymous__4856) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX5556] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX5556)
=> ( VX5556 = cCoq_2emicromega_2eRMicromega_2eC0
| VX5556 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__5557] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__5557)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__5557) )
| ? [Vvar__0__r__5558] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__5558)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__5558) )
| ? [Vvar__0__r1__5559] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__5559)
& ? [Vvar__1__r2__5560] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__5560)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__5559,Vvar__1__r2__5560) ) )
| ? [Vvar__0__r1__5561] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__5561)
& ? [Vvar__1__r2__5562] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__5562)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__5561,Vvar__1__r2__5562) ) )
| ? [Vvar__0__r1__5563] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__5563)
& ? [Vvar__1__r2__5564] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__5564)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__5563,Vvar__1__r2__5564) ) )
| ? [Vvar__0__r1__5565] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__5565)
& ? [Vvar__1__z__5566] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__5566)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__5565,Vvar__1__z__5566) ) )
| ? [Vvar__0__r__5567] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__5567)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__5567) )
| ? [Vvar__0__r__5568] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__5568)
& VX5556 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__5568) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__24165,VX24166] :
( cType___24t(Vvar__0__T__24165)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__24165,VX24166)
=> ? [Vvar__1__Flhs__24168] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__24165,Vvar__1__Flhs__24168)
& ? [Vvar__2__Fop__24169] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__24169)
& ? [Vvar__3__Frhs__24170] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__24165,Vvar__3__Frhs__24170)
& VX24166 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__24165,Vvar__1__Flhs__24168,Vvar__2__Fop__24169,Vvar__3__Frhs__24170) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX27153] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX27153)
=> ( VX27153 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX27153 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX27153 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX27153 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX27153 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX27153 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__5791,VX5792] :
( cType___24t(Vvar__0__C__5791)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__5791,VX5792)
=> ( ? [Vvar__1___24Anonymous__5794] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__5794)
& VX5792 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__5791,Vvar__1___24Anonymous__5794) )
| ? [Vvar__1___24Anonymous__5796] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__5791,Vvar__1___24Anonymous__5796)
& VX5792 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__5791,Vvar__1___24Anonymous__5796) )
| ? [Vvar__1___24Anonymous__5798] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__5791,Vvar__1___24Anonymous__5798)
& ? [Vvar__2___24Anonymous__5799] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__5791,Vvar__2___24Anonymous__5799)
& VX5792 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__5791,Vvar__1___24Anonymous__5798,Vvar__2___24Anonymous__5799) ) )
| ? [Vvar__1___24Anonymous__5801] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__5791,Vvar__1___24Anonymous__5801)
& ? [Vvar__2___24Anonymous__5802] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__5791,Vvar__2___24Anonymous__5802)
& VX5792 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__5791,Vvar__1___24Anonymous__5801,Vvar__2___24Anonymous__5802) ) )
| ? [Vvar__1___24Anonymous__5804] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__5791,Vvar__1___24Anonymous__5804)
& ? [Vvar__2___24Anonymous__5805] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__5791,Vvar__2___24Anonymous__5805)
& VX5792 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__5791,Vvar__1___24Anonymous__5804,Vvar__2___24Anonymous__5805) ) )
| ? [Vvar__1___24Anonymous__5807] :
( t(Vvar__1___24Anonymous__5807,Vvar__0__C__5791)
& VX5792 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__5791,Vvar__1___24Anonymous__5807) )
| VX5792 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__5791) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,VX27534] :
( cType___24t(Vvar__0__TA__27530)
=> ( cType___24t(Vvar__1__TX__27531)
=> ( cType___24t(Vvar__2__AA__27532)
=> ( cType___24t(Vvar__3__AF__27533)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,VX27534)
=> ( VX27534 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533)
| VX27534 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533)
| ? [Vvar__4___24Anonymous__27547] :
( t(Vvar__4___24Anonymous__27547,Vvar__1__TX__27531)
& VX27534 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27547) )
| ? [Vvar__4___24Anonymous__27552] :
( t(Vvar__4___24Anonymous__27552,Vvar__0__TA__27530)
& ? [Vvar__5___24Anonymous__27553] :
( t(Vvar__5___24Anonymous__27553,Vvar__2__AA__27532)
& VX27534 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27552,Vvar__5___24Anonymous__27553) ) )
| ? [Vvar__4___24Anonymous__27558] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27558)
& ? [Vvar__5___24Anonymous__27559] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__5___24Anonymous__27559)
& VX27534 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27558,Vvar__5___24Anonymous__27559) ) )
| ? [Vvar__4___24Anonymous__27564] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27564)
& ? [Vvar__5___24Anonymous__27565] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__5___24Anonymous__27565)
& VX27534 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27564,Vvar__5___24Anonymous__27565) ) )
| ? [Vvar__4___24Anonymous__27570] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27570)
& VX27534 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27570) )
| ? [Vvar__4___24Anonymous__27575] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27575)
& ? [Vvar__5___24Anonymous__27576] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__27533,Vvar__5___24Anonymous__27576)
& ? [Vvar__6___24Anonymous__27577] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__6___24Anonymous__27577)
& VX27534 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__27530,Vvar__1__TX__27531,Vvar__2__AA__27532,Vvar__3__AF__27533,Vvar__4___24Anonymous__27575,Vvar__5___24Anonymous__27576,Vvar__6___24Anonymous__27577) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__27973,VX27974] :
( cType___24t(Vvar__0__A__27973)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__27973,VX27974)
=> ( VX27974 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__27973)
| ? [Vvar__1___24Anonymous__27977] :
( t(Vvar__1___24Anonymous__27977,Vvar__0__A__27973)
& VX27974 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__27973,Vvar__1___24Anonymous__27977) )
| ? [Vvar__1___24Anonymous__27979] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__27973,Vvar__1___24Anonymous__27979)
& ? [Vvar__2___24Anonymous__27980] :
( t(Vvar__2___24Anonymous__27980,Vvar__0__A__27973)
& ? [Vvar__3___24Anonymous__27981] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__27973,Vvar__3___24Anonymous__27981)
& VX27974 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__27973,Vvar__1___24Anonymous__27979,Vvar__2___24Anonymous__27980,Vvar__3___24Anonymous__27981) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__4929,VX4930] :
( cType___24t(Vvar__0__C__4929)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,VX4930)
=> ( VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__4929)
| VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__4929)
| ? [Vvar__1___24Anonymous__4934] :
( t(Vvar__1___24Anonymous__4934,Vvar__0__C__4929)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__4929,Vvar__1___24Anonymous__4934) )
| ? [Vvar__1___24Anonymous__4936] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4936)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__4929,Vvar__1___24Anonymous__4936) )
| ? [Vvar__1___24Anonymous__4938] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__1___24Anonymous__4938)
& ? [Vvar__2___24Anonymous__4939] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__2___24Anonymous__4939)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__4929,Vvar__1___24Anonymous__4938,Vvar__2___24Anonymous__4939) ) )
| ? [Vvar__1___24Anonymous__4941] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__1___24Anonymous__4941)
& ? [Vvar__2___24Anonymous__4942] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__2___24Anonymous__4942)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__4929,Vvar__1___24Anonymous__4941,Vvar__2___24Anonymous__4942) ) )
| ? [Vvar__1___24Anonymous__4944] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__1___24Anonymous__4944)
& ? [Vvar__2___24Anonymous__4945] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__2___24Anonymous__4945)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__4929,Vvar__1___24Anonymous__4944,Vvar__2___24Anonymous__4945) ) )
| ? [Vvar__1___24Anonymous__4947] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__1___24Anonymous__4947)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__4929,Vvar__1___24Anonymous__4947) )
| ? [Vvar__1___24Anonymous__4949] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__1___24Anonymous__4949)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__4929,Vvar__1___24Anonymous__4949) )
| ? [Vvar__1___24Anonymous__4951] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__1___24Anonymous__4951)
& ? [Vvar__2___24Anonymous__4952] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__2___24Anonymous__4952)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__4929,Vvar__1___24Anonymous__4951,Vvar__2___24Anonymous__4952) ) )
| ? [Vvar__1___24Anonymous__4954] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__4929,Vvar__1___24Anonymous__4954)
& ? [Vvar__2___24Anonymous__4955] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__4955)
& VX4930 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__4929,Vvar__1___24Anonymous__4954,Vvar__2___24Anonymous__4955) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__5256,VX5257] :
( cType___24t(Vvar__0__C__5256)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__5256,VX5257)
=> ? [Vvar__1__num__5259] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5256,Vvar__1__num__5259)
& ? [Vvar__2__denum__5260] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5256,Vvar__2__denum__5260)
& ? [Vvar__3__condition__5261] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__5256),Vvar__3__condition__5261)
& VX5257 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__5256,Vvar__1__num__5259,Vvar__2__denum__5260,Vvar__3__condition__5261) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX1966] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX1966)
=> ( VX1966 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__1967] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1967)
& ? [Vvar__1___24Anonymous__1968] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1968)
& VX1966 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1967,Vvar__1___24Anonymous__1968) ) )
| ? [Vvar__0___24Anonymous__1969] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1969)
& ? [Vvar__1___24Anonymous__1970] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1970)
& VX1966 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1969,Vvar__1___24Anonymous__1970) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__1987,VX1988] :
( cType___24t(Vvar__0__C__1987)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,VX1988)
=> ( VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1987)
| VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1987)
| ? [Vvar__1___24Anonymous__1992] :
( t(Vvar__1___24Anonymous__1992,Vvar__0__C__1987)
& VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1987,Vvar__1___24Anonymous__1992) )
| ? [Vvar__1___24Anonymous__1994] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1994)
& VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1987,Vvar__1___24Anonymous__1994) )
| ? [Vvar__1___24Anonymous__1996] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__1___24Anonymous__1996)
& ? [Vvar__2___24Anonymous__1997] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__2___24Anonymous__1997)
& VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1987,Vvar__1___24Anonymous__1996,Vvar__2___24Anonymous__1997) ) )
| ? [Vvar__1___24Anonymous__1999] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__1___24Anonymous__1999)
& ? [Vvar__2___24Anonymous__2000] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__2___24Anonymous__2000)
& VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1987,Vvar__1___24Anonymous__1999,Vvar__2___24Anonymous__2000) ) )
| ? [Vvar__1___24Anonymous__2002] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__1___24Anonymous__2002)
& ? [Vvar__2___24Anonymous__2003] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__2___24Anonymous__2003)
& VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1987,Vvar__1___24Anonymous__2002,Vvar__2___24Anonymous__2003) ) )
| ? [Vvar__1___24Anonymous__2005] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__1___24Anonymous__2005)
& VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1987,Vvar__1___24Anonymous__2005) )
| ? [Vvar__1___24Anonymous__2007] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1987,Vvar__1___24Anonymous__2007)
& ? [Vvar__2___24Anonymous__2008] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2008)
& VX1988 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1987,Vvar__1___24Anonymous__2007,Vvar__2___24Anonymous__2008) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__1785,VX1786] :
( cType___24t(Vvar__0__C__1785)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1785,VX1786)
=> ( ? [Vvar__1___24Anonymous__1788] :
( t(Vvar__1___24Anonymous__1788,Vvar__0__C__1785)
& VX1786 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1785,Vvar__1___24Anonymous__1788) )
| ? [Vvar__1___24Anonymous__1790] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1790)
& ? [Vvar__2___24Anonymous__1791] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1785,Vvar__2___24Anonymous__1791)
& VX1786 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1785,Vvar__1___24Anonymous__1790,Vvar__2___24Anonymous__1791) ) )
| ? [Vvar__1___24Anonymous__1793] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1785,Vvar__1___24Anonymous__1793)
& ? [Vvar__2___24Anonymous__1794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1794)
& ? [Vvar__3___24Anonymous__1795] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1785,Vvar__3___24Anonymous__1795)
& VX1786 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1785,Vvar__1___24Anonymous__1793,Vvar__2___24Anonymous__1794,Vvar__3___24Anonymous__1795) ) ) ) ) ) ) ).
fof('$_inversion_Topology.CountabilityAxioms.second_countable',axiom,
! [Vvar__0__X__41250] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__41250)
=> ( cTopology_2eCountabilityAxioms_2esecond__countable___24a1(Vvar__0__X__41250)
=> ? [Vvar__1__B__41253] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__41250),Vvar__1__B__41253)
& cTopology_2eOpenBases_2eopen__basis___24a2(Vvar__0__X__41250,Vvar__1__B__41253)
& cZornsLemma_2eCountableTypes_2eCountable___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__41250)),Vvar__1__B__41253)
& p(c_24True) ) ) ) ).
fof('$_inversion_Topology.CountabilityAxioms.separable',axiom,
! [Vvar__0__X__41239] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__41239)
=> ( cTopology_2eCountabilityAxioms_2eseparable___24a1(Vvar__0__X__41239)
=> ? [Vvar__1__S__41242] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__41239),Vvar__1__S__41242)
& cZornsLemma_2eCountableTypes_2eCountable___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__41239),Vvar__1__S__41242)
& cTopology_2eInteriorsClosures_2edense___24a2(Vvar__0__X__41239,Vvar__1__S__41242)
& p(c_24True) ) ) ) ).
fof('$_inversion_Topology.DirectedSets.DirectedSet',axiom,
! [VX38273] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(VX38273)
=> ? [Vvar__0__DS__set__38274] :
( cType___24t(Vvar__0__DS__set__38274)
& ? [Vvar__1__DS__ord__38275] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__38274,Vvar__1__DS__ord__38275)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__38274,Vvar__1__DS__ord__38275)
& ! [Vvar__var__3__i__38278__38281] :
( t(Vvar__var__3__i__38278__38281,Vvar__0__DS__set__38274)
=> ! [Vvar__var__4__j__38280__38283] :
( t(Vvar__var__4__j__38280__38283,Vvar__0__DS__set__38274)
=> ? [Vvar__var__5__k__38279__38282] :
( t(Vvar__var__5__k__38279__38282,Vvar__0__DS__set__38274)
& p(happ(happ(Vvar__1__DS__ord__38275,Vvar__var__3__i__38278__38281),Vvar__var__5__k__38279__38282))
& p(happ(happ(Vvar__1__DS__ord__38275,Vvar__var__4__j__38280__38283),Vvar__var__5__k__38279__38282)) ) ) )
& VX38273 = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__38274,Vvar__1__DS__ord__38275) ) ) ) ).
fof('$_inversion_Topology.Filters.Filter',axiom,
! [Vvar__0__X__37645,VX37646] :
( cType___24t(Vvar__0__X__37645)
=> ( cTopology_2eFilters_2eFilter___24t(Vvar__0__X__37645,VX37646)
=> ? [Vvar__1__filter__family__37648] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__37645,Vvar__1__filter__family__37648)
& ! [Vvar__var__var__2__S1__37650__37654__37669] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37645,Vvar__var__var__2__S1__37650__37654__37669)
=> ! [Vvar__var__var__3__S2__37651__37655__37670] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37645,Vvar__var__var__3__S2__37651__37655__37670)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37645),Vvar__1__filter__family__37648,Vvar__var__var__2__S1__37650__37654__37669)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37645),Vvar__1__filter__family__37648,Vvar__var__var__3__S2__37651__37655__37670)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37645),Vvar__1__filter__family__37648,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__X__37645,Vvar__var__var__2__S1__37650__37654__37669,Vvar__var__var__3__S2__37651__37655__37670)) ) ) ) )
& ! [Vvar__var__var__3__S1__37659__37663__37673] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37645,Vvar__var__var__3__S1__37659__37663__37673)
=> ! [Vvar__var__var__4__S2__37660__37664__37674] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37645,Vvar__var__var__4__S2__37660__37664__37674)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37645),Vvar__1__filter__family__37648,Vvar__var__var__3__S1__37659__37663__37673)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__X__37645,Vvar__var__var__3__S1__37659__37663__37673,Vvar__var__var__4__S2__37660__37664__37674)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37645),Vvar__1__filter__family__37648,Vvar__var__var__4__S2__37660__37664__37674) ) ) ) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37645),Vvar__1__filter__family__37648,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__X__37645))
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37645),Vvar__1__filter__family__37648,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__X__37645))
& VX37646 = cTopology_2eFilters_2eBuild__Filter___24a2(Vvar__0__X__37645,Vvar__1__filter__family__37648) ) ) ) ).
fof('$_inversion_Topology.Filters.filter_basis',axiom,
! [Vvar__0__X__42411,Vvar__1__F__42412,Vvar__2__B__42413] :
( cType___24t(Vvar__0__X__42411)
=> ( cTopology_2eFilters_2eFilter___24t(Vvar__0__X__42411,Vvar__1__F__42412)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__42411,Vvar__2__B__42413)
=> ( cTopology_2eFilters_2efilter__basis___24a3(Vvar__0__X__42411,Vvar__1__F__42412,Vvar__2__B__42413)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42411),Vvar__2__B__42413,cTopology_2eFilters_2efilter__family___24a2(Vvar__0__X__42411,Vvar__1__F__42412))
& ! [Vvar__var__var__var__var__4__S__42420__42423__42426__42429__42432] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__42411,Vvar__var__var__var__var__4__S__42420__42423__42426__42429__42432)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42411),cTopology_2eFilters_2efilter__family___24a2(Vvar__0__X__42411,Vvar__1__F__42412),Vvar__var__var__var__var__4__S__42420__42423__42426__42429__42432)
=> ? [Vvar__var__var__var__var__6__S_27__42421__42424__42427__42430__42433] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__42411,Vvar__var__var__var__var__6__S_27__42421__42424__42427__42430__42433)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42411),Vvar__2__B__42413,Vvar__var__var__var__var__6__S_27__42421__42424__42427__42430__42433)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__X__42411,Vvar__var__var__var__var__6__S_27__42421__42424__42427__42430__42433,Vvar__var__var__var__var__4__S__42420__42423__42426__42429__42432) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Topology.Filters.filter_subbasis',axiom,
! [Vvar__0__X__42446,Vvar__1__F__42447,Vvar__2__B__42448] :
( cType___24t(Vvar__0__X__42446)
=> ( cTopology_2eFilters_2eFilter___24t(Vvar__0__X__42446,Vvar__1__F__42447)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__42446,Vvar__2__B__42448)
=> ( cTopology_2eFilters_2efilter__subbasis___24a3(Vvar__0__X__42446,Vvar__1__F__42447,Vvar__2__B__42448)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42446),Vvar__2__B__42448,cTopology_2eFilters_2efilter__family___24a2(Vvar__0__X__42446,Vvar__1__F__42447))
& ! [Vvar__var__var__var__var__4__S__42455__42461__42467__42473__42479] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__42446,Vvar__var__var__var__var__4__S__42455__42461__42467__42473__42479)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42446),cTopology_2eFilters_2efilter__family___24a2(Vvar__0__X__42446,Vvar__1__F__42447),Vvar__var__var__var__var__4__S__42455__42461__42467__42473__42479)
=> ? [Vvar__var__var__var__var__6__J__42456__42462__42468__42474__42480] :
( cType___24t(Vvar__var__var__var__var__6__J__42456__42462__42468__42474__42480)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__var__var__var__var__6__J__42456__42462__42468__42474__42480)
& ? [Vvar__var__var__var__var__7__T__42458__42464__42470__42476__42482] :
( c_24__type__42489___24t(Vvar__0__X__42446,Vvar__1__F__42447,Vvar__2__B__42448,Vvar__var__var__var__var__6__J__42456__42462__42468__42474__42480,Vvar__var__var__var__var__7__T__42458__42464__42470__42476__42482)
& ! [Vvar__var__var__var__var__8__j__42459__42465__42471__42477__42483] :
( t(Vvar__var__var__var__var__8__j__42459__42465__42471__42477__42483,Vvar__var__var__var__var__6__J__42456__42462__42468__42474__42480)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42446),Vvar__2__B__42448,happ(Vvar__var__var__var__var__7__T__42458__42464__42470__42476__42482,Vvar__var__var__var__var__8__j__42459__42465__42471__42477__42483)) )
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__X__42446,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(Vvar__var__var__var__var__6__J__42456__42462__42468__42474__42480,Vvar__0__X__42446,Vvar__var__var__var__var__7__T__42458__42464__42470__42476__42482),Vvar__var__var__var__var__4__S__42455__42461__42467__42473__42479) ) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Topology.FiltersAndNets.filter_to_net_DS_set',axiom,
! [Vvar__0__X__42630,Vvar__1__F__42631,VX42632] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__42630)
=> ( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__42630),Vvar__1__F__42631)
=> ( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(Vvar__0__X__42630,Vvar__1__F__42631,VX42632)
=> ? [Vvar__2__ftn__S__42635] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__42630),Vvar__2__ftn__S__42635)
& ? [Vvar__3__ftn__x__42636] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__42630,Vvar__3__ftn__x__42636)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__42630)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__42630),Vvar__1__F__42631),Vvar__2__ftn__S__42635)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__42630),Vvar__2__ftn__S__42635,Vvar__3__ftn__x__42636)
& VX42632 = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(Vvar__0__X__42630,Vvar__1__F__42631,Vvar__2__ftn__S__42635,Vvar__3__ftn__x__42636) ) ) ) ) ) ).
fof('$_inversion_Topology.FiniteIntersectionLemmas.finite_intersections_len',axiom,
! [Vvar__0__X__37963,Vvar__1__F__37964,Vvar__2___24Anonymous__37965,Vvar__1___24Anonymous__37966] :
( cType___24t(Vvar__0__X__37963)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__37963,Vvar__1__F__37964)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__37965)
=> ( c_24__type__37993___24t(Vvar__0__X__37963,Vvar__1__F__37964,Vvar__2___24Anonymous__37965,Vvar__1___24Anonymous__37966,Vvar__1___24Anonymous__37966)
=> ( cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a4(Vvar__0__X__37963,Vvar__1__F__37964,Vvar__2___24Anonymous__37965,Vvar__1___24Anonymous__37966)
=> ( ( Vvar__1___24Anonymous__37966 = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__X__37963)
& Vvar__2___24Anonymous__37965 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__U__37974] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37963,Vvar__2__U__37974)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37963),Vvar__1__F__37964,Vvar__2__U__37974)
& Vvar__1___24Anonymous__37966 = Vvar__2__U__37974
& Vvar__2___24Anonymous__37965 = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__2__U__37978] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37963,Vvar__2__U__37978)
& ? [Vvar__3__V__37979] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37963,Vvar__3__V__37979)
& ? [Vvar__4__m__37980] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__m__37980)
& ? [Vvar__5__k__37981] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__k__37981)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37963),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(Vvar__0__X__37963,Vvar__1__F__37964,Vvar__4__m__37980),Vvar__2__U__37978)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37963),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(Vvar__0__X__37963,Vvar__1__F__37964,Vvar__5__k__37981),Vvar__3__V__37979)
& Vvar__1___24Anonymous__37966 = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__X__37963,Vvar__2__U__37978,Vvar__3__V__37979)
& Vvar__2___24Anonymous__37965 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2438069___24a6(Vvar__0__X__37963,Vvar__1__F__37964,Vvar__2___24Anonymous__37965,Vvar__1___24Anonymous__37966,Vvar__4__m__37980,Vvar__5__k__37981) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Topology.Homeomorphisms.homeomorphic',axiom,
! [Vvar__0__X__43834,Vvar__1__Y__43835] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__43834)
=> ( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__1__Y__43835)
=> ( cTopology_2eHomeomorphisms_2ehomeomorphic___24a2(Vvar__0__X__43834,Vvar__1__Y__43835)
=> ? [Vvar__2__f__43839] :
( c_24__type__38915___24t(Vvar__0__X__43834,Vvar__1__Y__43835,Vvar__2__f__43839)
& cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(Vvar__0__X__43834,Vvar__1__Y__43835,Vvar__2__f__43839)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Topology.Homeomorphisms.homeomorphism',axiom,
! [Vvar__0__X__43757,Vvar__1__Y__43758,Vvar__2__f__43759] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__43757)
=> ( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__1__Y__43758)
=> ( c_24__type__43790___24t(Vvar__0__X__43757,Vvar__1__Y__43758,Vvar__2__f__43759,Vvar__2__f__43759)
=> ( cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(Vvar__0__X__43757,Vvar__1__Y__43758,Vvar__2__f__43759)
=> ? [Vvar__3__g__43768] :
( c_24__type__43797___24t(Vvar__0__X__43757,Vvar__1__Y__43758,Vvar__2__f__43759,Vvar__3__g__43768)
& cTopology_2eContinuity_2econtinuous___24a3(Vvar__0__X__43757,Vvar__1__Y__43758,Vvar__2__f__43759)
& cTopology_2eContinuity_2econtinuous___24a3(Vvar__1__Y__43758,Vvar__0__X__43757,Vvar__3__g__43768)
& ! [Vvar__var__var__var__6__x__43774__43775__43781__43782] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__43757,Vvar__var__var__var__6__x__43774__43775__43781__43782)
=> happ(Vvar__3__g__43768,happ(Vvar__2__f__43759,Vvar__var__var__var__6__x__43774__43775__43781__43782)) = Vvar__var__var__var__6__x__43774__43775__43781__43782 )
& ! [Vvar__var__var__var__7__y__43777__43778__43783__43784] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__1__Y__43758,Vvar__var__var__var__7__y__43777__43778__43783__43784)
=> happ(Vvar__2__f__43759,happ(Vvar__3__g__43768,Vvar__var__var__var__7__y__43777__43778__43783__43784)) = Vvar__var__var__var__7__y__43777__43778__43783__43784 )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Topology.MetricSpaces.metric',axiom,
! [Vvar__0__X__39056,Vvar__1__d__39057] :
( cType___24t(Vvar__0__X__39056)
=> ( c_24__type__39125___24t(Vvar__0__X__39056,Vvar__1__d__39057,Vvar__1__d__39057)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(Vvar__0__X__39056,Vvar__1__d__39057)
=> ( ! [Vvar__var__var__var__2__x__39070__39072__39096__39098] :
( t(Vvar__var__var__var__2__x__39070__39072__39096__39098,Vvar__0__X__39056)
=> ! [Vvar__var__var__var__3__y__39071__39073__39097__39099] :
( t(Vvar__var__var__var__3__y__39071__39073__39097__39099,Vvar__0__X__39056)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(Vvar__1__d__39057,Vvar__var__var__var__2__x__39070__39072__39096__39098),Vvar__var__var__var__3__y__39071__39073__39097__39099),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) )
& ! [Vvar__var__var__var__3__x__39075__39077__39100__39102] :
( t(Vvar__var__var__var__3__x__39075__39077__39100__39102,Vvar__0__X__39056)
=> ! [Vvar__var__var__var__4__y__39076__39078__39101__39103] :
( t(Vvar__var__var__var__4__y__39076__39078__39101__39103,Vvar__0__X__39056)
=> happ(happ(Vvar__1__d__39057,Vvar__var__var__var__3__x__39075__39077__39100__39102),Vvar__var__var__var__4__y__39076__39078__39101__39103) = happ(happ(Vvar__1__d__39057,Vvar__var__var__var__4__y__39076__39078__39101__39103),Vvar__var__var__var__3__x__39075__39077__39100__39102) ) )
& ! [Vvar__var__var__var__4__x__39080__39083__39104__39107] :
( t(Vvar__var__var__var__4__x__39080__39083__39104__39107,Vvar__0__X__39056)
=> ! [Vvar__var__var__var__5__y__39082__39085__39106__39109] :
( t(Vvar__var__var__var__5__y__39082__39085__39106__39109,Vvar__0__X__39056)
=> ! [Vvar__var__var__var__6__z__39081__39084__39105__39108] :
( t(Vvar__var__var__var__6__z__39081__39084__39105__39108,Vvar__0__X__39056)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(Vvar__1__d__39057,Vvar__var__var__var__4__x__39080__39083__39104__39107),Vvar__var__var__var__6__z__39081__39084__39105__39108),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(Vvar__1__d__39057,Vvar__var__var__var__4__x__39080__39083__39104__39107),Vvar__var__var__var__5__y__39082__39085__39106__39109),happ(happ(Vvar__1__d__39057,Vvar__var__var__var__5__y__39082__39085__39106__39109),Vvar__var__var__var__6__z__39081__39084__39105__39108)))) ) ) )
& ! [Vvar__var__var__var__5__x__39087__39088__39110__39111] :
( t(Vvar__var__var__var__5__x__39087__39088__39110__39111,Vvar__0__X__39056)
=> happ(happ(Vvar__1__d__39057,Vvar__var__var__var__5__x__39087__39088__39110__39111),Vvar__var__var__var__5__x__39087__39088__39110__39111) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
& ! [Vvar__var__var__var__6__x__39090__39093__39112__39115] :
( t(Vvar__var__var__var__6__x__39090__39093__39112__39115,Vvar__0__X__39056)
=> ! [Vvar__var__var__var__7__y__39091__39094__39113__39116] :
( t(Vvar__var__var__var__7__y__39091__39094__39113__39116,Vvar__0__X__39056)
=> ( happ(happ(Vvar__1__d__39057,Vvar__var__var__var__6__x__39090__39093__39112__39115),Vvar__var__var__var__7__y__39091__39094__39113__39116) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> Vvar__var__var__var__6__x__39090__39093__39112__39115 = Vvar__var__var__var__7__y__39091__39094__39113__39116 ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Topology.MetricSpaces.metric_topology_neighborhood_basis',axiom,
! [Vvar__0__X__38423,Vvar__1__d__38424,Vvar__2__x__38429,Vvar__1___24Anonymous__38430] :
( cType___24t(Vvar__0__X__38423)
=> ( c_24__type__38461___24t(Vvar__0__X__38423,Vvar__1__d__38424,Vvar__2__x__38429,Vvar__1___24Anonymous__38430,Vvar__1__d__38424)
=> ( t(Vvar__2__x__38429,Vvar__0__X__38423)
=> ( c_24__type__38472___24t(Vvar__0__X__38423,Vvar__1__d__38424,Vvar__2__x__38429,Vvar__1___24Anonymous__38430,Vvar__1___24Anonymous__38430)
=> ( cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a4(Vvar__0__X__38423,Vvar__1__d__38424,Vvar__2__x__38429,Vvar__1___24Anonymous__38430)
=> ? [Vvar__3__r__38441] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__3__r__38441)
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vvar__3__r__38441,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& Vvar__1___24Anonymous__38430 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__38423,c_24__lam__38484___24a5(Vvar__0__X__38423,Vvar__1__d__38424,Vvar__2__x__38429,Vvar__1___24Anonymous__38430,Vvar__3__r__38441)) ) ) ) ) ) ) ).
fof('$_inversion_Topology.MetricSpaces.metrizable',axiom,
! [Vvar__0__X__39180] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__39180)
=> ( cTopology_2eMetricSpaces_2emetrizable___24a1(Vvar__0__X__39180)
=> ? [Vvar__1__d__39183] :
( c_24__type__38499___24t(Vvar__0__X__39180,Vvar__1__d__39183)
& cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39180),Vvar__1__d__39183)
& cTopology_2eMetricSpaces_2emetrizes___24a2(Vvar__0__X__39180,Vvar__1__d__39183)
& p(c_24True) ) ) ) ).
fof('$_inversion_Topology.NeighborhoodBases.neighborhood_basis',axiom,
! [Vvar__0__X__44371,Vvar__1__NB__44372,Vvar__2__x__44373] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__44371)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__44371),Vvar__1__NB__44372)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__44371,Vvar__2__x__44373)
=> ( cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(Vvar__0__X__44371,Vvar__1__NB__44372,Vvar__2__x__44373)
=> ( ! [Vvar__var__var__var__var__3__N__44379__44381__44390__44392__44394] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__44371),Vvar__var__var__var__var__3__N__44379__44381__44390__44392__44394)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__44371)),Vvar__1__NB__44372,Vvar__var__var__var__var__3__N__44379__44381__44390__44392__44394)
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(Vvar__0__X__44371,Vvar__var__var__var__var__3__N__44379__44381__44390__44392__44394,Vvar__2__x__44373) ) )
& ! [Vvar__var__var__var__var__4__N__44384__44387__44396__44399__44402] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__44371),Vvar__var__var__var__var__4__N__44384__44387__44396__44399__44402)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(Vvar__0__X__44371,Vvar__var__var__var__var__4__N__44384__44387__44396__44399__44402,Vvar__2__x__44373)
=> ? [Vvar__var__var__var__var__6__N_27__44385__44388__44397__44400__44403] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__44371),Vvar__var__var__var__var__6__N_27__44385__44388__44397__44400__44403)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__44371)),Vvar__1__NB__44372,Vvar__var__var__var__var__6__N_27__44385__44388__44397__44400__44403)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__44371),Vvar__var__var__var__var__6__N_27__44385__44388__44397__44400__44403,Vvar__var__var__var__var__4__N__44384__44387__44396__44399__44402) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Topology.NeighborhoodBases.open_neighborhood_basis',axiom,
! [Vvar__0__X__38537,Vvar__1__NB__38538,Vvar__2__x__38539] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__38537)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38537),Vvar__1__NB__38538)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__38537,Vvar__2__x__38539)
=> ( cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(Vvar__0__X__38537,Vvar__1__NB__38538,Vvar__2__x__38539)
=> ( ! [Vvar__var__var__var__var__3__U__38545__38547__38556__38558__38560] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38537),Vvar__var__var__var__var__3__U__38545__38547__38556__38558__38560)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38537)),Vvar__1__NB__38538,Vvar__var__var__var__var__3__U__38545__38547__38556__38558__38560)
=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vvar__0__X__38537,Vvar__var__var__var__var__3__U__38545__38547__38556__38558__38560,Vvar__2__x__38539) ) )
& ! [Vvar__var__var__var__var__4__U__38550__38553__38562__38565__38568] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38537),Vvar__var__var__var__var__4__U__38550__38553__38562__38565__38568)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vvar__0__X__38537,Vvar__var__var__var__var__4__U__38550__38553__38562__38565__38568,Vvar__2__x__38539)
=> ? [Vvar__var__var__var__var__6__V__38551__38554__38563__38566__38569] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38537),Vvar__var__var__var__var__6__V__38551__38554__38563__38566__38569)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38537)),Vvar__1__NB__38538,Vvar__var__var__var__var__6__V__38551__38554__38563__38566__38569)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38537),Vvar__var__var__var__var__6__V__38551__38554__38563__38566__38569,Vvar__var__var__var__var__4__U__38550__38553__38562__38565__38568) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Topology.Nets.Subnet',axiom,
! [Vvar__0__X__39268,Vvar__1__I__39269,Vvar__2__x__39270,Vvar__3__J__39271,Vvar__4___24Anonymous__39272] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__39268)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(Vvar__1__I__39269)
=> ( cTopology_2eNets_2eNet___24t(Vvar__1__I__39269,Vvar__0__X__39268,Vvar__2__x__39270)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(Vvar__3__J__39271)
=> ( cTopology_2eNets_2eNet___24t(Vvar__3__J__39271,Vvar__0__X__39268,Vvar__4___24Anonymous__39272)
=> ( cTopology_2eNets_2eSubnet___24a5(Vvar__0__X__39268,Vvar__1__I__39269,Vvar__2__x__39270,Vvar__3__J__39271,Vvar__4___24Anonymous__39272)
=> ? [Vvar__4__h__39278] :
( c_24__type__39313___24t(Vvar__0__X__39268,Vvar__1__I__39269,Vvar__2__x__39270,Vvar__3__J__39271,Vvar__4___24Anonymous__39272,Vvar__4__h__39278)
& ! [Vvar__var__var__var__5__j1__39282__39285__39296__39299] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vvar__3__J__39271,Vvar__var__var__var__5__j1__39282__39285__39296__39299)
=> ! [Vvar__var__var__var__6__j2__39283__39286__39297__39300] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vvar__3__J__39271,Vvar__var__var__var__6__j2__39283__39286__39297__39300)
=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(Vvar__3__J__39271,Vvar__var__var__var__5__j1__39282__39285__39296__39299,Vvar__var__var__var__6__j2__39283__39286__39297__39300)
=> cTopology_2eDirectedSets_2eDS__ord___24a3(Vvar__1__I__39269,happ(Vvar__4__h__39278,Vvar__var__var__var__5__j1__39282__39285__39296__39299),happ(Vvar__4__h__39278,Vvar__var__var__var__6__j2__39283__39286__39297__39300)) ) ) )
& cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(Vvar__1__I__39269,c_24__lam__39336___24a6(Vvar__0__X__39268,Vvar__1__I__39269,Vvar__2__x__39270,Vvar__3__J__39271,Vvar__4___24Anonymous__39272,Vvar__4__h__39278))
& Vvar__4___24Anonymous__39272 = c_24__lam__39350___24a6(Vvar__0__X__39268,Vvar__1__I__39269,Vvar__2__x__39270,Vvar__3__J__39271,Vvar__4___24Anonymous__39272,Vvar__4__h__39278) ) ) ) ) ) ) ) ).
fof('$_inversion_Topology.Nets.cluster_point_subnet_DS_set',axiom,
! [Vvar__0__X__39414,Vvar__1__I__39415,Vvar__2__x__39416,Vvar__3__x0__39417,VX39418] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__39414)
=> ( cTopology_2eDirectedSets_2eDirectedSet___24t(Vvar__1__I__39415)
=> ( cTopology_2eNets_2eNet___24t(Vvar__1__I__39415,Vvar__0__X__39414,Vvar__2__x__39416)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__39414,Vvar__3__x0__39417)
=> ( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vvar__0__X__39414,Vvar__1__I__39415,Vvar__2__x__39416,Vvar__3__x0__39417,VX39418)
=> ? [Vvar__4__cps__i__39423] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vvar__1__I__39415,Vvar__4__cps__i__39423)
& ? [Vvar__5__cps__U__39424] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39414),Vvar__5__cps__U__39424)
& cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vvar__0__X__39414,Vvar__5__cps__U__39424,Vvar__3__x0__39417)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39414),Vvar__5__cps__U__39424,happ(Vvar__2__x__39416,Vvar__4__cps__i__39423))
& VX39418 = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(Vvar__0__X__39414,Vvar__1__I__39415,Vvar__2__x__39416,Vvar__3__x0__39417,Vvar__4__cps__i__39423,Vvar__5__cps__U__39424) ) ) ) ) ) ) ) ).
fof('$_inversion_Topology.Nets.neighborhood_net_DS_set',axiom,
! [Vvar__0__X__38596,Vvar__1__x__38597,VX38598] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__38596)
=> ( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__38596,Vvar__1__x__38597)
=> ( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vvar__0__X__38596,Vvar__1__x__38597,VX38598)
=> ? [Vvar__2__U__38601] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38596),Vvar__2__U__38601)
& ? [Vvar__3__y__38602] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__38596,Vvar__3__y__38602)
& cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__38596,Vvar__2__U__38601)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38596),Vvar__2__U__38601,Vvar__1__x__38597)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__38596),Vvar__2__U__38601,Vvar__3__y__38602)
& VX38598 = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(Vvar__0__X__38596,Vvar__1__x__38597,Vvar__2__U__38601,Vvar__3__y__38602) ) ) ) ) ) ).
fof('$_inversion_Topology.OpenBases.B_open',axiom,
! [Vvar__0__X__37381,Vvar__1__B__37382,Vvar__2___24Anonymous__37383] :
( cType___24t(Vvar__0__X__37381)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__37381,Vvar__1__B__37382)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__37381,Vvar__2___24Anonymous__37383)
=> ( cTopology_2eOpenBases_2eB__open___24a3(Vvar__0__X__37381,Vvar__1__B__37382,Vvar__2___24Anonymous__37383)
=> ? [Vvar__2__F__37387] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__37381,Vvar__2__F__37387)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__37381),Vvar__2__F__37387,Vvar__1__B__37382)
& Vvar__2___24Anonymous__37383 = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__X__37381,Vvar__2__F__37387) ) ) ) ) ) ).
fof('$_inversion_Topology.OpenBases.open_basis',axiom,
! [Vvar__0__X__39580,Vvar__1__B__39581] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__39580)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580),Vvar__1__B__39581)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(Vvar__0__X__39580,Vvar__1__B__39581)
=> ( ! [Vvar__var__var__var__2__V__39586__39588__39601__39603] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580),Vvar__var__var__var__2__V__39586__39588__39601__39603)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580)),Vvar__1__B__39581,Vvar__var__var__var__2__V__39586__39588__39601__39603)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__39580,Vvar__var__var__var__2__V__39586__39588__39601__39603) ) )
& ! [Vvar__var__var__var__3__x__39592__39597__39606__39611] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__39580,Vvar__var__var__var__3__x__39592__39597__39606__39611)
=> ! [Vvar__var__var__var__4__U__39591__39596__39605__39610] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580),Vvar__var__var__var__4__U__39591__39596__39605__39610)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__39580,Vvar__var__var__var__4__U__39591__39596__39605__39610)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580),Vvar__var__var__var__4__U__39591__39596__39605__39610,Vvar__var__var__var__3__x__39592__39597__39606__39611)
=> ? [Vvar__var__var__var__7__V__39593__39598__39607__39612] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580),Vvar__var__var__var__7__V__39593__39598__39607__39612)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580)),Vvar__1__B__39581,Vvar__var__var__var__7__V__39593__39598__39607__39612)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580),Vvar__var__var__var__7__V__39593__39598__39607__39612,Vvar__var__var__var__4__U__39591__39596__39605__39610)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39580),Vvar__var__var__var__7__V__39593__39598__39607__39612,Vvar__var__var__var__3__x__39592__39597__39606__39611) ) ) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Topology.OrderTopology.order_topology_subbasis',axiom,
! [Vvar__0__X__44848,Vvar__1__R__44849,Vvar__1___24Anonymous__44850] :
( cType___24t(Vvar__0__X__44848)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__X__44848,Vvar__1__R__44849)
=> ( c_24__type__44871___24t(Vvar__0__X__44848,Vvar__1__R__44849,Vvar__1___24Anonymous__44850,Vvar__1___24Anonymous__44850)
=> ( cTopology_2eOrderTopology_2eorder__topology__subbasis___24a3(Vvar__0__X__44848,Vvar__1__R__44849,Vvar__1___24Anonymous__44850)
=> ( ? [Vvar__2__x__44856] :
( t(Vvar__2__x__44856,Vvar__0__X__44848)
& Vvar__1___24Anonymous__44850 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__44848,c_24__lam__44879___24a4(Vvar__0__X__44848,Vvar__1__R__44849,Vvar__1___24Anonymous__44850,Vvar__2__x__44856)) )
| ? [Vvar__2__x__44862] :
( t(Vvar__2__x__44862,Vvar__0__X__44848)
& Vvar__1___24Anonymous__44850 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__44848,c_24__lam__44886___24a4(Vvar__0__X__44848,Vvar__1__R__44849,Vvar__1___24Anonymous__44850,Vvar__2__x__44862)) ) ) ) ) ) ) ).
fof('$_inversion_Topology.Subbases.subbasis',axiom,
! [Vvar__0__X__39632,Vvar__1__SB__39633] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vvar__0__X__39632)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),Vvar__1__SB__39633)
=> ( cTopology_2eSubbases_2esubbasis___24a2(Vvar__0__X__39632,Vvar__1__SB__39633)
=> ( ! [Vvar__var__var__var__2__U__39638__39640__39659__39661] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),Vvar__var__var__var__2__U__39638__39640__39659__39661)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632)),Vvar__1__SB__39633,Vvar__var__var__var__2__U__39638__39640__39659__39661)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__39632,Vvar__var__var__var__2__U__39638__39640__39659__39661) ) )
& ! [Vvar__var__var__var__3__U__39643__39651__39663__39671] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),Vvar__var__var__var__3__U__39643__39651__39663__39671)
=> ! [Vvar__var__var__var__4__x__39644__39652__39664__39672] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vvar__0__X__39632,Vvar__var__var__var__4__x__39644__39652__39664__39672)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),Vvar__var__var__var__3__U__39643__39651__39663__39671,Vvar__var__var__var__4__x__39644__39652__39664__39672)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vvar__0__X__39632,Vvar__var__var__var__3__U__39643__39651__39663__39671)
=> ? [Vvar__var__var__var__7__A__39645__39653__39665__39673] :
( cType___24t(Vvar__var__var__var__7__A__39645__39653__39665__39673)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__var__var__var__7__A__39645__39653__39665__39673)
& ? [Vvar__var__var__var__8__V__39647__39655__39667__39675] :
( c_24__type__39684___24t(Vvar__0__X__39632,Vvar__1__SB__39633,Vvar__var__var__var__7__A__39645__39653__39665__39673,Vvar__var__var__var__8__V__39647__39655__39667__39675)
& ! [Vvar__var__var__var__9__a__39648__39656__39668__39676] :
( t(Vvar__var__var__var__9__a__39648__39656__39668__39676,Vvar__var__var__var__7__A__39645__39653__39665__39673)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632)),Vvar__1__SB__39633,happ(Vvar__var__var__var__8__V__39647__39655__39667__39675,Vvar__var__var__var__9__a__39648__39656__39668__39676)) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(Vvar__var__var__var__7__A__39645__39653__39665__39673,cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),Vvar__var__var__var__8__V__39647__39655__39667__39675),Vvar__var__var__var__4__x__39644__39652__39664__39672)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(Vvar__var__var__var__7__A__39645__39653__39665__39673,cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vvar__0__X__39632),Vvar__var__var__var__8__V__39647__39655__39667__39675),Vvar__var__var__var__3__U__39643__39651__39663__39671) ) ) ) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Topology.TopologicalSpaces.TopologicalSpace',axiom,
! [VX37412] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(VX37412)
=> ? [Vvar__0__point__set__37413] :
( cType___24t(Vvar__0__point__set__37413)
& ? [Vvar__1__open__37414] :
( c_24__type__37437___24t(Vvar__0__point__set__37413,Vvar__1__open__37414)
& ! [Vvar__var__2__F__37418__37422] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__37413,Vvar__var__2__F__37418__37422)
=> ( ! [Vvar__var__3__S__37419__37423] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37413,Vvar__var__3__S__37419__37423)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__37413),Vvar__var__2__F__37418__37422,Vvar__var__3__S__37419__37423)
=> p(happ(Vvar__1__open__37414,Vvar__var__3__S__37419__37423)) ) )
=> p(happ(Vvar__1__open__37414,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__37413,Vvar__var__2__F__37418__37422))) ) )
& ! [Vvar__var__3__U__37427__37431] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37413,Vvar__var__3__U__37427__37431)
=> ! [Vvar__var__4__V__37428__37432] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__37413,Vvar__var__4__V__37428__37432)
=> ( p(happ(Vvar__1__open__37414,Vvar__var__3__U__37427__37431))
=> ( p(happ(Vvar__1__open__37414,Vvar__var__4__V__37428__37432))
=> p(happ(Vvar__1__open__37414,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__37413,Vvar__var__3__U__37427__37431,Vvar__var__4__V__37428__37432))) ) ) ) )
& p(happ(Vvar__1__open__37414,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__37413)))
& VX37412 = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__37413,Vvar__1__open__37414) ) ) ) ).
fof('$_inversion_Topology.WeakTopology.weak_topology_subbasis',axiom,
! [Vvar__0__X__49450,Vvar__1__A__49451,Vvar__2__Y__49452,Vvar__3__f__49455,Vvar__1___24Anonymous__49460] :
( cType___24t(Vvar__0__X__49450)
=> ( cType___24t(Vvar__1__A__49451)
=> ( c_24__type__49558___24t(Vvar__0__X__49450,Vvar__1__A__49451,Vvar__2__Y__49452,Vvar__3__f__49455,Vvar__1___24Anonymous__49460,Vvar__2__Y__49452)
=> ( c_24__type__49583___24t(Vvar__0__X__49450,Vvar__1__A__49451,Vvar__2__Y__49452,Vvar__3__f__49455,Vvar__1___24Anonymous__49460,Vvar__3__f__49455)
=> ( c_24__type__49602___24t(Vvar__0__X__49450,Vvar__1__A__49451,Vvar__2__Y__49452,Vvar__3__f__49455,Vvar__1___24Anonymous__49460,Vvar__1___24Anonymous__49460)
=> ( cTopology_2eWeakTopology_2eweak__topology__subbasis___24a5(Vvar__0__X__49450,Vvar__1__A__49451,Vvar__2__Y__49452,Vvar__3__f__49455,Vvar__1___24Anonymous__49460)
=> ? [Vvar__4__a__49474] :
( t(Vvar__4__a__49474,Vvar__1__A__49451)
& ? [Vvar__5__V__49475] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(happ(Vvar__2__Y__49452,Vvar__4__a__49474)),Vvar__5__V__49475)
& cTopology_2eTopologicalSpaces_2eopen___24a2(happ(Vvar__2__Y__49452,Vvar__4__a__49474),Vvar__5__V__49475)
& Vvar__1___24Anonymous__49460 = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(Vvar__0__X__49450,c_24__lam__49784___24a7(Vvar__0__X__49450,Vvar__1__A__49451,Vvar__2__Y__49452,Vvar__3__f__49455,Vvar__1___24Anonymous__49460,Vvar__4__a__49474,Vvar__5__V__49475)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.CountableTypes.CountableT',axiom,
! [Vvar__0__X__38258] :
( cType___24t(Vvar__0__X__38258)
=> ( cZornsLemma_2eCountableTypes_2eCountableT___24a1(Vvar__0__X__38258)
=> ? [Vvar__1__f__38261] :
( c_24__type__8907___24t(Vvar__0__X__38258,Vvar__1__f__38261)
& cZornsLemma_2eFunctionProperties_2einjective___24a3(Vvar__0__X__38258,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__f__38261)
& p(c_24True) ) ) ) ).
fof('$_inversion_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction',axiom,
! [Vvar__0__X__37308,Vvar__1__P__37309,Vvar__2__x__37312] :
( cType___24t(Vvar__0__X__37308)
=> ( c_24__type__37324___24t(Vvar__0__X__37308,Vvar__1__P__37309,Vvar__2__x__37312,Vvar__1__P__37309)
=> ( t(Vvar__2__x__37312,Vvar__0__X__37308)
=> ( cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(Vvar__0__X__37308,Vvar__1__P__37309,Vvar__2__x__37312)
=> ( p(happ(Vvar__1__P__37309,Vvar__2__x__37312))
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.Families.FamilyIntersection',axiom,
! [Vvar__0__T__37342,Vvar__1__F__37343,Vvar__1___24Anonymous__37344] :
( cType___24t(Vvar__0__T__37342)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__T__37342,Vvar__1__F__37343)
=> ( t(Vvar__1___24Anonymous__37344,Vvar__0__T__37342)
=> ( cZornsLemma_2eFamilies_2eFamilyIntersection___24a3(Vvar__0__T__37342,Vvar__1__F__37343,Vvar__1___24Anonymous__37344)
=> ? [Vvar__2__x__37348] :
( t(Vvar__2__x__37348,Vvar__0__T__37342)
& ! [Vvar__var__var__var__3__S__37350__37352__37354__37356] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__37342,Vvar__var__var__var__3__S__37350__37352__37354__37356)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__T__37342),Vvar__1__F__37343,Vvar__var__var__var__3__S__37350__37352__37354__37356)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__37342,Vvar__var__var__var__3__S__37350__37352__37354__37356,Vvar__2__x__37348) ) )
& Vvar__1___24Anonymous__37344 = Vvar__2__x__37348 ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.Families.FamilyUnion',axiom,
! [Vvar__0__T__37332,Vvar__1__F__37333,Vvar__1___24Anonymous__37334] :
( cType___24t(Vvar__0__T__37332)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__T__37332,Vvar__1__F__37333)
=> ( t(Vvar__1___24Anonymous__37334,Vvar__0__T__37332)
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a3(Vvar__0__T__37332,Vvar__1__F__37333,Vvar__1___24Anonymous__37334)
=> ? [Vvar__2__S__37338] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__37332,Vvar__2__S__37338)
& ? [Vvar__3__x__37339] :
( t(Vvar__3__x__37339,Vvar__0__T__37332)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__T__37332),Vvar__1__F__37333,Vvar__2__S__37338)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__37332,Vvar__2__S__37338,Vvar__3__x__37339)
& Vvar__1___24Anonymous__37334 = Vvar__3__x__37339 ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.FiniteIntersections.finite_intersections',axiom,
! [Vvar__0__X__42811,Vvar__1__S__42812,Vvar__1___24Anonymous__42813] :
( cType___24t(Vvar__0__X__42811)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__X__42811,Vvar__1__S__42812)
=> ( c_24__type__42834___24t(Vvar__0__X__42811,Vvar__1__S__42812,Vvar__1___24Anonymous__42813,Vvar__1___24Anonymous__42813)
=> ( cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a3(Vvar__0__X__42811,Vvar__1__S__42812,Vvar__1___24Anonymous__42813)
=> ( Vvar__1___24Anonymous__42813 = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__X__42811)
| ? [Vvar__2__U__42821] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__42811,Vvar__2__U__42821)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42811),Vvar__1__S__42812,Vvar__2__U__42821)
& Vvar__1___24Anonymous__42813 = Vvar__2__U__42821 )
| ? [Vvar__2__U__42825] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__42811,Vvar__2__U__42825)
& ? [Vvar__3__V__42826] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__X__42811,Vvar__3__V__42826)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42811),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(Vvar__0__X__42811,Vvar__1__S__42812),Vvar__2__U__42825)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__X__42811),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(Vvar__0__X__42811,Vvar__1__S__42812),Vvar__3__V__42826)
& Vvar__1___24Anonymous__42813 = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__X__42811,Vvar__2__U__42825,Vvar__3__V__42826) ) ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.FiniteTypes.FiniteT',axiom,
! [Vvar__0___24Anonymous__38993] :
( cType___24t(Vvar__0___24Anonymous__38993)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__0___24Anonymous__38993)
=> ( Vvar__0___24Anonymous__38993 = c_24False
| ? [Vvar__0__T__38995] :
( cType___24t(Vvar__0__T__38995)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__0__T__38995)
& Vvar__0___24Anonymous__38993 = cCoq_2eInit_2eDatatypes_2eoption___24a1(Vvar__0__T__38995) )
| ? [Vvar__0__X__38997] :
( cType___24t(Vvar__0__X__38997)
& ? [Vvar__1__Y__38998] :
( cType___24t(Vvar__1__Y__38998)
& ? [Vvar__2__f__38999] :
( c_24__type__39007___24t(Vvar__0___24Anonymous__38993,Vvar__0__X__38997,Vvar__1__Y__38998,Vvar__2__f__38999)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__0__X__38997)
& cZornsLemma_2eFunctionProperties_2einvertible___24a3(Vvar__0__X__38997,Vvar__1__Y__38998,Vvar__2__f__38999)
& Vvar__0___24Anonymous__38993 = Vvar__1__Y__38998 ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.FunctionProperties.invertible',axiom,
! [Vvar__0__X__42898,Vvar__1__Y__42899,Vvar__2__f__42900] :
( cType___24t(Vvar__0__X__42898)
=> ( cType___24t(Vvar__1__Y__42899)
=> ( c_24__type__42929___24t(Vvar__0__X__42898,Vvar__1__Y__42899,Vvar__2__f__42900,Vvar__2__f__42900)
=> ( cZornsLemma_2eFunctionProperties_2einvertible___24a3(Vvar__0__X__42898,Vvar__1__Y__42899,Vvar__2__f__42900)
=> ? [Vvar__3__g__42909] :
( c_24__type__42936___24t(Vvar__0__X__42898,Vvar__1__Y__42899,Vvar__2__f__42900,Vvar__3__g__42909)
& ! [Vvar__var__var__var__4__x__42913__42914__42920__42921] :
( t(Vvar__var__var__var__4__x__42913__42914__42920__42921,Vvar__0__X__42898)
=> happ(Vvar__3__g__42909,happ(Vvar__2__f__42900,Vvar__var__var__var__4__x__42913__42914__42920__42921)) = Vvar__var__var__var__4__x__42913__42914__42920__42921 )
& ! [Vvar__var__var__var__5__y__42916__42917__42922__42923] :
( t(Vvar__var__var__var__5__y__42916__42917__42922__42923,Vvar__1__Y__42899)
=> happ(Vvar__2__f__42900,happ(Vvar__3__g__42909,Vvar__var__var__var__5__y__42916__42917__42922__42923)) = Vvar__var__var__var__5__y__42916__42917__42922__42923 )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.IndexedFamilies.IndexedIntersection',axiom,
! [Vvar__0__A__38404,Vvar__1__T__38405,Vvar__2__F__38406,Vvar__1___24Anonymous__38407] :
( cType___24t(Vvar__0__A__38404)
=> ( cType___24t(Vvar__1__T__38405)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(Vvar__0__A__38404,Vvar__1__T__38405,Vvar__2__F__38406)
=> ( t(Vvar__1___24Anonymous__38407,Vvar__1__T__38405)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a4(Vvar__0__A__38404,Vvar__1__T__38405,Vvar__2__F__38406,Vvar__1___24Anonymous__38407)
=> ? [Vvar__3__x__38412] :
( t(Vvar__3__x__38412,Vvar__1__T__38405)
& ! [Vvar__var__var__var__var__4__a__38414__38415__38416__38417__38418] :
( t(Vvar__var__var__var__var__4__a__38414__38415__38416__38417__38418,Vvar__0__A__38404)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__1__T__38405,happ(Vvar__2__F__38406,Vvar__var__var__var__var__4__a__38414__38415__38416__38417__38418),Vvar__3__x__38412) )
& Vvar__1___24Anonymous__38407 = Vvar__3__x__38412 ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.IndexedFamilies.IndexedUnion',axiom,
! [Vvar__0__A__37360,Vvar__1__T__37361,Vvar__2__F__37362,Vvar__1___24Anonymous__37363] :
( cType___24t(Vvar__0__A__37360)
=> ( cType___24t(Vvar__1__T__37361)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(Vvar__0__A__37360,Vvar__1__T__37361,Vvar__2__F__37362)
=> ( t(Vvar__1___24Anonymous__37363,Vvar__1__T__37361)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a4(Vvar__0__A__37360,Vvar__1__T__37361,Vvar__2__F__37362,Vvar__1___24Anonymous__37363)
=> ? [Vvar__3__a__37368] :
( t(Vvar__3__a__37368,Vvar__0__A__37360)
& ? [Vvar__4__x__37369] :
( t(Vvar__4__x__37369,Vvar__1__T__37361)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__1__T__37361,happ(Vvar__2__F__37362,Vvar__3__a__37368),Vvar__4__x__37369)
& Vvar__1___24Anonymous__37363 = Vvar__4__x__37369 ) ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.ZornsLemma.tower',axiom,
! [Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196,Vvar__1___24Anonymous__50207] :
( cType___24t(Vvar__0__T__50175)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__T__50175,Vvar__1__R__50176)
=> ( c_24__type__50483___24t(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196,Vvar__1___24Anonymous__50207,Vvar__2__chain__sup__50177)
=> ( c_24__type__50588___24t(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196,Vvar__1___24Anonymous__50207,Vvar__3__inflation__50196)
=> ( t(Vvar__1___24Anonymous__50207,Vvar__0__T__50175)
=> ( cZornsLemma_2eZornsLemma_2etower___24a5(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196,Vvar__1___24Anonymous__50207)
=> ( ? [Vvar__4__S__50241] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__50175,Vvar__4__S__50241)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__T__50175,Vvar__4__S__50241,cZornsLemma_2eZornsLemma_2etower___24a4(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196))
& cZornsLemma_2eZornsLemma_2echain___24a3(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__4__S__50241)
& Vvar__1___24Anonymous__50207 = c_24__case__Coq_2eInit_2eSpecif_2esig_2450774___24a6(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196,Vvar__1___24Anonymous__50207,Vvar__4__S__50241) )
| ? [Vvar__4__x__50337] :
( t(Vvar__4__x__50337,Vvar__0__T__50175)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__50175,cZornsLemma_2eZornsLemma_2etower___24a4(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196),Vvar__4__x__50337)
& Vvar__1___24Anonymous__50207 = c_24__case__Coq_2eInit_2eSpecif_2esig_2451063___24a6(Vvar__0__T__50175,Vvar__1__R__50176,Vvar__2__chain__sup__50177,Vvar__3__inflation__50196,Vvar__1___24Anonymous__50207,Vvar__4__x__50337) ) ) ) ) ) ) ) ) ).
fof('$_lam_2297',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__2297___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__2225___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('$_lam_35677',axiom,
! [Vv__CANONICAL__0] : c_24__lam__35677___24a1(Vv__CANONICAL__0) = cCoq_2emicromega_2eRMicromega_2eRWeakChecker___24a1(cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit),cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2efst___24a2(cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(cCoq_2eQArith_2eQArith__base_2eQ),cCoq_2eInit_2eDatatypes_2eunit),Vv__CANONICAL__0)) ).
fof('$_lam_35703',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__35703___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eReals_2eRaxioms_2eis__lub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_37275',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__37275___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(cX,Vv__CANONICAL__2)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),Vv__CANONICAL__0,Vv__CANONICAL__2)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cTopology_2eInteriorsClosures_2eclosure___24a2(cX,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_lam_37373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__37373___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__2) ) ) ).
fof('$_lam_37632',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__37632___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cTopology_2eNeighborhoods_2eneighborhood___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1) ) ).
fof('$_lam_37771',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__37771___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ? [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__3)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__2) ) ) ).
fof('$_lam_38116',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__38116___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2)),Vv__CANONICAL__3) ) ).
fof('$_lam_38120',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__38120___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3) ) ).
fof('$_lam_38124',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__38124___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),Vv__CANONICAL__3) ) ).
fof('$_lam_38269',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__38269___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_38422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__38422___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) ) ).
fof('$_lam_38484',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__38484___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__5),Vv__CANONICAL__4)) ) ).
fof('$_lam_38507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__38507___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cTopology_2eSupInf_2eis__glb___24a2(cCoq_2eSets_2eImage_2eIm___24a4(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eR,Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__3)),Vv__CANONICAL__4) ) ).
fof('$_lam_38587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__38587___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__1),Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ).
fof('$_lam_38864',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__38864___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__38269___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__3)),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__38269___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4)) ).
fof('$_lam_38900',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__38900___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__38269___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__3)),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__38269___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4)) ).
fof('$_lam_39032',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__39032___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__1) ) ) ).
fof('$_lam_39043',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__39043___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ).
fof('$_lam_39150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__39150___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__4),Vv__CANONICAL__3)) ) ).
fof('$_lam_39212',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__39212___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_39227',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__39227___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_39252',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__39252___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_39336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__39336___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> ? [Vv__CANONICAL__7] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__3,Vv__CANONICAL__7)
& happ(Vv__CANONICAL__5,Vv__CANONICAL__7) = Vv__CANONICAL__6 ) ) ).
fof('$_lam_39350',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__39350___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_39386',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__39386___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ? [Vv__CANONICAL__5] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__2,Vv__CANONICAL__5)
& happ(Vv__CANONICAL__3,Vv__CANONICAL__5) = Vv__CANONICAL__4 ) ) ).
fof('$_lam_39398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__39398___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_39712',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__39712___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_39741',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__39741___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cTopology_2eSupInf_2eis__glb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ).
fof('$_lam_41013',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__41013___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ).
fof('$_lam_41027',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__41027___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__1,c_24__lam__41013___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ).
fof('$_lam_41148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__41148___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_41181',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__41181___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_41198',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__41198___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_41217',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__41217___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ).
fof('$_lam_41614',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__41614___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_41963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__41963___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eSets_2eCpo_2eDirected__rect___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_42253',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__42253___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_42592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__42592___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cTopology_2eDirectedSets_2eDS__ord___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ) ).
fof('$_lam_43870',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__43870___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cTopology_2eInteriorsClosures_2eclosure___24a2(Vv__CANONICAL__0,cTopology_2eInteriorsClosures_2einterior___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_43872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__43872___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cTopology_2eInteriorsClosures_2einterior___24a2(Vv__CANONICAL__0,cTopology_2eInteriorsClosures_2eclosure___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_43888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__43888___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> happ(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ) ).
fof('$_lam_44263',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__44263___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_44306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__44306___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_44321',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__44321___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__6)),Vv__CANONICAL__5)) ) ).
fof('$_lam_44370',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__44370___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cTopology_2eMetricSpaces_2edist__to__set___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4),cTopology_2eMetricSpaces_2edist__to__set___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ).
fof('$_lam_44418',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__44418___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__1,Vv__CANONICAL__3)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__2) ) ) ).
fof('$_lam_44587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__44587___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ) ).
fof('$_lam_44737',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__44737___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_44879',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__44879___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
& Vv__CANONICAL__4 != Vv__CANONICAL__3 ) ) ).
fof('$_lam_44886',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__44886___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& Vv__CANONICAL__4 != Vv__CANONICAL__3 ) ) ).
fof('$_lam_44890',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__44890___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2))
& Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ) ).
fof('$_lam_44894',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__44894___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3))
& Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ) ).
fof('$_lam_45132',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__45132___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)) ).
fof('$_lam_45144',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__45144___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('$_lam_45294',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__45294___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_45298',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__45298___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_45302',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__45302___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_45306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__45306___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_45314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__45314___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),cZornsLemma_2eQuotients_2eequiv__classes___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2) ) ).
fof('$_lam_45401',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__45401___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ) ).
fof('$_lam_45651',axiom,
! [Vv__CANONICAL__0] : c_24__lam__45651___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRtrigo__def_2esin__n___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0)),cCoq_2eReals_2eRtrigo__def_2esin__n___24a1(Vv__CANONICAL__0))) ).
fof('$_lam_49387',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__49387___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ? [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vv__CANONICAL__3)
& ? [Vv__CANONICAL__4] :
( c_24__type__39698___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
& ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__1,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) )
& Vv__CANONICAL__2 = cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(Vv__CANONICAL__3,cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__4) ) ) ) ).
fof('$_lam_49784',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] :
( c_24__lam__49784___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2449888___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__7)) ) ).
fof('$_lam_50093',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] : c_24__lam__50093___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)) ).
fof('$_lam_50156',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__50156___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_50517',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__50517___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> p(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)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__4)) ) )
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ).
fof('$_lam_50608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__50608___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3))
& Vv__CANONICAL__2 != Vv__CANONICAL__3
& ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__4))
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> ( Vv__CANONICAL__4 = Vv__CANONICAL__2
| Vv__CANONICAL__4 = Vv__CANONICAL__3 ) ) ) ) ) ) ).
fof('$_lam_51609',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__51609___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cZornsLemma_2eZornsLemma_2echain___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_52139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__52139___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ( p(happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
& ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_prop_18281',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__18281___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_18344',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__18344___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_18345',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__18345___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_35440',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__35440___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_35441',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__35441___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_35684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__35684___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_42312',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__42312___24a1(Vv__CANONICAL__0))
<=> ~ p(Vv__CANONICAL__0) ) ).
fof('$_type_1034',axiom,
! [Vvar__1035] :
( c_24__type__1034___24t(Vvar__1035)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__0),happ(happ(Vvar__1035,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10955',axiom,
! [Vvar__10956] :
( c_24__type__10955___24t(Vvar__10956)
<=> ! [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__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__10973___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__10978___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__10987___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__10956,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_10973',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10974] :
( c_24__type__10973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10974)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__10974,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_10978',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10979] :
( c_24__type__10978___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10979)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__10979,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_10987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10988] :
( c_24__type__10987___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10988)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__10988,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10998',axiom,
! [Vvar__10999] :
( c_24__type__10998___24t(Vvar__10999)
<=> ! [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__10999,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11',axiom,
! [Vvar__12] :
( c_24__type__11___24t(Vvar__12)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__12,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11018',axiom,
! [Vvar__11019] :
( c_24__type__11018___24t(Vvar__11019)
<=> ! [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__11019,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1114',axiom,
! [Vvar__1115] :
( c_24__type__1114___24t(Vvar__1115)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1115,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11237',axiom,
! [Vvar__11238] :
( c_24__type__11237___24t(Vvar__11238)
<=> ! [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__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__529___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__10973___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__10978___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__10987___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__11238,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_1137',axiom,
! [Vvar__1138] :
( c_24__type__1137___24t(Vvar__1138)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__919___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__1142___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__1138,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_11381',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11382] :
( c_24__type__11381___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11382)
<=> ! [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__11382,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_1142',axiom,
! [Vv__CANONICAL__0,Vvar__1143] :
( c_24__type__1142___24t(Vv__CANONICAL__0,Vvar__1143)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__1143,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_1159',axiom,
! [Vvar__1160] :
( c_24__type__1159___24t(Vvar__1160)
<=> ! [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__1160,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1161',axiom,
! [Vvar__1162] :
( c_24__type__1161___24t(Vvar__1162)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__1162,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11647',axiom,
! [Vvar__11648] :
( c_24__type__11647___24t(Vvar__11648)
<=> ! [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__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1950___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__11648,Vv__CANONICAL__0),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('$_type_1171',axiom,
! [Vvar__1172] :
( c_24__type__1171___24t(Vvar__1172)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1172,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11775',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__11776] :
( c_24__type__11775___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__11776)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__11776,Vv__CANONICAL__3)) ) ) ).
fof('$_type_11788',axiom,
! [Vvar__11789] :
( c_24__type__11788___24t(Vvar__11789)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__11789,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11790',axiom,
! [Vvar__11791] :
( c_24__type__11790___24t(Vvar__11791)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11791,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11793',axiom,
! [Vvar__11794] :
( c_24__type__11793___24t(Vvar__11794)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__11794,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11798',axiom,
! [Vvar__11799] :
( c_24__type__11798___24t(Vvar__11799)
<=> ! [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__11799,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11806',axiom,
! [Vvar__11807] :
( c_24__type__11806___24t(Vvar__11807)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__11807,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1191',axiom,
! [Vvar__1192] :
( c_24__type__1191___24t(Vvar__1192)
<=> ! [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__1192,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_11999',axiom,
! [Vvar__12000] :
( c_24__type__11999___24t(Vvar__12000)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__10973___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__10978___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__10987___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__12000,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1211',axiom,
! [Vvar__1212] :
( c_24__type__1211___24t(Vvar__1212)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__1212,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1216',axiom,
! [Vvar__1217] :
( c_24__type__1216___24t(Vvar__1217)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1217,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1232',axiom,
! [Vvar__1233] :
( c_24__type__1232___24t(Vvar__1233)
<=> ! [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__1233,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1244',axiom,
! [Vvar__1245] :
( c_24__type__1244___24t(Vvar__1245)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1245,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12668',axiom,
! [Vvar__12669] :
( c_24__type__12668___24t(Vvar__12669)
<=> ! [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__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___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__11381___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__10973___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__10978___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__10987___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__11775___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__12669,Vv__CANONICAL__0),Vv__CANONICAL__1),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('$_type_14',axiom,
! [Vvar__15] :
( c_24__type__14___24t(Vvar__15)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__15,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15187',axiom,
! [Vvar__15188] :
( c_24__type__15187___24t(Vvar__15188)
<=> ! [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__15188,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_15246',axiom,
! [Vvar__15247] :
( c_24__type__15246___24t(Vvar__15247)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__15247,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1584',axiom,
! [Vvar__1585] :
( c_24__type__1584___24t(Vvar__1585)
<=> ! [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_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__1585,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16032',axiom,
! [Vvar__16033] :
( c_24__type__16032___24t(Vvar__16033)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__16033,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16035',axiom,
! [Vvar__16036] :
( c_24__type__16035___24t(Vvar__16036)
<=> ! [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__16036,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16040',axiom,
! [Vvar__16041] :
( c_24__type__16040___24t(Vvar__16041)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__16041,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_16051',axiom,
! [Vvar__16052] :
( c_24__type__16051___24t(Vvar__16052)
<=> ! [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__16052,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_16069',axiom,
! [Vvar__16070] :
( c_24__type__16069___24t(Vvar__16070)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__16074___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__16070,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_16074',axiom,
! [Vv__CANONICAL__0,Vvar__16075] :
( c_24__type__16074___24t(Vv__CANONICAL__0,Vvar__16075)
<=> ! [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__16075,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_16196',axiom,
! [Vvar__16197] :
( c_24__type__16196___24t(Vvar__16197)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1950___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2451___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__10)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__16197,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_16677',axiom,
! [Vvar__16678] :
( c_24__type__16677___24t(Vvar__16678)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(happ(Vvar__16678,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1688',axiom,
! [Vvar__1689] :
( c_24__type__1688___24t(Vvar__1689)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,happ(happ(happ(happ(Vvar__1689,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_16948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16949] :
( c_24__type__16948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16949)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__16949,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_17',axiom,
! [Vvar__18] :
( c_24__type__17___24t(Vvar__18)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__18,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1737',axiom,
! [Vv__CANONICAL__0,Vvar__1738] :
( c_24__type__1737___24t(Vv__CANONICAL__0,Vvar__1738)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__1738,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_1757',axiom,
! [Vvar__1758] :
( c_24__type__1757___24t(Vvar__1758)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__1758,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1767',axiom,
! [Vvar__1768] :
( c_24__type__1767___24t(Vvar__1768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__1768,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1770',axiom,
! [Vvar__1771] :
( c_24__type__1770___24t(Vvar__1771)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__1771,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1774',axiom,
! [Vvar__1775] :
( c_24__type__1774___24t(Vvar__1775)
<=> ! [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__1775,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1781',axiom,
! [Vvar__1782] :
( c_24__type__1781___24t(Vvar__1782)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__1782,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18227',axiom,
! [Vvar__18228] :
( c_24__type__18227___24t(Vvar__18228)
<=> ! [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__18228,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18279',axiom,
! [Vvar__18280] :
( c_24__type__18279___24t(Vvar__18280)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__18281___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__18280,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18296',axiom,
! [Vvar__18297] :
( c_24__type__18296___24t(Vvar__18297)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__18297,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18306',axiom,
! [Vvar__18307] :
( c_24__type__18306___24t(Vvar__18307)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__18307,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18348',axiom,
! [Vvar__18349] :
( c_24__type__18348___24t(Vvar__18349)
<=> ! [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__18349,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18617',axiom,
! [Vvar__18618] :
( c_24__type__18617___24t(Vvar__18618)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__18618,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18622',axiom,
! [Vvar__18623] :
( c_24__type__18622___24t(Vvar__18623)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1757___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__18623,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1950',axiom,
! [Vv__CANONICAL__0,Vvar__1951] :
( c_24__type__1950___24t(Vv__CANONICAL__0,Vvar__1951)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__1951,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1961',axiom,
! [Vvar__1962] :
( c_24__type__1961___24t(Vvar__1962)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1950___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__1962,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2210',axiom,
! [Vvar__2211] :
( c_24__type__2210___24t(Vvar__2211)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__2211,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2213',axiom,
! [Vvar__2214] :
( c_24__type__2213___24t(Vvar__2214)
<=> ! [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__2214,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2218',axiom,
! [Vvar__2219] :
( c_24__type__2218___24t(Vvar__2219)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2219,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24018',axiom,
! [Vvar__24019] :
( c_24__type__24018___24t(Vvar__24019)
<=> ! [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__24019,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2429',axiom,
! [Vvar__2430] :
( c_24__type__2429___24t(Vvar__2430)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1950___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2451___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2430,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_24307',axiom,
! [Vvar__24308] :
( c_24__type__24307___24t(Vvar__24308)
<=> ! [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__24308,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2434',axiom,
! [Vv__CANONICAL__0,Vvar__2435] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vvar__2435)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2435,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2443',axiom,
! [Vv__CANONICAL__0,Vvar__2444] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vvar__2444)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__2444,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_2451',axiom,
! [Vv__CANONICAL__0,Vvar__2452] :
( c_24__type__2451___24t(Vv__CANONICAL__0,Vvar__2452)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__2452,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_24641',axiom,
! [Vvar__24642] :
( c_24__type__24641___24t(Vvar__24642)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8715___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__24642,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_24658',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24659] :
( c_24__type__24658___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24659)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__24659,Vv__CANONICAL__2)) ) ) ).
fof('$_type_24662',axiom,
! [Vvar__24663] :
( c_24__type__24662___24t(Vvar__24663)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__24663,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24680',axiom,
! [Vvar__24681] :
( c_24__type__24680___24t(Vvar__24681)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__24681,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_24818',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24819] :
( c_24__type__24818___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24819)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24819,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_2611',axiom,
! [Vvar__2612] :
( c_24__type__2611___24t(Vvar__2612)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__2434___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1950___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__2451___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2612,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2632',axiom,
! [Vvar__2633] :
( c_24__type__2632___24t(Vvar__2633)
<=> ! [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__2633,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2644',axiom,
! [Vvar__2645] :
( c_24__type__2644___24t(Vvar__2645)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2645,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2667',axiom,
! [Vvar__2668] :
( c_24__type__2667___24t(Vvar__2668)
<=> ! [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__2668,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_2672',axiom,
! [Vvar__2673] :
( c_24__type__2672___24t(Vvar__2673)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__2673,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_2728',axiom,
! [Vvar__2729] :
( c_24__type__2728___24t(Vvar__2729)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2729,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27584',axiom,
! [Vvar__27585] :
( c_24__type__27584___24t(Vvar__27585)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__27585,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2769',axiom,
! [Vvar__2770] :
( c_24__type__2769___24t(Vvar__2770)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2770,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28214',axiom,
! [Vvar__28215] :
( c_24__type__28214___24t(Vvar__28215)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__28215,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28244',axiom,
! [Vvar__28245] :
( c_24__type__28244___24t(Vvar__28245)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__28245,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2890',axiom,
! [Vvar__2891] :
( c_24__type__2890___24t(Vvar__2891)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2891,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2907',axiom,
! [Vvar__2908] :
( c_24__type__2907___24t(Vvar__2908)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__2908,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2915',axiom,
! [Vvar__2916] :
( c_24__type__2915___24t(Vvar__2916)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__2916,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_29998',axiom,
! [Vvar__29999] :
( c_24__type__29998___24t(Vvar__29999)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29999,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30510',axiom,
! [Vvar__30511] :
( c_24__type__30510___24t(Vvar__30511)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__30511,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30513',axiom,
! [Vvar__30514] :
( c_24__type__30513___24t(Vvar__30514)
<=> ! [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__30514,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3119',axiom,
! [Vvar__3120] :
( c_24__type__3119___24t(Vvar__3120)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3120,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3122',axiom,
! [Vvar__3123] :
( c_24__type__3122___24t(Vvar__3123)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__3123,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3130',axiom,
! [Vvar__3131] :
( c_24__type__3130___24t(Vvar__3131)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__3131,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3162',axiom,
! [Vvar__3163] :
( c_24__type__3162___24t(Vvar__3163)
<=> ! [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__3163,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3165',axiom,
! [Vvar__3166] :
( c_24__type__3165___24t(Vvar__3166)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__3166,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3172',axiom,
! [Vvar__3173] :
( c_24__type__3172___24t(Vvar__3173)
<=> ! [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__3173,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3185',axiom,
! [Vvar__3186] :
( c_24__type__3185___24t(Vvar__3186)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__3186,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31982',axiom,
! [Vvar__31983] :
( c_24__type__31982___24t(Vvar__31983)
<=> ! [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__31983,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32071',axiom,
! [Vvar__32072] :
( c_24__type__32071___24t(Vvar__32072)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__32072,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32518',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32519] :
( c_24__type__32518___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32519)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__32519,Vv__CANONICAL__2)) ) ) ).
fof('$_type_32524',axiom,
! [Vvar__32525] :
( c_24__type__32524___24t(Vvar__32525)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__32525,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_32553',axiom,
! [Vvar__32554] :
( c_24__type__32553___24t(Vvar__32554)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__32554,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32558',axiom,
! [Vvar__32559] :
( c_24__type__32558___24t(Vvar__32559)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__32559,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_32584',axiom,
! [Vvar__32585] :
( c_24__type__32584___24t(Vvar__32585)
<=> ! [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__32585,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_32601',axiom,
! [Vvar__32602] :
( c_24__type__32601___24t(Vvar__32602)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__32602,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_32609',axiom,
! [Vvar__32610] :
( c_24__type__32609___24t(Vvar__32610)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(Vvar__32610,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32612',axiom,
! [Vvar__32613] :
( c_24__type__32612___24t(Vvar__32613)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(Vvar__32613,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35072',axiom,
! [Vvar__35073] :
( c_24__type__35072___24t(Vvar__35073)
<=> ! [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__35073,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_35099',axiom,
! [Vvar__35100] :
( c_24__type__35099___24t(Vvar__35100)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__35100,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_35122',axiom,
! [Vvar__35123] :
( c_24__type__35122___24t(Vvar__35123)
<=> ! [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__35123,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_35532',axiom,
! [Vvar__35533] :
( c_24__type__35532___24t(Vvar__35533)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35533,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35549',axiom,
! [Vvar__35550] :
( c_24__type__35549___24t(Vvar__35550)
<=> ! [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__35550,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_35554',axiom,
! [Vvar__35555] :
( c_24__type__35554___24t(Vvar__35555)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__35555,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35679',axiom,
! [Vvar__35680] :
( c_24__type__35679___24t(Vvar__35680)
<=> ! [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__35680,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35682',axiom,
! [Vvar__35683] :
( c_24__type__35682___24t(Vvar__35683)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__35684___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__35683,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35686',axiom,
! [Vvar__35687] :
( c_24__type__35686___24t(Vvar__35687)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__35532___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35687,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35688',axiom,
! [Vvar__35689] :
( c_24__type__35688___24t(Vvar__35689)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__35532___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35689,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35699',axiom,
! [Vvar__35700] :
( c_24__type__35699___24t(Vvar__35700)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__35532___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__35703___24a1(Vv__CANONICAL__0),happ(Vvar__35700,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_35841',axiom,
! [Vvar__35842] :
( c_24__type__35841___24t(Vvar__35842)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1757___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35842,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36107',axiom,
! [Vvar__36108] :
( c_24__type__36107___24t(Vvar__36108)
<=> ! [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__36108,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3701',axiom,
! [Vvar__3702] :
( c_24__type__3701___24t(Vvar__3702)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__3702,Vv__CANONICAL__0)) ) ) ).
fof('$_type_372',axiom,
! [Vvar__373] :
( c_24__type__372___24t(Vvar__373)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__373,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37271',axiom,
! [Vvar__37272] :
( c_24__type__37271___24t(Vvar__37272)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),Vv__CANONICAL__1)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(cX,Vv__CANONICAL__0)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(cX,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX)),c_24__lam__37275___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__37272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_37280',axiom,
! [Vvar__37281] :
( c_24__type__37280___24t(Vvar__37281)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__37281,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37285',axiom,
! [Vvar__37286] :
( c_24__type__37285___24t(Vvar__37286)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__37286,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37299',axiom,
! [Vvar__37300] :
( c_24__type__37299___24t(Vvar__37300)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__37300,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37324',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37325] :
( c_24__type__37324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37325)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37325,Vv__CANONICAL__3)) ) ) ).
fof('$_type_37329',axiom,
! [Vvar__37330] :
( c_24__type__37329___24t(Vvar__37330)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__37330,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37375',axiom,
! [Vvar__37376] :
( c_24__type__37375___24t(Vvar__37376)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(Vvar__37376,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37378',axiom,
! [Vvar__37379] :
( c_24__type__37378___24t(Vvar__37379)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__37379,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37437',axiom,
! [Vv__CANONICAL__0,Vvar__37438] :
( c_24__type__37437___24t(Vv__CANONICAL__0,Vvar__37438)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__37438,Vv__CANONICAL__1)) ) ) ).
fof('$_type_37524',axiom,
! [Vvar__37525] :
( c_24__type__37524___24t(Vvar__37525)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__37525,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37592',axiom,
! [Vvar__37593] :
( c_24__type__37592___24t(Vvar__37593)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__37593,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37638',axiom,
! [Vvar__37639] :
( c_24__type__37638___24t(Vvar__37639)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(Vvar__37639,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37643',axiom,
! [Vvar__37644] :
( c_24__type__37643___24t(Vvar__37644)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__37644,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37759',axiom,
! [Vvar__37760] :
( c_24__type__37759___24t(Vvar__37760)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,happ(happ(Vvar__37760,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37816',axiom,
! [Vvar__37817] :
( c_24__type__37816___24t(Vvar__37817)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vv__CANONICAL__0))
=> ( ! [Vv__CANONICAL__4] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ? [Vv__CANONICAL__8] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__8)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__8,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)) ) ) ) ) )
=> cTopology_2eFilters_2eFilter___24t(Vv__CANONICAL__0,happ(happ(Vvar__37817,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_37993',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37994] :
( c_24__type__37993___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37994)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37994,Vv__CANONICAL__4)) ) ) ).
fof('$_type_38111',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__38112] :
( c_24__type__38111___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__38112)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),c_24__lam__38116___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),c_24__lam__38120___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)),cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),c_24__lam__38124___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)),happ(Vvar__38112,Vv__CANONICAL__3)) ) ) ).
fof('$_type_38175',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38176] :
( c_24__type__38175___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__38176)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__38176,Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ).
fof('$_type_38182',axiom,
! [Vvar__38183] :
( c_24__type__38182___24t(Vvar__38183)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__38183,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38228',axiom,
! [Vvar__38229] :
( c_24__type__38228___24t(Vvar__38229)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__37437___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__3)
=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3)) ) )
=> p(happ(Vv__CANONICAL__1,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))) ) )
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__4))
=> p(happ(Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) )
=> ( p(happ(Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vv__CANONICAL__0)))
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(Vvar__38229,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_38256',axiom,
! [Vvar__38257] :
( c_24__type__38256___24t(Vvar__38257)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__38257,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38271',axiom,
! [Vvar__38272] :
( c_24__type__38271___24t(Vvar__38272)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38313',axiom,
! [Vvar__38314] :
( c_24__type__38313___24t(Vvar__38314)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ? [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__5))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) )
=> cTopology_2eDirectedSets_2eDirectedSet___24t(happ(happ(Vvar__38314,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_type_38346',axiom,
! [Vvar__38347] :
( c_24__type__38346___24t(Vvar__38347)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__38347,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38376',axiom,
! [Vvar__38377] :
( c_24__type__38376___24t(Vvar__38377)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cTopology_2eDirectedSets_2eDS__set___24a1(Vv__CANONICAL__0),happ(Vvar__38377,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38380',axiom,
! [Vvar__38381] :
( c_24__type__38380___24t(Vvar__38381)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38383___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38381,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38383',axiom,
! [Vv__CANONICAL__0,Vvar__38384] :
( c_24__type__38383___24t(Vv__CANONICAL__0,Vvar__38384)
<=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__38384,Vv__CANONICAL__1)) ) ) ).
fof('$_type_38400',axiom,
! [Vvar__38401] :
( c_24__type__38400___24t(Vvar__38401)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__16948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__38401,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38462] :
( c_24__type__38461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38462)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__38462,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_38472',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38473] :
( c_24__type__38472___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38473)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__38473,Vv__CANONICAL__4)) ) ) ).
fof('$_type_38488',axiom,
! [Vv__CANONICAL__0,Vvar__38489] :
( c_24__type__38488___24t(Vv__CANONICAL__0,Vvar__38489)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__38489,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_38494',axiom,
! [Vvar__38495] :
( c_24__type__38494___24t(Vvar__38495)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38499___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38495,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38499',axiom,
! [Vv__CANONICAL__0,Vvar__38500] :
( c_24__type__38499___24t(Vv__CANONICAL__0,Vvar__38500)
<=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__38500,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_38529',axiom,
! [Vvar__38530] :
( c_24__type__38529___24t(Vvar__38530)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(happ(Vvar__38530,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_38578',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38579] :
( c_24__type__38578___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38579)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,happ(Vvar__38579,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38581',axiom,
! [Vvar__38582] :
( c_24__type__38581___24t(Vvar__38582)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__38582,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38594',axiom,
! [Vvar__38595] :
( c_24__type__38594___24t(Vvar__38595)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__38595,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38607',axiom,
! [Vvar__38608] :
( c_24__type__38607___24t(Vvar__38608)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__38608,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38644',axiom,
! [Vvar__38645] :
( c_24__type__38644___24t(Vvar__38645)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__38645,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ) ).
fof('$_type_38720',axiom,
! [Vvar__38721] :
( c_24__type__38720___24t(Vvar__38721)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__38721,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38725',axiom,
! [Vvar__38726] :
( c_24__type__38725___24t(Vvar__38726)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cTopology_2eDirectedSets_2eDirectedSet___24t(happ(happ(Vvar__38726,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38762',axiom,
! [Vvar__38763] :
( c_24__type__38762___24t(Vvar__38763)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cTopology_2eNets_2eNet___24t(cTopology_2eNets_2eneighborhood__net__DS___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0,happ(happ(Vvar__38763,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38807',axiom,
! [Vvar__38808] :
( c_24__type__38807___24t(Vvar__38808)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1737___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__38808,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38820',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38821] :
( c_24__type__38820___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38821)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__38821,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_38828',axiom,
! [Vvar__38829] :
( c_24__type__38828___24t(Vvar__38829)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38829,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_38915',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38916] :
( c_24__type__38915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38916)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,happ(Vvar__38916,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38983',axiom,
! [Vvar__38984] :
( c_24__type__38983___24t(Vvar__38984)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) )
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__4) ) ) ) )
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vv__CANONICAL__0))
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vv__CANONICAL__0))
=> cTopology_2eFilters_2eFilter___24t(Vv__CANONICAL__0,happ(happ(Vvar__38984,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ) ).
fof('$_type_39007',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39008] :
( c_24__type__39007___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39008)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__39008,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_39022',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39023] :
( c_24__type__39022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39023)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__1,happ(Vvar__39023,Vv__CANONICAL__2)) ) ) ).
fof('$_type_39028',axiom,
! [Vvar__39029] :
( c_24__type__39028___24t(Vvar__39029)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__39029,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_39052',axiom,
! [Vvar__39053] :
( c_24__type__39052___24t(Vvar__39053)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__16948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__39053,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_39125',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39126] :
( c_24__type__39125___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39126)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__39126,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_39160',axiom,
! [Vvar__39161] :
( c_24__type__39160___24t(Vvar__39161)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__39161,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_39313',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__39314] :
( c_24__type__39313___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__39314)
<=> ! [Vv__CANONICAL__5] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,happ(Vvar__39314,Vv__CANONICAL__5)) ) ) ).
fof('$_type_39369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39370] :
( c_24__type__39369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39370)
<=> ! [Vv__CANONICAL__3] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,happ(Vvar__39370,Vv__CANONICAL__3)) ) ) ).
fof('$_type_39433',axiom,
! [Vvar__39434] :
( c_24__type__39433___24t(Vvar__39434)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__39434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_39479',axiom,
! [Vvar__39480] :
( c_24__type__39479___24t(Vvar__39480)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__5)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
=> cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__39480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_39517',axiom,
! [Vvar__39518] :
( c_24__type__39517___24t(Vvar__39518)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,happ(happ(happ(happ(happ(Vvar__39518,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_39547',axiom,
! [Vvar__39548] :
( c_24__type__39547___24t(Vvar__39548)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(Vvar__39548,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_39564',axiom,
! [Vvar__39565] :
( c_24__type__39564___24t(Vvar__39565)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__39565,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_39578',axiom,
! [Vvar__39579] :
( c_24__type__39578___24t(Vvar__39579)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eDirectedSets_2eDirectedSet___24t(happ(happ(happ(happ(Vvar__39579,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_39684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39685] :
( c_24__type__39684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39685)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(Vvar__39685,Vv__CANONICAL__3)) ) ) ).
fof('$_type_39698',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39699] :
( c_24__type__39698___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39699)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(Vvar__39699,Vv__CANONICAL__2)) ) ) ).
fof('$_type_39716',axiom,
! [Vvar__39717] :
( c_24__type__39716___24t(Vvar__39717)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(Vvar__39717,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_39723',axiom,
! [Vvar__39724] :
( c_24__type__39723___24t(Vvar__39724)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__39724,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_39737',axiom,
! [Vvar__39738] :
( c_24__type__39737___24t(Vvar__39738)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__35532___24t(Vv__CANONICAL__0)
=> ( cTopology_2eSupInf_2elower__bound___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__39741___24a1(Vv__CANONICAL__0),happ(Vvar__39738,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_39840',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39841] :
( c_24__type__39840___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39841)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,happ(Vvar__39841,Vv__CANONICAL__2)) ) ) ).
fof('$_type_410',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__411] :
( c_24__type__410___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__411)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__411,Vv__CANONICAL__3)) ) ) ).
fof('$_type_41094',axiom,
! [Vvar__41095] :
( c_24__type__41094___24t(Vvar__41095)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__38915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__41095,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_41106',axiom,
! [Vvar__41107] :
( c_24__type__41106___24t(Vvar__41107)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__38915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__41107,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_41134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__41135] :
( c_24__type__41134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__41135)
<=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,happ(Vvar__41135,Vv__CANONICAL__3)) ) ) ).
fof('$_type_41554',axiom,
! [Vvar__41555] :
( c_24__type__41554___24t(Vvar__41555)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__41582___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(happ(happ(Vvar__41555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ) ) ) ) ) ).
fof('$_type_41582',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41583] :
( c_24__type__41582___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41583)
<=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),Vv__CANONICAL__2)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__5) ) ) ) ) )
=> t(Vvar__41583,Vv__CANONICAL__3) ) ) ).
fof('$_type_41882',axiom,
! [Vvar__41883] :
( c_24__type__41882___24t(Vvar__41883)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__41929___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(happ(happ(Vvar__41883,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ) ) ) ) ) ).
fof('$_type_41929',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41930] :
( c_24__type__41929___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41930)
<=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vv__CANONICAL__0,Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__2)
=> ? [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__9)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vv__CANONICAL__0,Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__9) ) ) ) )
=> t(Vvar__41930,Vv__CANONICAL__3) ) ) ) ) ).
fof('$_type_42195',axiom,
! [Vvar__42196] :
( c_24__type__42195___24t(Vvar__42196)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__42223___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> t(happ(happ(happ(happ(Vvar__42196,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ) ) ) ) ).
fof('$_type_42223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42224] :
( c_24__type__42223___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42224)
<=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ( ? [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5) )
=> ? [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) )
=> t(Vvar__42224,Vv__CANONICAL__2) ) ) ).
fof('$_type_42310',axiom,
! [Vvar__42311] :
( c_24__type__42310___24t(Vvar__42311)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,c_24__prop__42312___24a1(Vv__CANONICAL__0),happ(Vvar__42311,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42344',axiom,
! [Vvar__42345] :
( c_24__type__42344___24t(Vvar__42345)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__42345,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42365',axiom,
! [Vvar__42366] :
( c_24__type__42365___24t(Vvar__42366)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__42366,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42381',axiom,
! [Vvar__42382] :
( c_24__type__42381___24t(Vvar__42382)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__42382,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42489',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__42490] :
( c_24__type__42489___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__42490)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(Vvar__42490,Vv__CANONICAL__4)) ) ) ).
fof('$_type_42499',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42500] :
( c_24__type__42499___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42500)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(Vvar__42500,Vv__CANONICAL__2)) ) ) ).
fof('$_type_42564',axiom,
! [Vvar__42565] :
( c_24__type__42564___24t(Vvar__42565)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__42565,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42599',axiom,
! [Vvar__42600] :
( c_24__type__42599___24t(Vvar__42600)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eDirectedSets_2eDS__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__42600,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_42604',axiom,
! [Vvar__42605] :
( c_24__type__42604___24t(Vvar__42605)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__42605,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42640',axiom,
! [Vvar__42641] :
( c_24__type__42640___24t(Vvar__42641)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__42641,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42669',axiom,
! [Vvar__42670] :
( c_24__type__42669___24t(Vvar__42670)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__42670,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).
fof('$_type_42688',axiom,
! [Vvar__42689] :
( c_24__type__42688___24t(Vvar__42689)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__42689,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42722',axiom,
! [Vvar__42723] :
( c_24__type__42722___24t(Vvar__42723)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__42723,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42738',axiom,
! [Vvar__42739] :
( c_24__type__42738___24t(Vvar__42739)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cTopology_2eNets_2eNet___24t(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__0,happ(happ(Vvar__42739,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42834',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42835] :
( c_24__type__42834___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42835)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__42835,Vv__CANONICAL__3)) ) ) ).
fof('$_type_42929',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42930] :
( c_24__type__42929___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42930)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__42930,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_42936',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42937] :
( c_24__type__42936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42937)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__42937,Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ).
fof('$_type_4368',axiom,
! [Vvar__4369] :
( c_24__type__4368___24t(Vvar__4369)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__4369,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4372',axiom,
! [Vvar__4373] :
( c_24__type__4372___24t(Vvar__4373)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4373,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43790',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43791] :
( c_24__type__43790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43791)
<=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,happ(Vvar__43791,Vv__CANONICAL__3)) ) ) ).
fof('$_type_43797',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43798] :
( c_24__type__43797___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43798)
<=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,happ(Vvar__43798,Vv__CANONICAL__3)) ) ) ).
fof('$_type_43805',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__43806] :
( c_24__type__43805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__43806)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,happ(Vvar__43806,Vv__CANONICAL__2)) ) ) ).
fof('$_type_43856',axiom,
! [Vvar__43857] :
( c_24__type__43856___24t(Vvar__43857)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__38256___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__43857,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43866',axiom,
! [Vvar__43867] :
( c_24__type__43866___24t(Vvar__43867)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2443___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43867,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43878',axiom,
! [Vv__CANONICAL__0,Vvar__43879] :
( c_24__type__43878___24t(Vv__CANONICAL__0,Vvar__43879)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(Vvar__43879,Vv__CANONICAL__1)) ) ) ).
fof('$_type_43912',axiom,
! [Vvar__43913] :
( c_24__type__43912___24t(Vvar__43913)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__43878___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) )
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> happ(Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) )
=> ( happ(Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vv__CANONICAL__0)) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(Vvar__43913,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_4403',axiom,
! [Vvar__4404] :
( c_24__type__4403___24t(Vvar__4404)
<=> ! [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__4404,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4406',axiom,
! [Vvar__4407] :
( c_24__type__4406___24t(Vvar__4407)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4407,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44249',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44250] :
( c_24__type__44249___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44250)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__44250,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_44329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44330] :
( c_24__type__44329___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44330)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__44330,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_44336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44337] :
( c_24__type__44336___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44337)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__44337,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_44420',axiom,
! [Vv__CANONICAL__0,Vvar__44421] :
( c_24__type__44420___24t(Vv__CANONICAL__0,Vvar__44421)
<=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(Vvar__44421,Vv__CANONICAL__1)) ) ) ).
fof('$_type_44548',axiom,
! [Vv__CANONICAL__0,Vvar__44549] :
( c_24__type__44548___24t(Vv__CANONICAL__0,Vvar__44549)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,happ(Vvar__44549,Vv__CANONICAL__1)) ) ) ).
fof('$_type_44608',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44609] :
( c_24__type__44608___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44609)
<=> ! [Vv__CANONICAL__3] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cType___24t(happ(Vvar__44609,Vv__CANONICAL__3)) ) ) ).
fof('$_type_44647',axiom,
! [Vvar__44648] :
( c_24__type__44647___24t(Vvar__44648)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__44651___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__44680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__44648,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_44651',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44652] :
( c_24__type__44651___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44652)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__44652,Vv__CANONICAL__2)) ) ) ).
fof('$_type_44680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44681] :
( c_24__type__44680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44681)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__44681,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ) ) ).
fof('$_type_44684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44685] :
( c_24__type__44684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44685)
<=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__44685,Vv__CANONICAL__2)) ) ) ).
fof('$_type_4476',axiom,
! [Vvar__4477] :
( c_24__type__4476___24t(Vvar__4477)
<=> ! [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__4477,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4479',axiom,
! [Vvar__4480] :
( c_24__type__4479___24t(Vvar__4480)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4480,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44843',axiom,
! [Vvar__44844] :
( c_24__type__44843___24t(Vvar__44844)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cTopology_2eNets_2eNet___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eNets_2eNet___24t(cTopology_2eNets_2ecluster__point__subnet__DS___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__44844,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ).
fof('$_type_44871',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44872] :
( c_24__type__44871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__44872)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__44872,Vv__CANONICAL__3)) ) ) ).
fof('$_type_4488',axiom,
! [Vv__CANONICAL__0,Vvar__4489] :
( c_24__type__4488___24t(Vv__CANONICAL__0,Vvar__4489)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__4489,Vv__CANONICAL__1)) ) ) ).
fof('$_type_45151',axiom,
! [Vvar__45152] :
( c_24__type__45151___24t(Vvar__45152)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1757___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__45152,Vv__CANONICAL__0)) ) ) ).
fof('$_type_45206',axiom,
! [Vvar__45207] :
( c_24__type__45206___24t(Vvar__45207)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__45207,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_45221',axiom,
! [Vvar__45222] :
( c_24__type__45221___24t(Vvar__45222)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__45222,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45236',axiom,
! [Vvar__45237] :
( c_24__type__45236___24t(Vvar__45237)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__45237,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45239',axiom,
! [Vvar__45240] :
( c_24__type__45239___24t(Vvar__45240)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2ePartial__Order_2eRel___24t(Vv__CANONICAL__0,happ(happ(Vvar__45240,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45278',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45279] :
( c_24__type__45278___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45279)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__45279,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45287',axiom,
! [Vvar__45288] :
( c_24__type__45287___24t(Vvar__45288)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2ePartial__Order_2ePO___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),happ(happ(Vvar__45288,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45316',axiom,
! [Vvar__45317] :
( c_24__type__45316___24t(Vvar__45317)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__45317,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45328',axiom,
! [Vvar__45329] :
( c_24__type__45328___24t(Vvar__45329)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRList_2eRlist___24t(happ(happ(Vvar__45329,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4535',axiom,
! [Vvar__4536] :
( c_24__type__4535___24t(Vvar__4536)
<=> ! [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__4536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_45364',axiom,
! [Vvar__45365] :
( c_24__type__45364___24t(Vvar__45365)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__45365,Vv__CANONICAL__0)) ) ) ).
fof('$_type_45374',axiom,
! [Vvar__45375] :
( c_24__type__45374___24t(Vvar__45375)
<=> ! [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__45375,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45380',axiom,
! [Vvar__45381] :
( c_24__type__45380___24t(Vvar__45381)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRList_2eRlist___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__45381,Vv__CANONICAL__0)) ) ) ).
fof('$_type_45392',axiom,
! [Vvar__45393] :
( c_24__type__45392___24t(Vvar__45393)
<=> ! [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__45393,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45411',axiom,
! [Vvar__45412] :
( c_24__type__45411___24t(Vvar__45412)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1767___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__35532___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__45412,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45416',axiom,
! [Vvar__45417] :
( c_24__type__45416___24t(Vvar__45417)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1767___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__45417,Vv__CANONICAL__0)) ) ) ).
fof('$_type_45424',axiom,
! [Vvar__45425] :
( c_24__type__45424___24t(Vvar__45425)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__45425,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45432',axiom,
! [Vvar__45433] :
( c_24__type__45432___24t(Vvar__45433)
<=> ! [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__45433,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__45483] :
( c_24__type__45482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__45483)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__45483,Vv__CANONICAL__2)) ) ) ).
fof('$_type_45485',axiom,
! [Vvar__45486] :
( c_24__type__45485___24t(Vvar__45486)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__45486,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45522',axiom,
! [Vvar__45523] :
( c_24__type__45522___24t(Vvar__45523)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__3)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(happ(Vvar__45523,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_45617',axiom,
! [Vvar__45618] :
( c_24__type__45617___24t(Vvar__45618)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___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__45618,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45622',axiom,
! [Vvar__45623] :
( c_24__type__45622___24t(Vvar__45623)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__45623,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45634',axiom,
! [Vvar__45635] :
( c_24__type__45634___24t(Vvar__45635)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1757___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__45635,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_45777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45778] :
( c_24__type__45777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45778)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__45778,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45785',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45786] :
( c_24__type__45785___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45786)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cType___24t(happ(Vvar__45786,Vv__CANONICAL__3)) ) ) ).
fof('$_type_45807',axiom,
! [Vvar__45808] :
( c_24__type__45807___24t(Vvar__45808)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__45813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__45825___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__45808,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_45813',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__45814] :
( c_24__type__45813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__45814)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__45814,Vv__CANONICAL__2)) ) ) ).
fof('$_type_45825',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45826] :
( c_24__type__45825___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__45826)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(Vvar__45826,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).
fof('$_type_487',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__488] :
( c_24__type__487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__488)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__488,Vv__CANONICAL__3)) ) ) ).
fof('$_type_49393',axiom,
! [Vvar__49394] :
( c_24__type__49393___24t(Vvar__49394)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(Vvar__49394,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_49417',axiom,
! [Vvar__49418] :
( c_24__type__49417___24t(Vvar__49418)
<=> ! [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__49418,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_49448',axiom,
! [Vvar__49449] :
( c_24__type__49448___24t(Vvar__49449)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__49449,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_49558',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__49559] :
( c_24__type__49558___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__49559)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(Vvar__49559,Vv__CANONICAL__5)) ) ) ).
fof('$_type_49583',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__49584] :
( c_24__type__49583___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__49584)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),happ(happ(Vvar__49584,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_49602',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__49603] :
( c_24__type__49602___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__49603)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__49603,Vv__CANONICAL__5)) ) ) ).
fof('$_type_49944',axiom,
! [Vv__CANONICAL__0,Vvar__49945] :
( c_24__type__49944___24t(Vv__CANONICAL__0,Vvar__49945)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(Vvar__49945,Vv__CANONICAL__1)) ) ) ).
fof('$_type_49948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__49949] :
( c_24__type__49948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__49949)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__49949,Vv__CANONICAL__2)) ) ) ).
fof('$_type_49970',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__49971] :
( c_24__type__49970___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__49971)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__49971,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_49982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__49983] :
( c_24__type__49982___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__49983)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__49983,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_49989',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__49990] :
( c_24__type__49989___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__49990)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__49990,Vv__CANONICAL__3)) ) ) ).
fof('$_type_50009',axiom,
! [Vvar__50010] :
( c_24__type__50009___24t(Vvar__50010)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__49944___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__50021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(happ(happ(Vvar__50010,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_50021',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50022] :
( c_24__type__50021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50022)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__50022,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_50033',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50034] :
( c_24__type__50033___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50034)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__50034,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_50045',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50046] :
( c_24__type__50045___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50046)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__50046,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_50076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50077] :
( c_24__type__50076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__50077)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cTopology_2eTopologicalSpaces_2epoint__set___24t(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__50077,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_50164',axiom,
! [Vvar__50165] :
( c_24__type__50164___24t(Vvar__50165)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__39840___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(happ(Vvar__50165,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50173',axiom,
! [Vvar__50174] :
( c_24__type__50173___24t(Vvar__50174)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__50174,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50483',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__50484] :
( c_24__type__50483___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__50484)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( cZornsLemma_2eZornsLemma_2echain___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__50517___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5),happ(Vvar__50484,Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_50588',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__50589] :
( c_24__type__50588___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__50589)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__50608___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5),happ(Vvar__50589,Vv__CANONICAL__5)) ) ) ).
fof('$_type_50842',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__50843] :
( c_24__type__50842___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__50843)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cZornsLemma_2eZornsLemma_2echain___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__50517___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(Vvar__50843,Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_51101',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51102] :
( c_24__type__51101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51102)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__50608___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(Vvar__51102,Vv__CANONICAL__2)) ) ) ).
fof('$_type_51405',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51406] :
( c_24__type__51405___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__51406)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__51406,Vv__CANONICAL__2)) ) ) ).
fof('$_type_51621',axiom,
! [Vvar__51622] :
( c_24__type__51621___24t(Vvar__51622)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cZornsLemma_2eZornsLemma_2echains___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cZornsLemma_2eZornsLemma_2echains___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__51622,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_51813',axiom,
! [Vvar__51814] :
( c_24__type__51813___24t(Vvar__51814)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),happ(Vvar__51814,Vv__CANONICAL__0)) ) ) ).
fof('$_type_52005',axiom,
! [Vvar__52006] :
( c_24__type__52005___24t(Vvar__52006)
<=> ! [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__52006,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_52090',axiom,
! [Vvar__52091] :
( c_24__type__52090___24t(Vvar__52091)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1767___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1767___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__52091,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_52112',axiom,
! [Vvar__52113] :
( c_24__type__52112___24t(Vvar__52113)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__17___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__52113,Vv__CANONICAL__0)) ) ) ).
fof('$_type_52130',axiom,
! [Vvar__52131] :
( c_24__type__52130___24t(Vvar__52131)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__17___24t(Vv__CANONICAL__0)
=> ( ? [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
& p(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) )
=> ( cCoq_2eReals_2eRiemannInt__SF_2eNbound___24a1(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__52139___24a1(Vv__CANONICAL__0),happ(Vvar__52131,Vv__CANONICAL__0)) ) ) ) ) ).
fof('$_type_524',axiom,
! [Vvar__525] :
( c_24__type__524___24t(Vvar__525)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__525,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_529',axiom,
! [Vv__CANONICAL__0,Vvar__530] :
( c_24__type__529___24t(Vv__CANONICAL__0,Vvar__530)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__530,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_531',axiom,
! [Vvar__532] :
( c_24__type__531___24t(Vvar__532)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__532,Vv__CANONICAL__0)) ) ) ).
fof('$_type_536',axiom,
! [Vvar__537] :
( c_24__type__536___24t(Vvar__537)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__537,Vv__CANONICAL__0)) ) ) ).
fof('$_type_589',axiom,
! [Vvar__590] :
( c_24__type__589___24t(Vvar__590)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__590,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6',axiom,
! [Vvar__7] :
( c_24__type__6___24t(Vvar__7)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__7,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64956',axiom,
! [Vvar__64957] :
( c_24__type__64956___24t(Vvar__64957)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),happ(happ(happ(Vvar__64957,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_64978',axiom,
! [Vvar__64979] :
( c_24__type__64978___24t(Vvar__64979)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__64979,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64980',axiom,
! [Vvar__64981] :
( c_24__type__64980___24t(Vvar__64981)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(Vvar__64981,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64985',axiom,
! [Vv__CANONICAL__0,Vvar__64986] :
( c_24__type__64985___24t(Vv__CANONICAL__0,Vvar__64986)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__64986,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_65007',axiom,
! [Vvar__65008] :
( c_24__type__65007___24t(Vvar__65008)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__6___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__65008,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_674',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__675] :
( c_24__type__674___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__675)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__675,Vv__CANONICAL__5)) ) ) ).
fof('$_type_682',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__683] :
( c_24__type__682___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__683)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__683,Vv__CANONICAL__5)) ) ) ).
fof('$_type_710',axiom,
! [Vvar__711] :
( c_24__type__710___24t(Vvar__711)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__711,Vv__CANONICAL__0)) ) ) ).
fof('$_type_723',axiom,
! [Vvar__724] :
( c_24__type__723___24t(Vvar__724)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__724,Vv__CANONICAL__0)) ) ) ).
fof('$_type_736',axiom,
! [Vvar__737] :
( c_24__type__736___24t(Vvar__737)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__737,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8709] :
( c_24__type__8708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8709)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8709,Vv__CANONICAL__2)) ) ) ).
fof('$_type_8712',axiom,
! [Vvar__8713] :
( c_24__type__8712___24t(Vvar__8713)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__8713,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8715',axiom,
! [Vv__CANONICAL__0,Vvar__8716] :
( c_24__type__8715___24t(Vv__CANONICAL__0,Vvar__8716)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8716,Vv__CANONICAL__1)) ) ) ).
fof('$_type_8907',axiom,
! [Vv__CANONICAL__0,Vvar__8908] :
( c_24__type__8907___24t(Vv__CANONICAL__0,Vvar__8908)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__8908,Vv__CANONICAL__1)) ) ) ).
fof('$_type_9027',axiom,
! [Vvar__9028] :
( c_24__type__9027___24t(Vvar__9028)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__9028,Vv__CANONICAL__0)) ) ) ).
fof('$_type_919',axiom,
! [Vvar__920] :
( c_24__type__919___24t(Vvar__920)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__920,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9380',axiom,
! [Vv__CANONICAL__0,Vvar__9381] :
( c_24__type__9380___24t(Vv__CANONICAL__0,Vvar__9381)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9381,Vv__CANONICAL__1)) ) ) ).
fof('$_typeof_Coq.Arith.Compare.le_or_le_S',axiom,
c_24__type__1034___24t(cCoq_2eArith_2eCompare_2ele__or__le__S) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__14___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__6___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.Even',axiom,
c_24__type__17___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eEven) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__589___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt_alt',axiom,
c_24__type__14___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt__alt) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__11___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Bool.Bvector.Bcons',axiom,
c_24__type__64956___24t(cCoq_2eBool_2eBvector_2eBcons) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__919___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__1161___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__6___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__1159___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__1244___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__1216___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__15187___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.id',axiom,
cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__1232___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__531___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rec',axiom,
c_24__type__1137___24t(cCoq_2eInit_2eDatatypes_2enat__rec) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__1137___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__1114___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__1211___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__531___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__4535___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__1171___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__1191___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__1171___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.Decimal.nb_digits',axiom,
c_24__type__64978___24t(cCoq_2eInit_2eDecimal_2enb__digits) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.divmod',axiom,
c_24__type__1688___24t(cCoq_2eInit_2eNat_2edivmod) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__536___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__524___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.ltb',axiom,
c_24__type__372___24t(cCoq_2eInit_2eNat_2eltb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__536___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sqrt',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2esqrt) ).
fof('$_typeof_Coq.Init.Nat.sqrt_iter',axiom,
c_24__type__524___24t(cCoq_2eInit_2eNat_2esqrt__iter) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__11___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__372___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__14___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__14___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__14___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__24641___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__24680___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__32553___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__32558___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__2667___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__32524___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__2672___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__8712___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__24662___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
c_24__type__45807___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).
fof('$_typeof_Coq.Init.Specif.sig_rect',axiom,
c_24__type__45807___24t(cCoq_2eInit_2eSpecif_2esig__rect) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__2644___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__2728___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Lists.List.seq',axiom,
c_24__type__1584___24t(cCoq_2eLists_2eList_2eseq) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalDependentChoice_on',axiom,
c_24__type__28214___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__3130___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__3122___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__3172___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__3122___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__3162___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__3130___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__3185___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__3122___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__3165___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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__723___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__736___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__736___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__710___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__710___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__9027___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__3701___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__18227___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.Reals.AltSeries.positivity_seq',axiom,
c_24__type__45151___24t(cCoq_2eReals_2eAltSeries_2epositivity__seq) ).
fof('$_typeof_Coq.Reals.AltSeries.tg_alt',axiom,
c_24__type__18622___24t(cCoq_2eReals_2eAltSeries_2etg__alt) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_dec',axiom,
c_24__type__18279___24t(cCoq_2eReals_2eRIneq_2eRle__dec) ).
fof('$_typeof_Coq.Reals.RIneq.mkposreal',axiom,
c_24__type__35549___24t(cCoq_2eReals_2eRIneq_2emkposreal) ).
fof('$_typeof_Coq.Reals.RIneq.pos',axiom,
c_24__type__35554___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__45374___24t(cCoq_2eReals_2eRList_2eIn) ).
fof('$_typeof_Coq.Reals.RList.Rlength',axiom,
c_24__type__45380___24t(cCoq_2eReals_2eRList_2eRlength) ).
fof('$_typeof_Coq.Reals.RList.Rlist',axiom,
cType___24t(cCoq_2eReals_2eRList_2eRlist) ).
fof('$_typeof_Coq.Reals.RList.cons',axiom,
c_24__type__45328___24t(cCoq_2eReals_2eRList_2econs) ).
fof('$_typeof_Coq.Reals.RList.nil',axiom,
cCoq_2eReals_2eRList_2eRlist___24t(cCoq_2eReals_2eRList_2enil) ).
fof('$_typeof_Coq.Reals.RList.ordered_Rlist',axiom,
c_24__type__45364___24t(cCoq_2eReals_2eRList_2eordered__Rlist) ).
fof('$_typeof_Coq.Reals.RList.pos_Rl',axiom,
c_24__type__45392___24t(cCoq_2eReals_2eRList_2epos__Rl) ).
fof('$_typeof_Coq.Reals.Ranalysis1.constant_D_eq',axiom,
c_24__type__45411___24t(cCoq_2eReals_2eRanalysis1_2econstant__D__eq) ).
fof('$_typeof_Coq.Reals.Ranalysis1.continuity',axiom,
c_24__type__45416___24t(cCoq_2eReals_2eRanalysis1_2econtinuity) ).
fof('$_typeof_Coq.Reals.Ranalysis1.fct_cte',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRanalysis1_2efct__cte) ).
fof('$_typeof_Coq.Reals.Ranalysis1.mult_fct',axiom,
c_24__type__52090___24t(cCoq_2eReals_2eRanalysis1_2emult__fct) ).
fof('$_typeof_Coq.Reals.Ranalysis1.plus_fct',axiom,
c_24__type__52090___24t(cCoq_2eReals_2eRanalysis1_2eplus__fct) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__1757___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Raxioms.bound',axiom,
c_24__type__35688___24t(cCoq_2eReals_2eRaxioms_2ebound) ).
fof('$_typeof_Coq.Reals.Raxioms.completeness',axiom,
c_24__type__35699___24t(cCoq_2eReals_2eRaxioms_2ecompleteness) ).
fof('$_typeof_Coq.Reals.Raxioms.is_lub',axiom,
c_24__type__35686___24t(cCoq_2eReals_2eRaxioms_2eis__lub) ).
fof('$_typeof_Coq.Reals.Raxioms.is_upper_bound',axiom,
c_24__type__35686___24t(cCoq_2eReals_2eRaxioms_2eis__upper__bound) ).
fof('$_typeof_Coq.Reals.Raxioms.total_order_T',axiom,
c_24__type__35682___24t(cCoq_2eReals_2eRaxioms_2etotal__order__T) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rabs',axiom,
c_24__type__1767___24t(cCoq_2eReals_2eRbasic__fun_2eRabs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmax',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRbasic__fun_2eRmax) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmin',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRbasic__fun_2eRmin) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__1781___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__1774___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__1774___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__1767___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__1774___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__1774___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__1767___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__28244___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.R_dist',axiom,
c_24__type__1770___24t(cCoq_2eReals_2eRfunctions_2eR__dist) ).
fof('$_typeof_Coq.Reals.Rfunctions.infinite_sum',axiom,
c_24__type__35841___24t(cCoq_2eReals_2eRfunctions_2einfinite__sum) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_f_R0',axiom,
c_24__type__18622___24t(cCoq_2eReals_2eRfunctions_2esum__f__R0) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_nat_f_O',axiom,
c_24__type__65007___24t(cCoq_2eReals_2eRfunctions_2esum__nat__f__O) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.Nbound',axiom,
c_24__type__52112___24t(cCoq_2eReals_2eRiemannInt__SF_2eNbound) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.Nzorn',axiom,
c_24__type__52130___24t(cCoq_2eReals_2eRiemannInt__SF_2eNzorn) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.StepFun',axiom,
c_24__type__45485___24t(cCoq_2eReals_2eRiemannInt__SF_2eStepFun) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.co_interval',axiom,
c_24__type__45432___24t(cCoq_2eReals_2eRiemannInt__SF_2eco__interval) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.fe',axiom,
c_24__type__45522___24t(cCoq_2eReals_2eRiemannInt__SF_2efe) ).
fof('$_typeof_Coq.Reals.RiemannInt_SF.open_interval',axiom,
c_24__type__45432___24t(cCoq_2eReals_2eRiemannInt__SF_2eopen__interval) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__2632___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Reals.Rprod.prod_f_R0',axiom,
c_24__type__18622___24t(cCoq_2eReals_2eRprod_2eprod__f__R0) ).
fof('$_typeof_Coq.Reals.Rseries.EUn',axiom,
c_24__type__35841___24t(cCoq_2eReals_2eRseries_2eEUn) ).
fof('$_typeof_Coq.Reals.Rseries.Pser',axiom,
c_24__type__45634___24t(cCoq_2eReals_2eRseries_2ePser) ).
fof('$_typeof_Coq.Reals.Rseries.Rmax_N',axiom,
c_24__type__18622___24t(cCoq_2eReals_2eRseries_2eRmax__N) ).
fof('$_typeof_Coq.Reals.Rseries.Un_cv',axiom,
c_24__type__35841___24t(cCoq_2eReals_2eRseries_2eUn__cv) ).
fof('$_typeof_Coq.Reals.Rseries.Un_growing',axiom,
c_24__type__45151___24t(cCoq_2eReals_2eRseries_2eUn__growing) ).
fof('$_typeof_Coq.Reals.SeqProp.Un_decreasing',axiom,
c_24__type__45151___24t(cCoq_2eReals_2eSeqProp_2eUn__decreasing) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__29998___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__531___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__29998___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Sets.Cpo.Conditionally_complete_rec',axiom,
c_24__type__42195___24t(cCoq_2eSets_2eCpo_2eConditionally__complete__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Conditionally_complete_rect',axiom,
c_24__type__42195___24t(cCoq_2eSets_2eCpo_2eConditionally__complete__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Directed_rec',axiom,
c_24__type__41882___24t(cCoq_2eSets_2eCpo_2eDirected__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Directed_rect',axiom,
c_24__type__41882___24t(cCoq_2eSets_2eCpo_2eDirected__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Totally_ordered_rec',axiom,
c_24__type__41554___24t(cCoq_2eSets_2eCpo_2eTotally__ordered__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Totally_ordered_rect',axiom,
c_24__type__41554___24t(cCoq_2eSets_2eCpo_2eTotally__ordered__rect) ).
fof('$_typeof_Coq.Sets.Ensembles.Add',axiom,
c_24__type__42344___24t(cCoq_2eSets_2eEnsembles_2eAdd) ).
fof('$_typeof_Coq.Sets.Ensembles.Complement',axiom,
c_24__type__37299___24t(cCoq_2eSets_2eEnsembles_2eComplement) ).
fof('$_typeof_Coq.Sets.Ensembles.Ensemble',axiom,
c_24__type__531___24t(cCoq_2eSets_2eEnsembles_2eEnsemble) ).
fof('$_typeof_Coq.Sets.Ensembles.In',axiom,
c_24__type__37280___24t(cCoq_2eSets_2eEnsembles_2eIn) ).
fof('$_typeof_Coq.Sets.Ensembles.Included',axiom,
c_24__type__37285___24t(cCoq_2eSets_2eEnsembles_2eIncluded) ).
fof('$_typeof_Coq.Sets.Ensembles.Same_set',axiom,
c_24__type__37285___24t(cCoq_2eSets_2eEnsembles_2eSame__set) ).
fof('$_typeof_Coq.Sets.Ensembles.Setminus',axiom,
c_24__type__42365___24t(cCoq_2eSets_2eEnsembles_2eSetminus) ).
fof('$_typeof_Coq.Sets.Ensembles.Strict_Included',axiom,
c_24__type__37285___24t(cCoq_2eSets_2eEnsembles_2eStrict__Included) ).
fof('$_typeof_Coq.Sets.Ensembles.Subtract',axiom,
c_24__type__42344___24t(cCoq_2eSets_2eEnsembles_2eSubtract) ).
fof('$_typeof_Coq.Sets.Partial_Order.Carrier_of',axiom,
c_24__type__45221___24t(cCoq_2eSets_2ePartial__Order_2eCarrier__of) ).
fof('$_typeof_Coq.Sets.Partial_Order.Definition_of_PO',axiom,
c_24__type__45206___24t(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO) ).
fof('$_typeof_Coq.Sets.Partial_Order.PO',axiom,
c_24__type__531___24t(cCoq_2eSets_2ePartial__Order_2ePO) ).
fof('$_typeof_Coq.Sets.Partial_Order.Rel_of',axiom,
c_24__type__45236___24t(cCoq_2eSets_2ePartial__Order_2eRel__of) ).
fof('$_typeof_Coq.Sets.Partial_Order.Strict_Rel_of',axiom,
c_24__type__45239___24t(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of) ).
fof('$_typeof_Coq.Sets.Powerset.Power_set_PO',axiom,
c_24__type__45287___24t(cCoq_2eSets_2ePowerset_2ePower__set__PO) ).
fof('$_typeof_Coq.Sets.Relations_1.Antisymmetric',axiom,
c_24__type__18617___24t(cCoq_2eSets_2eRelations__1_2eAntisymmetric) ).
fof('$_typeof_Coq.Sets.Relations_1.Reflexive',axiom,
c_24__type__18617___24t(cCoq_2eSets_2eRelations__1_2eReflexive) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__531___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Sets.Relations_1.Transitive',axiom,
c_24__type__18617___24t(cCoq_2eSets_2eRelations__1_2eTransitive) ).
fof('$_typeof_Coq.Sets.Relations_1.contains',axiom,
c_24__type__45424___24t(cCoq_2eSets_2eRelations__1_2econtains) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.length',axiom,
c_24__type__2769___24t(cCoq_2eStrings_2eString_2elength) ).
fof('$_typeof_Coq.Vectors.Fin.F1',axiom,
c_24__type__64980___24t(cCoq_2eVectors_2eFin_2eF1) ).
fof('$_typeof_Coq.Vectors.Fin.FS',axiom,
c_24__type__16677___24t(cCoq_2eVectors_2eFin_2eFS) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__919___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__2915___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__2907___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__2890___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__4479___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__4479___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__4479___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__4479___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__4479___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__4368___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__4403___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__4368___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__4406___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__4372___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__4476___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__4368___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__4372___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__3119___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__30513___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__42381___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__30510___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEmul',axiom,
c_24__type__42381___24t(cCoq_2emicromega_2eEnvRing_2ePEmul) ).
fof('$_typeof_Coq.micromega.EnvRing.PEopp',axiom,
c_24__type__52005___24t(cCoq_2emicromega_2eEnvRing_2ePEopp) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__42381___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__531___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__15246___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__531___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__18306___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__18296___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.RTautoChecker',axiom,
c_24__type__35679___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__36107___24t(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__531___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__531___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__45622___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__31982___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__24018___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulC',axiom,
c_24__type__45617___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__45622___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__32601___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__531___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.Cj',axiom,
c_24__type__35072___24t(cCoq_2emicromega_2eTauto_2eCj) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__27584___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.I',axiom,
c_24__type__35122___24t(cCoq_2emicromega_2eTauto_2eI) ).
fof('$_typeof_Coq.micromega.Tauto.N',axiom,
c_24__type__35099___24t(cCoq_2emicromega_2eTauto_2eN) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__32584___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.VarMap.Branch',axiom,
c_24__type__49417___24t(cCoq_2emicromega_2eVarMap_2eBranch) ).
fof('$_typeof_Coq.micromega.VarMap.Elt',axiom,
c_24__type__32612___24t(cCoq_2emicromega_2eVarMap_2eElt) ).
fof('$_typeof_Coq.micromega.VarMap.Empty',axiom,
c_24__type__32609___24t(cCoq_2emicromega_2eVarMap_2eEmpty) ).
fof('$_typeof_Coq.micromega.VarMap.find',axiom,
c_24__type__49448___24t(cCoq_2emicromega_2eVarMap_2efind) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__531___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__16035___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__16040___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__16032___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__16040___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__10955___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__16040___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__531___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__16069___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__16196___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fnorm',axiom,
c_24__type__11647___24t(cCoq_2esetoid__ring_2eField__theory_2eFnorm) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__11237___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__11018___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__10998___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__531___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__16051___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__10998___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__11788___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__2213___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__2218___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__2210___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__11999___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__2218___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__24307___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__32071___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__2218___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__531___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__11806___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__11793___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__1961___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__11798___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__531___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__12668___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__2611___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__2429___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Topology.Compactness.compact',axiom,
c_24__type__38256___24t(cTopology_2eCompactness_2ecompact) ).
fof('$_typeof_Topology.Completeness.cauchy',axiom,
c_24__type__38807___24t(cTopology_2eCompleteness_2ecauchy) ).
fof('$_typeof_Topology.Completeness.complete',axiom,
c_24__type__38828___24t(cTopology_2eCompleteness_2ecomplete) ).
fof('$_typeof_Topology.Connectedness.clopen',axiom,
c_24__type__37592___24t(cTopology_2eConnectedness_2eclopen) ).
fof('$_typeof_Topology.Connectedness.connected',axiom,
c_24__type__38256___24t(cTopology_2eConnectedness_2econnected) ).
fof('$_typeof_Topology.Continuity.continuous',axiom,
c_24__type__41094___24t(cTopology_2eContinuity_2econtinuous) ).
fof('$_typeof_Topology.Continuity.continuous_at',axiom,
c_24__type__41106___24t(cTopology_2eContinuity_2econtinuous__at) ).
fof('$_typeof_Topology.CountabilityAxioms.Lindelof',axiom,
c_24__type__38256___24t(cTopology_2eCountabilityAxioms_2eLindelof) ).
fof('$_typeof_Topology.CountabilityAxioms.first_countable',axiom,
c_24__type__38256___24t(cTopology_2eCountabilityAxioms_2efirst__countable) ).
fof('$_typeof_Topology.DirectedSets.Build_DirectedSet',axiom,
c_24__type__38313___24t(cTopology_2eDirectedSets_2eBuild__DirectedSet) ).
fof('$_typeof_Topology.DirectedSets.DS_ord',axiom,
c_24__type__38376___24t(cTopology_2eDirectedSets_2eDS__ord) ).
fof('$_typeof_Topology.DirectedSets.DS_set',axiom,
c_24__type__38346___24t(cTopology_2eDirectedSets_2eDS__set) ).
fof('$_typeof_Topology.DirectedSets.DirectedSet',axiom,
cType___24t(cTopology_2eDirectedSets_2eDirectedSet) ).
fof('$_typeof_Topology.DirectedSets.eventually',axiom,
c_24__type__38380___24t(cTopology_2eDirectedSets_2eeventually) ).
fof('$_typeof_Topology.DirectedSets.exists_arbitrarily_large',axiom,
c_24__type__38380___24t(cTopology_2eDirectedSets_2eexists__arbitrarily__large) ).
fof('$_typeof_Topology.DirectedSets.nat_DS',axiom,
cTopology_2eDirectedSets_2eDirectedSet___24t(cTopology_2eDirectedSets_2enat__DS) ).
fof('$_typeof_Topology.FilterLimits.filter_cluster_point',axiom,
c_24__type__37643___24t(cTopology_2eFilterLimits_2efilter__cluster__point) ).
fof('$_typeof_Topology.FilterLimits.filter_limit',axiom,
c_24__type__37643___24t(cTopology_2eFilterLimits_2efilter__limit) ).
fof('$_typeof_Topology.FilterLimits.neighborhood_filter',axiom,
c_24__type__37638___24t(cTopology_2eFilterLimits_2eneighborhood__filter) ).
fof('$_typeof_Topology.Filters.Build_Filter',axiom,
c_24__type__38983___24t(cTopology_2eFilters_2eBuild__Filter) ).
fof('$_typeof_Topology.Filters.Build_Filter_from_basis',axiom,
c_24__type__37816___24t(cTopology_2eFilters_2eBuild__Filter__from__basis) ).
fof('$_typeof_Topology.Filters.Filter',axiom,
c_24__type__531___24t(cTopology_2eFilters_2eFilter) ).
fof('$_typeof_Topology.Filters.filter_family',axiom,
c_24__type__37759___24t(cTopology_2eFilters_2efilter__family) ).
fof('$_typeof_Topology.Filters.ultrafilter',axiom,
c_24__type__42564___24t(cTopology_2eFilters_2eultrafilter) ).
fof('$_typeof_Topology.FiltersAndNets.Build_filter_to_net_DS_set',axiom,
c_24__type__42669___24t(cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set) ).
fof('$_typeof_Topology.FiltersAndNets.filter_to_net',axiom,
c_24__type__42738___24t(cTopology_2eFiltersAndNets_2efilter__to__net) ).
fof('$_typeof_Topology.FiltersAndNets.filter_to_net_DS_set',axiom,
c_24__type__42640___24t(cTopology_2eFiltersAndNets_2efilter__to__net__DS__set) ).
fof('$_typeof_Topology.FiltersAndNets.ftn_S',axiom,
c_24__type__42688___24t(cTopology_2eFiltersAndNets_2eftn__S) ).
fof('$_typeof_Topology.FiltersAndNets.ftn_x',axiom,
c_24__type__42722___24t(cTopology_2eFiltersAndNets_2eftn__x) ).
fof('$_typeof_Topology.FiltersAndNets.net_tail',axiom,
c_24__type__42599___24t(cTopology_2eFiltersAndNets_2enet__tail) ).
fof('$_typeof_Topology.FiltersAndNets.tail_filter_basis',axiom,
c_24__type__42604___24t(cTopology_2eFiltersAndNets_2etail__filter__basis) ).
fof('$_typeof_Topology.Homeomorphisms.open_map',axiom,
c_24__type__41094___24t(cTopology_2eHomeomorphisms_2eopen__map) ).
fof('$_typeof_Topology.Homeomorphisms.topological_property',axiom,
c_24__type__43856___24t(cTopology_2eHomeomorphisms_2etopological__property) ).
fof('$_typeof_Topology.InteriorsClosures.Build_TopologicalSpace_from_closure_operator',axiom,
c_24__type__43912___24t(cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__closure__operator) ).
fof('$_typeof_Topology.InteriorsClosures.closure',axiom,
c_24__type__37375___24t(cTopology_2eInteriorsClosures_2eclosure) ).
fof('$_typeof_Topology.InteriorsClosures.dense',axiom,
c_24__type__37592___24t(cTopology_2eInteriorsClosures_2edense) ).
fof('$_typeof_Topology.InteriorsClosures.idempotent',axiom,
c_24__type__43866___24t(cTopology_2eInteriorsClosures_2eidempotent) ).
fof('$_typeof_Topology.InteriorsClosures.interior',axiom,
c_24__type__37375___24t(cTopology_2eInteriorsClosures_2einterior) ).
fof('$_typeof_Topology.MetricSpaces.dist_to_set',axiom,
c_24__type__38529___24t(cTopology_2eMetricSpaces_2edist__to__set) ).
fof('$_typeof_Topology.MetricSpaces.metrizes',axiom,
c_24__type__38494___24t(cTopology_2eMetricSpaces_2emetrizes) ).
fof('$_typeof_Topology.MetricSpaces.open_ball',axiom,
c_24__type__39160___24t(cTopology_2eMetricSpaces_2eopen__ball) ).
fof('$_typeof_Topology.Neighborhoods.neighborhood',axiom,
c_24__type__38182___24t(cTopology_2eNeighborhoods_2eneighborhood) ).
fof('$_typeof_Topology.Neighborhoods.open_neighborhood',axiom,
c_24__type__38182___24t(cTopology_2eNeighborhoods_2eopen__neighborhood) ).
fof('$_typeof_Topology.Nets.Build_cluster_point_subnet_DS_set',axiom,
c_24__type__39479___24t(cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set) ).
fof('$_typeof_Topology.Nets.Net',axiom,
c_24__type__38581___24t(cTopology_2eNets_2eNet) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet',axiom,
c_24__type__44843___24t(cTopology_2eNets_2ecluster__point__subnet) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet_DS',axiom,
c_24__type__39578___24t(cTopology_2eNets_2ecluster__point__subnet__DS) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet_DS_ord',axiom,
c_24__type__39564___24t(cTopology_2eNets_2ecluster__point__subnet__DS__ord) ).
fof('$_typeof_Topology.Nets.cluster_point_subnet_DS_set',axiom,
c_24__type__39433___24t(cTopology_2eNets_2ecluster__point__subnet__DS__set) ).
fof('$_typeof_Topology.Nets.cps_U',axiom,
c_24__type__39547___24t(cTopology_2eNets_2ecps__U) ).
fof('$_typeof_Topology.Nets.cps_i',axiom,
c_24__type__39517___24t(cTopology_2eNets_2ecps__i) ).
fof('$_typeof_Topology.Nets.intro_neighborhood_net_DS',axiom,
c_24__type__38644___24t(cTopology_2eNets_2eintro__neighborhood__net__DS) ).
fof('$_typeof_Topology.Nets.neighborhood_net',axiom,
c_24__type__38762___24t(cTopology_2eNets_2eneighborhood__net) ).
fof('$_typeof_Topology.Nets.neighborhood_net_DS',axiom,
c_24__type__38725___24t(cTopology_2eNets_2eneighborhood__net__DS) ).
fof('$_typeof_Topology.Nets.neighborhood_net_DS_ord',axiom,
c_24__type__38720___24t(cTopology_2eNets_2eneighborhood__net__DS__ord) ).
fof('$_typeof_Topology.Nets.neighborhood_net_DS_set',axiom,
c_24__type__38607___24t(cTopology_2eNets_2eneighborhood__net__DS__set) ).
fof('$_typeof_Topology.Nets.neighborhood_net_DS_set_rec',axiom,
c_24__type__44647___24t(cTopology_2eNets_2eneighborhood__net__DS__set__rec) ).
fof('$_typeof_Topology.Nets.neighborhood_net_DS_set_rect',axiom,
c_24__type__44647___24t(cTopology_2eNets_2eneighborhood__net__DS__set__rect) ).
fof('$_typeof_Topology.Nets.net_cluster_point',axiom,
c_24__type__38594___24t(cTopology_2eNets_2enet__cluster__point) ).
fof('$_typeof_Topology.Nets.net_limit',axiom,
c_24__type__38594___24t(cTopology_2eNets_2enet__limit) ).
fof('$_typeof_Topology.OpenBases.open_basis_cond',axiom,
c_24__type__37378___24t(cTopology_2eOpenBases_2eopen__basis__cond) ).
fof('$_typeof_Topology.OpenBases.open_basis_cover_cond',axiom,
c_24__type__37378___24t(cTopology_2eOpenBases_2eopen__basis__cover__cond) ).
fof('$_typeof_Topology.RTopology.RTop',axiom,
cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(cTopology_2eRTopology_2eRTop) ).
fof('$_typeof_Topology.SeparatednessAxioms.Hausdorff',axiom,
c_24__type__38256___24t(cTopology_2eSeparatednessAxioms_2eHausdorff) ).
fof('$_typeof_Topology.SeparatednessAxioms.T0_sep',axiom,
c_24__type__38256___24t(cTopology_2eSeparatednessAxioms_2eT0__sep) ).
fof('$_typeof_Topology.SeparatednessAxioms.T1_sep',axiom,
c_24__type__38256___24t(cTopology_2eSeparatednessAxioms_2eT1__sep) ).
fof('$_typeof_Topology.SeparatednessAxioms.T3_sep',axiom,
c_24__type__38256___24t(cTopology_2eSeparatednessAxioms_2eT3__sep) ).
fof('$_typeof_Topology.SeparatednessAxioms.normal_sep',axiom,
c_24__type__38256___24t(cTopology_2eSeparatednessAxioms_2enormal__sep) ).
fof('$_typeof_Topology.Subbases.Build_TopologicalSpace_from_subbasis',axiom,
c_24__type__49393___24t(cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis) ).
fof('$_typeof_Topology.SubspaceTopology.SubspaceTopology',axiom,
c_24__type__39716___24t(cTopology_2eSubspaceTopology_2eSubspaceTopology) ).
fof('$_typeof_Topology.SubspaceTopology.subspace_inc',axiom,
c_24__type__39723___24t(cTopology_2eSubspaceTopology_2esubspace__inc) ).
fof('$_typeof_Topology.SupInf.inf',axiom,
c_24__type__39737___24t(cTopology_2eSupInf_2einf) ).
fof('$_typeof_Topology.SupInf.is_glb',axiom,
c_24__type__35686___24t(cTopology_2eSupInf_2eis__glb) ).
fof('$_typeof_Topology.SupInf.is_lower_bound',axiom,
c_24__type__35686___24t(cTopology_2eSupInf_2eis__lower__bound) ).
fof('$_typeof_Topology.TopologicalSpaces.Build_TopologicalSpace',axiom,
c_24__type__38228___24t(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace) ).
fof('$_typeof_Topology.TopologicalSpaces.TopologicalSpace',axiom,
cType___24t(cTopology_2eTopologicalSpaces_2eTopologicalSpace) ).
fof('$_typeof_Topology.TopologicalSpaces.closed',axiom,
c_24__type__37592___24t(cTopology_2eTopologicalSpaces_2eclosed) ).
fof('$_typeof_Topology.TopologicalSpaces.open',axiom,
c_24__type__37592___24t(cTopology_2eTopologicalSpaces_2eopen) ).
fof('$_typeof_Topology.TopologicalSpaces.point_set',axiom,
c_24__type__37524___24t(cTopology_2eTopologicalSpaces_2epoint__set) ).
fof('$_typeof_Topology.WeakTopology.WeakTopology',axiom,
c_24__type__50009___24t(cTopology_2eWeakTopology_2eWeakTopology) ).
fof('$_typeof_Topology.WeakTopology.WeakTopology1',axiom,
c_24__type__50164___24t(cTopology_2eWeakTopology_2eWeakTopology1) ).
fof('$_typeof_U0',axiom,
cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cU0) ).
fof('$_typeof_U1',axiom,
cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cU1) ).
fof('$_typeof_UrysohnsLemma.Urysohns_Lemma_construction.Un',axiom,
c_24__type__51813___24t(cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn) ).
fof('$_typeof_X',axiom,
cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(cX) ).
fof('$_typeof_ZornsLemma.CountableTypes.Countable',axiom,
c_24__type__38271___24t(cZornsLemma_2eCountableTypes_2eCountable) ).
fof('$_typeof_ZornsLemma.DecidableDec.classic_dec',axiom,
c_24__type__42310___24t(cZornsLemma_2eDecidableDec_2eclassic__dec) ).
fof('$_typeof_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
c_24__type__37329___24t(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble) ).
fof('$_typeof_ZornsLemma.Families.Family',axiom,
c_24__type__531___24t(cZornsLemma_2eFamilies_2eFamily) ).
fof('$_typeof_ZornsLemma.FunctionProperties.injective',axiom,
c_24__type__38400___24t(cZornsLemma_2eFunctionProperties_2einjective) ).
fof('$_typeof_ZornsLemma.FunctionProperties.surjective',axiom,
c_24__type__38400___24t(cZornsLemma_2eFunctionProperties_2esurjective) ).
fof('$_typeof_ZornsLemma.IndexedFamilies.ImageFamily',axiom,
c_24__type__39028___24t(cZornsLemma_2eIndexedFamilies_2eImageFamily) ).
fof('$_typeof_ZornsLemma.IndexedFamilies.IndexedFamily',axiom,
c_24__type__1171___24t(cZornsLemma_2eIndexedFamilies_2eIndexedFamily) ).
fof('$_typeof_ZornsLemma.InverseImage.inverse_image',axiom,
c_24__type__39052___24t(cZornsLemma_2eInverseImage_2einverse__image) ).
fof('$_typeof_ZornsLemma.Quotients.quotient',axiom,
c_24__type__45316___24t(cZornsLemma_2eQuotients_2equotient) ).
fof('$_typeof_ZornsLemma.ZornsLemma.chain',axiom,
c_24__type__50173___24t(cZornsLemma_2eZornsLemma_2echain) ).
fof('$_typeof_ZornsLemma.ZornsLemma.chains',axiom,
c_24__type__45316___24t(cZornsLemma_2eZornsLemma_2echains) ).
fof('$_typeof_ZornsLemma.ZornsLemma.chains_ord',axiom,
c_24__type__51621___24t(cZornsLemma_2eZornsLemma_2echains__ord) ).
fof('$_typeof_normal_sep_fun',axiom,
c_24__type__37271___24t(cnormal__sep__fun) ).
fof('Coq.Arith.Between.bet_S',axiom,
! [V0__P] :
( c_24__type__17___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V2__l)
=> ( p(happ(V0__P,V2__l))
=> cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__l)) ) ) ) ) ) ).
fof('Coq.Arith.Between.between_ind',axiom,
! [V0__P] :
( c_24__type__17___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__P] :
( c_24__type__17___24t(V2__P)
=> ( p(happ(V2__P,V1__k))
=> ( ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__l)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V4__l)
=> ( p(happ(V2__P,V4__l))
=> ( p(happ(V0__P,V4__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__l))) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V5__n)
=> p(happ(V2__P,V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.between_sind',axiom,
! [V0__P] :
( c_24__type__17___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__P] :
( c_24__type__17___24t(V2__P)
=> ( p(happ(V2__P,V1__k))
=> ( ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__l)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V4__l)
=> ( p(happ(V2__P,V4__l))
=> ( p(happ(V0__P,V4__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__l))) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V5__n)
=> p(happ(V2__P,V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.exists_S',axiom,
! [V0__Q] :
( c_24__type__17___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,V2__l)
=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__l)) ) ) ) ) ).
fof('Coq.Arith.Between.exists_le',axiom,
! [V0__Q] :
( c_24__type__17___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V2__l))
=> ( p(happ(V0__Q,V2__l))
=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__l)) ) ) ) ) ) ).
fof('Coq.Arith.Between.exists_le_S',axiom,
! [V0__Q] :
( c_24__type__17___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,V2__l)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k),V2__l)) ) ) ) ) ).
fof('Coq.Arith.Between.in_int_S',axiom,
! [V0__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__r)
=> ( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
=> cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__q),V2__r) ) ) ) ) ).
fof('Coq.Arith.Compare.le_le_S_eq',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),V1__m))
| 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_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Even.even_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(V0__n)
=> cCoq_2eArith_2eEven_2eeven___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ) ).
fof('Coq.Arith.Even.odd_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(V0__n)
=> cCoq_2eArith_2eEven_2eodd___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_Sn_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Gt.gt_Sn_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.le_gt_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))
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n) ) ) ) ).
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.S_pred',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(V1__m,V0__n))
=> V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_n_Sm',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_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_or_eq',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_2elt___24a2(V0__n,V1__m))
| V0__n = 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.lt_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_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_Sm_le',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(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.minus_Sn_m',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_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Minus.minus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Mult.mult_S_lt_compat_l',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(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m),cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V2__p))) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_1_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_1_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2eS___24a1(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.add_succ_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(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_succ_r',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_add_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ? [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
& cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p) )
<=> ( ? [V2__n_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n_27)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n_27) )
| ? [V2__m_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m_27)
& V1__m = cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m_27) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.lbase',axiom,
! [V0__A] :
( c_24__type__17___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__z)
=> ! [Vvar__3__m__3257] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__3257)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__3__m__3257,V1__z))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__z),Vvar__3__m__3257))
=> p(happ(V0__A,Vvar__3__m__3257)) ) ) ) ) ) ).
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_div2',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)),V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',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(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',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_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_le_succ_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(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,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_succ_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(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_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(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
<=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ) ).
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.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__14,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__17,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_1',axiom,
p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).
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_1_2',axiom,
p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_exists_pred',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__z,V1__n))
=> ? [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V3__k)
& p(cCoq_2eInit_2ePeano_2ele___24a2(V0__z,V3__k)) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_exists_pred_strong',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__z,V2__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__m,V1__n))
=> ? [V5__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__k)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(V5__k)
& p(cCoq_2eInit_2ePeano_2ele___24a2(V0__z,V5__k)) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( 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_lt_succ_r',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_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
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.lt_succ_r',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',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))
| V0__n = V1__m
| p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m),V1__m) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_succ_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m),V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),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.PeanoNat.Nat.nlt_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.pred_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj_wd',axiom,
! [V0__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
<=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj_wd_neg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)
<=> V0__n != V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_le_mono',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.PeanoNat.Nat.succ_lt_mono',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_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2eS) ).
fof('Coq.Arith.PeanoNat.Nat.two_succ',axiom,
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_2eO)) ).
fof('Coq.Arith.PeanoNat.Nat.zero_or_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n = cCoq_2eInit_2eDatatypes_2eO
| ? [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).
fof('Coq.Arith.Plus.n_SSSSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)))) ) ).
fof('Coq.Arith.Plus.n_SSSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.Plus.n_SSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.Plus.plus_Snm_nSm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__17___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.nat_sind',axiom,
! [V0__P] :
( c_24__type__17___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.O_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.eq_S',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__y) ) ) ) ).
fof('Coq.Init.Peano.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_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Init.Peano.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.Init.Peano.le_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__17___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.Peano.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.Init.Peano.le_sind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__17___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.n_Sn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.not_eq_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).
fof('Coq.Init.Peano.plus_Sn_m',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Init.Peano.pred_Sn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Init.Specif.proj2_sig',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__8715___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.Logic.ClassicalChoice.choice',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__24818___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__16948___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__8715___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_ex_all_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__8715___24t(V0__U,V1__P)
=> ( ~ ? [V2__n] :
( t(V2__n,V0__U)
& p(happ(V1__P,V2__n)) )
=> ! [V3__n] :
( t(V3__n,V0__U)
=> ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ( p(V0__P)
& ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Classical_Prop.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
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.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.ProofIrrelevance.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.is_succ',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ? [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n) ) ) ).
fof('Coq.PArith.Pnat.SuccNat2Pos.id_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
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.PartSum.sum_eq',axiom,
! [V0__An] :
( c_24__type__1757___24t(V0__An)
=> ! [V1__Bn] :
( c_24__type__1757___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.tech2',axiom,
! [V0__An] :
( c_24__type__1757___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__45132___24a2(V0__An,V1__m),cCoq_2eInit_2eNat_2esub___24a2(V2__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))) ) ) ) ) ).
fof('Coq.Reals.PartSum.tech5',axiom,
! [V0__An] :
( c_24__type__1757___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.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.IZR_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( 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__18348___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__1750___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__1750___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.Req_ge',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_2eRge___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_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.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.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_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_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_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_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_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.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_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_lt',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_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_1_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = V0__r ) ).
fof('Coq.Reals.RIneq.Rmult_eq_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V1__r1 = V2__r2 ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_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_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_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_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_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.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.Rplus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_le_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( 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_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_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_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.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.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_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.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.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.RList.Rlist_ind',axiom,
! [V0__P] :
( c_24__type__45364___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.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.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.Rbasic_fun.Rabs_R0',axiom,
cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Rabsolu',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_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_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_right',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_triang',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__a,V1__b)),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__a),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__b)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_Rgt_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r))
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V2__r)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__r1,V1__r2),V2__r)) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_l',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y),V0__x)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_r',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y),V1__y)) ) ) ).
fof('Coq.Reals.Rfunctions.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_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.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.Rtrigo_def.Alembert_sin',axiom,
cCoq_2eReals_2eRseries_2eUn__cv___24a2(c_24__lam__45651,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Sets.Classical_sets.Complement_Complement',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,V1__A)) = V1__A ) ) ).
fof('Coq.Sets.Classical_sets.Included_Strict_Included',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y)
| V1__X = V2__Y ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Inhabited_Setminus',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__Y,V1__X)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V2__Y,V1__X)) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Strict_Included_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V2__Y,V1__X)) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Strict_super_set_contains_new_element',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> ( V1__X != V2__Y
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V2__Y,V1__X)) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Subtract_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
=> ( V2__x != V3__y
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__A,V2__x),V3__y) ) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Subtract_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__A,V2__x),V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
& V2__x != V3__y ) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.not_included_empty_Inhabited',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U))
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__A) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_intro1',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_intro2',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V2__x) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
| V2__x = V3__y ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Included_Empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__A) ) ) ).
fof('Coq.Sets.Constructive_sets.Noone_in_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__x) ) ) ).
fof('Coq.Sets.Constructive_sets.Setminus_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V1__A,V2__B),V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Singleton_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V2__y) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Singleton_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V2__y)
=> V1__x = V2__y ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Strict_Included_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
& V1__X != V2__Y )
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y) ) ) ) ) ).
fof('Coq.Sets.Cpo.Conditionally_complete_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( ? [V5__maj] :
( t(V5__maj,V0__U)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V3__X,V5__maj) )
=> ? [V6__bsup] :
( t(V6__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V3__X,V6__bsup) ) ) ) )
=> p(V2__P) )
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V0__U,V1__D)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Conditionally_complete_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( ? [V5__maj] :
( t(V5__maj,V0__U)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V3__X,V5__maj) )
=> ? [V6__bsup] :
( t(V6__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V3__X,V6__bsup) ) ) ) )
=> p(V2__P) )
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V0__U,V1__D)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Definition_of_Conditionally_complete',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ( ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( ? [V4__maj] :
( t(V4__maj,V0__U)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__X,V4__maj) )
=> ? [V5__bsup] :
( t(V5__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V2__X,V5__bsup) ) ) ) )
=> cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V0__U,V1__D) ) ) ) ).
fof('Coq.Sets.Cpo.Definition_of_Directed',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V2__X)
=> ( ! [V5__x1] :
( t(V5__x1,V0__U)
=> ! [V6__x2] :
( t(V6__x2,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V5__x1,V6__x2),V2__X)
=> ? [V8__x3] :
( t(V8__x3,V0__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V8__x3)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V5__x1,V6__x2),V8__x3) ) ) ) )
=> cCoq_2eSets_2eCpo_2eDirected___24a3(V0__U,V1__D,V2__X) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Directed_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V2__X)
=> ( ! [V6__x1] :
( t(V6__x1,V0__U)
=> ! [V7__x2] :
( t(V7__x2,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V6__x1,V7__x2),V2__X)
=> ? [V9__x3] :
( t(V9__x3,V0__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V9__x3)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V6__x1,V7__x2),V9__x3) ) ) ) )
=> p(V3__P) ) ) )
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(V0__U,V1__D,V2__X)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Directed_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V2__X)
=> ( ! [V6__x1] :
( t(V6__x1,V0__U)
=> ! [V7__x2] :
( t(V7__x2,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V6__x1,V7__x2),V2__X)
=> ? [V9__x3] :
( t(V9__x3,V0__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V9__x3)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V6__x1,V7__x2),V9__x3) ) ) ) )
=> p(V3__P) ) ) )
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(V0__U,V1__D,V2__X)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Glb_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__y,V3__x) ) )
=> cCoq_2eSets_2eCpo_2eGlb___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lower_Bound_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V5__y) ) )
=> cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lub_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V5__y) ) )
=> cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Totally_ordered_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V4__x,V5__y),V2__B)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V4__x,V5__y)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__y,V4__x) ) ) ) ) )
=> cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V0__U,V1__D,V2__B) ) ) ) ) ).
fof('Coq.Sets.Cpo.Totally_ordered_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ! [V5__x] :
( t(V5__x,V0__U)
=> ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V5__x,V6__y),V2__B)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__x,V6__y)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V5__x) ) ) ) ) )
=> p(V3__P) )
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V0__U,V1__D,V2__B)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Totally_ordered_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ! [V5__x] :
( t(V5__x,V0__U)
=> ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V5__x,V6__y),V2__B)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__x,V6__y)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V5__x) ) ) ) ) )
=> p(V3__P) )
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V0__U,V1__D,V2__B)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Upper_Bound_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__y,V3__x) ) )
=> cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__P] :
( c_24__type__8715___24t(V0__U,V3__P)
=> ( p(happ(V3__P,V1__x))
=> ( p(happ(V3__P,V2__y))
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eCouple___24a4(V0__U,V1__x,V2__y,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y),V1__x) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y),V2__y) ) ) ) ).
fof('Coq.Sets.Ensembles.Empty_set_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__8715___24t(V0__U,V1__P)
=> ! [V2__u] :
( t(V2__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eEmpty__set___24a2(V0__U,V2__u)
=> p(happ(V1__P,V2__u)) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Extensionality_Ensembles',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ( cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__A,V2__B)
=> V1__A = V2__B ) ) ) ) ).
fof('Coq.Sets.Ensembles.Full_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__U),V1__x) ) ) ).
fof('Coq.Sets.Ensembles.In_singleton',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V1__x) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> p(V2__P) ) )
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__8715___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V4__x)
=> p(happ(V3__P,V4__x)) ) ) )
=> ! [V5__u] :
( t(V5__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V0__U,V1__B,V2__C,V5__u)
=> p(happ(V3__P,V5__u)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Singleton_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__8715___24t(V0__U,V2__P)
=> ( p(happ(V2__P,V1__x))
=> ! [V4__u] :
( t(V4__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(V0__U,V1__x,V4__u)
=> p(happ(V2__P,V4__u)) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__8715___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> p(happ(V3__P,V4__x)) ) )
=> ( ! [V5__x] :
( t(V5__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V5__x)
=> p(happ(V3__P,V5__x)) ) )
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(V0__U,V1__B,V2__C,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_introl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_intror',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.Empty_is_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) ) ).
fof('Coq.Sets.Finite_sets.Finite_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__37437___24t(V0__U,V1__P)
=> ( p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)))
=> ( ! [V3__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__A)
=> ( p(happ(V1__P,V3__A))
=> ! [V6__x] :
( t(V6__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V3__A,V6__x)
=> p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V3__A,V6__x))) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V4__e)
=> p(happ(V1__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.Union_is_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__A)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.card_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__A,V2__n)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V4__x)
=> cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V4__x),cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.cardinal_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__64985___24t(V0__U,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)),cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V3__A,V4__n)
=> ( p(happ(happ(V1__P,V3__A),V4__n))
=> ! [V7__x] :
( t(V7__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V3__A,V7__x)
=> p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V3__A,V7__x)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n))) ) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__e,V5__n)
=> p(happ(happ(V1__P,V4__e),V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.cardinal_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__64985___24t(V0__U,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)),cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V3__A,V4__n)
=> ( p(happ(happ(V1__P,V3__A),V4__n))
=> ! [V7__x] :
( t(V7__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V3__A,V7__x)
=> p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V3__A,V7__x)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n))) ) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__e,V5__n)
=> p(happ(happ(V1__P,V4__e),V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Finite_downward_closed',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__A)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__X) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.card_Add_gen',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__n_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n_27)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__A,V3__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V4__n_27)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V4__n_27,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n))) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinal_unicity',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V4__m)
=> V2__n = V4__m ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.incl_card_le',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V3__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V2__Y,V4__m)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V4__m)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.incl_st_card_lt',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__c1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__c1)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__c1)
=> ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ! [V5__c2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__c2)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__Y,V5__c2)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V4__Y)
=> cCoq_2eInit_2ePeano_2egt___24a2(V5__c2,V2__c1) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Image.Im_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__V] :
( cType___24t(V1__V)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ! [V3__f] :
( c_24__type__16948___24t(V0__U,V1__V,V3__f)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V4__x)
=> ! [V6__y] :
( t(V6__y,V1__V)
=> ( V6__y = happ(V3__f,V4__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__V,cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,V2__X,V3__f),V6__y) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Image.finite_image',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__V] :
( cType___24t(V1__V)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ! [V3__f] :
( c_24__type__16948___24t(V0__U,V1__V,V3__f)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V2__X)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V1__V,cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,V2__X,V3__f)) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Definition_of_Power_set',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,V1__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__A),V2__X) ) ) ) ) ).
fof('Coq.Sets.Powerset.Empty_set_minimal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__X) ) ) ).
fof('Coq.Sets.Powerset.Inclusion_is_an_order',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Inclusion_is_transitive',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V1__a) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V2__b) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_is_Glb',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__b)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__b,V1__A)
=> cCoq_2eSets_2eCpo_2eGlb___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eCouple___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),V2__a,V3__b),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V2__a,V3__b)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_maximal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__a)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Power_set_Inhabited',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__X)) ) ) ).
fof('Coq.Sets.Powerset.Power_set_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__P] :
( c_24__type__37437___24t(V0__U,V2__P)
=> ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> p(happ(V2__P,V3__X)) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(V0__U,V1__A,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Power_set_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__P] :
( c_24__type__37437___24t(V0__U,V2__P)
=> ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> p(happ(V2__P,V3__X)) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(V0__U,V1__A,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Strict_inclusion_is_transitive_with_inclusion',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__x)
=> ! [V2__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__y)
=> ! [V3__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__z)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V2__y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__y,V3__z)
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V3__z) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Strict_inclusion_is_transitive_with_inclusion_left',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__x)
=> ! [V2__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__y)
=> ! [V3__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__z)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__x,V2__y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__y,V3__z)
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V3__z) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Union_increases_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__a,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b)) ) ) ) ).
fof('Coq.Sets.Powerset.Union_increases_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__b,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b)) ) ) ) ).
fof('Coq.Sets.Powerset.Union_is_Lub',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__b)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__b,V1__A)
=> cCoq_2eSets_2eCpo_2eLub___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eCouple___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),V2__a,V3__b),cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__a,V3__b)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Union_minimal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__a,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__b,V3__X)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b),V3__X) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Add_covers',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V4__x)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__a,V4__x)
=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__a,V4__x),V2__a) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Included_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__A)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__A,V3__x))
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__A)
| ? [V5__A_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V5__A_27)
& V1__X = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V5__A_27,V3__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V5__A_27,V2__A) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.add_soustr_1',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x),V2__x),V1__X) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.add_soustr_2',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x),V2__x)) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.covers_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__a_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__a_27)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__a_27,V1__A)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__a_27,V2__a)
=> ? [V7__x] :
( t(V7__x,V0__U)
& V3__a_27 = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__a,V7__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V7__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__a,V7__x) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.covers_is_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__a_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__a_27)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__a_27,V1__A)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__a_27,V2__a)
<=> ? [V6__x] :
( t(V6__x,V0__U)
& V3__a_27 = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__a,V6__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V6__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__a,V6__x) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V3__x),cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V2__Y,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr_add_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x),V2__x),V1__X) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr_add_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x),V2__x)) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr_in',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x),V1__X) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.setcover_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__x)
=> ! [V3__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__y)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__y,V2__x)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__x,V3__y)
& ! [V5__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V5__z)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__x,V5__z)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V5__z,V3__y)
=> ( V2__x = V5__z
| V5__z = V3__y ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Add_distributes',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__y] :
( t(V4__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,V1__A)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),V4__y) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Intersection_commutative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__A,V2__B) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V2__B,V1__A) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Non_disjoint_union',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x) = V1__X ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Setminus_Included_empty',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s1)
=> ! [V2__s2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V2__s2)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__A,V1__s1,V2__s2)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s1,V2__s2) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_absorbs',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,V1__A)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B) = V1__A ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),V3__x) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_associative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__C)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),V3__C) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__B,V3__C)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_commutative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__B,V1__A) ) ) ) ).
fof('Coq.Sets.Powerset_facts.incl_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__A,V2__B)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.incl_add_x',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x))
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__A,V2__B) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.less_than_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U))
=> V1__X = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Powerset_facts.setcover_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__x)
=> ! [V3__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__x,V3__y)
=> ( ~ ? [V5__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V5__z)
& cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__x,V5__z)
& cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V5__z,V3__y) )
=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__y,V2__x) ) ) ) ) ) ) ).
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_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_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.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> 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.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> 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.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.RMicromega.RTautoChecker_sound',axiom,
! [V0__f] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),V0__f)
=> ! [V1__w] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRMicromega_2eRWitness,V1__w)
=> ( cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V0__f,V1__w) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V3__env] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eReals_2eRdefinitions_2eR,V3__env)
=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V3__env),V0__f) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)
=> 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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> 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.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( 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_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__11790___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_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__11790___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_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__11790___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_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__11790___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_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__11790___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__11790___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__11790___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__11790___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_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__11790___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__11790___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
& 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('Topology.Compactness.closed_compact',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__S)
=> cTopology_2eCompactness_2ecompact___24a1(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V0__X,V1__S)) ) ) ) ) ).
fof('Topology.Compactness.compact_closed',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X)
=> ( cTopology_2eCompactness_2ecompact___24a1(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V0__X,V1__S))
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__S) ) ) ) ) ).
fof('Topology.Compactness.compact_finite_nonempty_closed_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ! [V2__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( ! [V3__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__G)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V2__F,V3__G)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V3__G) ) )
=> ( ! [V4__F_27] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__F_27)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__F_27)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V4__F_27,V2__F)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__F_27)) ) ) )
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ) ).
fof('Topology.Compactness.compact_image',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
=> ( cZornsLemma_2eFunctionProperties_2esurjective___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f)
=> cTopology_2eCompactness_2ecompact___24a1(V1__Y) ) ) ) ) ) ) ).
fof('Topology.Compactness.compact_impl_filter_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ! [V2__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ? [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
& cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V2__F,V3__x0) ) ) ) ) ).
fof('Topology.Compactness.compact_impl_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ! [V2__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V2__I)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(V2__I,V0__X,V3__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V2__I))
=> ? [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
& cTopology_2eNets_2enet__cluster__point___24a4(V2__I,V0__X,V3__x,V5__x0) ) ) ) ) ) ) ).
fof('Topology.Compactness.compactness_on_indexed_covers',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__C] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__C)
=> ( cTopology_2eCompactness_2ecompact___24a1(V0__X)
=> ( ! [V4__a] :
( t(V4__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,happ(V2__C,V4__a)) )
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__C) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))
=> ? [V6__A_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__A,V6__A_27)
& cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V1__A,V6__A_27)
& cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(V1__A,c_24__lam__41013___24a3(V0__X,V1__A,V6__A_27)),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),c_24__lam__41027___24a4(V0__X,V1__A,V2__C,V6__A_27)) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)) ) ) ) ) ) ) ) ).
fof('Topology.Compactness.filter_cluster_point_impl_compact',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ? [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
& cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0) ) )
=> cTopology_2eCompactness_2ecompact___24a1(V0__X) ) ) ).
fof('Topology.Compactness.finite_nonempty_closed_intersection_impl_compact',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ( ! [V2__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__G)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__F,V2__G)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__G) ) )
=> ( ! [V3__F_27] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__F_27)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V3__F_27)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V3__F_27,V1__F)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__F_27)) ) ) )
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ) )
=> cTopology_2eCompactness_2ecompact___24a1(V0__X) ) ) ).
fof('Topology.Compactness.net_cluster_point_impl_compact',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__I))
=> ? [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x0)
& cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V4__x0) ) ) ) )
=> cTopology_2eCompactness_2ecompact___24a1(V0__X) ) ) ).
fof('Topology.Compactness.ultrafilter_limit_impl_compact',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__U] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ( cTopology_2eFilters_2eultrafilter___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ? [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
& cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V1__U,V3__x0) ) ) )
=> cTopology_2eCompactness_2ecompact___24a1(V0__X) ) ) ).
fof('Topology.Completeness.complete_subset_is_closed',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__F)
=> ( cTopology_2eCompleteness_2ecomplete___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(V0__X,c_24__lam__38269___24a2(V0__X,V3__F)),c_24__lam__38900___24a3(V0__X,V1__d,V3__F),cTopology_2eCompleteness_2ed__restriction__metric___24a3(V0__X,V1__d,V3__F))
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V3__F) ) ) ) ) ) ).
fof('Topology.Completeness.convergent_sequence_is_cauchy',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(cTopology_2eDirectedSets_2enat__DS,cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V3__x)
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V4__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(cTopology_2eDirectedSets_2enat__DS,cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V3__x,V4__x0)
=> cTopology_2eCompleteness_2ecauchy___24a3(V0__X,V1__d,V3__x) ) ) ) ) ) ) ).
fof('Topology.Completeness.d_restriction_metric',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__F)
=> cTopology_2eMetricSpaces_2emetric___24a2(cCoq_2eInit_2eSpecif_2esig___24a2(V0__X,c_24__lam__38269___24a2(V0__X,V3__F)),c_24__lam__38864___24a3(V0__X,V1__d,V3__F)) ) ) ) ) ).
fof('Topology.Connectedness.connected_img',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( cTopology_2eConnectedness_2econnected___24a1(V0__X)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
=> ( cZornsLemma_2eFunctionProperties_2esurjective___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f)
=> cTopology_2eConnectedness_2econnected___24a1(V1__Y) ) ) ) ) ) ) ).
fof('Topology.Connectedness.connected_union',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__S] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__S)
=> ( ! [V3__a] :
( t(V3__a,V1__A)
=> cTopology_2eConnectedness_2econnected___24a1(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V0__X,happ(V2__S,V3__a))) )
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__S))
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__S) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))
=> cTopology_2eConnectedness_2econnected___24a1(V0__X) ) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_at_is_local',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ! [V3__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V3__f)
=> ! [V4__g] :
( c_24__type__38915___24t(V0__X,V1__Y,V4__g)
=> ! [V5__N] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__N)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V5__N,V2__x0)
=> ( ! [V7__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V7__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V5__N,V7__x)
=> happ(V3__f,V7__x) = happ(V4__g,V7__x) ) )
=> ( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V3__f,V2__x0)
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V4__g,V2__x0) ) ) ) ) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_at_neighborhood_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ! [V4__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V4__NB)
=> ( cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V1__Y,V4__NB,happ(V2__f,V3__x))
=> ( ! [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V6__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y)),V4__NB,V6__V)
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V6__V),V3__x) ) )
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x) ) ) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_at_open_neighborhoods',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ( ! [V4__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V4__V)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V1__Y,V4__V,happ(V2__f,V3__x))
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V4__V),V3__x) ) )
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_composition',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__Z] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V2__Z)
=> ! [V3__f] :
( c_24__type__38915___24t(V1__Y,V2__Z,V3__f)
=> ! [V4__g] :
( c_24__type__41134___24t(V0__X,V1__Y,V2__Z,V4__g)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V1__Y,V2__Z,V3__f)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V4__g)
=> cTopology_2eContinuity_2econtinuous___24a3(V0__X,V2__Z,c_24__lam__41181___24a5(V0__X,V1__Y,V2__Z,V3__f,V4__g)) ) ) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_composition_at',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__Z] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V2__Z)
=> ! [V3__f] :
( c_24__type__38915___24t(V1__Y,V2__Z,V3__f)
=> ! [V4__g] :
( c_24__type__41134___24t(V0__X,V1__Y,V2__Z,V4__g)
=> ! [V5__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x)
=> ( cTopology_2eContinuity_2econtinuous__at___24a4(V1__Y,V2__Z,V3__f,happ(V4__g,V5__x))
=> ( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V4__g,V5__x)
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V2__Z,c_24__lam__41148___24a5(V0__X,V1__Y,V2__Z,V3__f,V4__g),V5__x) ) ) ) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_constant',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__y0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__Y,V2__y0)
=> cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,c_24__lam__41217___24a3(V0__X,V1__Y,V2__y0)) ) ) ) ).
fof('Topology.Continuity.continuous_func_continuous_everywhere',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
=> ! [V4__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x)
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V4__x) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_identity',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> cTopology_2eContinuity_2econtinuous___24a3(V0__X,V0__X,c_24__lam__41198___24a1(V0__X)) ) ).
fof('Topology.Continuity.continuous_open_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V3__B)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V1__Y,V3__B)
=> ( ! [V5__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V5__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y)),V3__B,V5__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V5__V)) ) )
=> cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ) ) ).
fof('Topology.Continuity.continuous_subbasis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__SB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V3__SB)
=> ( cTopology_2eSubbases_2esubbasis___24a2(V1__Y,V3__SB)
=> ( ! [V5__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V5__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y)),V3__SB,V5__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V5__V)) ) )
=> cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ) ) ).
fof('Topology.Continuity.pointwise_continuity',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x) )
=> cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ).
fof('Topology.CountabilityAxioms.first_countable_open_neighborhood_bases',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eCountabilityAxioms_2efirst__countable___24a1(V0__X)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ? [V3__NBx] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__NBx)
& cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,V3__NBx,V2__x)
& cZornsLemma_2eCountableTypes_2eCountable___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V3__NBx) ) ) ) ) ).
fof('Topology.CountabilityAxioms.first_countable_sequence_closure',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eCountabilityAxioms_2efirst__countable___24a1(V0__X)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x)
=> ? [V5__y] :
( cTopology_2eNets_2eNet___24t(cTopology_2eDirectedSets_2enat__DS,V0__X,V5__y)
& ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,happ(V5__y,V6__n)) )
& cTopology_2eNets_2enet__limit___24a4(cTopology_2eDirectedSets_2enat__DS,V0__X,V5__y,V2__x) ) ) ) ) ) ) ).
fof('Topology.CountabilityAxioms.intro_ctbl_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__B)
=> ( cZornsLemma_2eCountableTypes_2eCountable___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__B)
=> cTopology_2eCountabilityAxioms_2esecond__countable___24a1(V0__X) ) ) ) ) ).
fof('Topology.CountabilityAxioms.intro_dense_ctbl',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cZornsLemma_2eCountableTypes_2eCountable___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eInteriorsClosures_2edense___24a2(V0__X,V1__S)
=> cTopology_2eCountabilityAxioms_2eseparable___24a1(V0__X) ) ) ) ) ).
fof('Topology.CountabilityAxioms.second_countable_ind',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__P] :
( cProp___24t(V1__P)
=> ( ! [V2__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__B)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V2__B)
=> ( cZornsLemma_2eCountableTypes_2eCountable___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V2__B)
=> p(V1__P) ) ) )
=> ( cTopology_2eCountabilityAxioms_2esecond__countable___24a1(V0__X)
=> p(V1__P) ) ) ) ) ).
fof('Topology.CountabilityAxioms.separable_ind',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__P] :
( cProp___24t(V1__P)
=> ( ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__S)
=> ( cZornsLemma_2eCountableTypes_2eCountable___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__S)
=> ( cTopology_2eInteriorsClosures_2edense___24a2(V0__X,V2__S)
=> p(V1__P) ) ) )
=> ( cTopology_2eCountabilityAxioms_2eseparable___24a1(V0__X)
=> p(V1__P) ) ) ) ) ).
fof('Topology.DirectedSets.DS_join_cond',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> ! [V1__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__d,V1__i)
=> ! [V2__j] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__d,V2__j)
=> ? [V3__k] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__d,V3__k)
& cTopology_2eDirectedSets_2eDS__ord___24a3(V0__d,V1__i,V3__k)
& cTopology_2eDirectedSets_2eDS__ord___24a3(V0__d,V2__j,V3__k) ) ) ) ) ).
fof('Topology.DirectedSets.DS_ord_cond',axiom,
! [V0__d] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__d)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(cTopology_2eDirectedSets_2eDS__set___24a1(V0__d),cTopology_2eDirectedSets_2eDS__ord___24a1(V0__d)) ) ).
fof('Topology.DirectedSets.eventually_impl_base',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__P] :
( c_24__type__38383___24t(V0__I,V1__P)
=> ! [V2__Q] :
( c_24__type__38383___24t(V0__I,V2__Q)
=> ( ! [V3__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V0__I,V3__i)
=> ( p(happ(V1__P,V3__i))
=> p(happ(V2__Q,V3__i)) ) )
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V1__P)
=> cTopology_2eDirectedSets_2eeventually___24a2(V0__I,V2__Q) ) ) ) ) ) ).
fof('Topology.FilterLimits.closure_impl_filter_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x0)
=> ? [V4__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__F)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__F),V1__S)
& cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V4__F,V2__x0) ) ) ) ) ) ).
fof('Topology.FilterLimits.continuous_function_preserves_filter_limits',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ! [V4__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__F)
=> ( cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V4__F,V3__x)
=> ( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x)
=> cTopology_2eFilterLimits_2efilter__limit___24a3(V1__Y,cTopology_2eFilters_2efilter__direct__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V4__F),happ(V2__f,V3__x)) ) ) ) ) ) ) ) ).
fof('Topology.FilterLimits.filter_limit_is_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V1__F,V2__x0)
=> cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0) ) ) ) ) ).
fof('Topology.FilterLimits.func_preserving_filter_limits_is_continuous',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ( ! [V4__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__F)
=> ( cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V4__F,V3__x)
=> cTopology_2eFilterLimits_2efilter__limit___24a3(V1__Y,cTopology_2eFilters_2efilter__direct__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V4__F),happ(V2__f,V3__x)) ) )
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x) ) ) ) ) ) ).
fof('Topology.FilterLimits.ultrafilter_cluster_point_is_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0)
=> ( cTopology_2eFilters_2eultrafilter___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V1__F,V2__x0) ) ) ) ) ) ).
fof('Topology.Filters.Build_filter_basis',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__F)
=> ! [V2__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V2__B)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__B,cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F))
=> ( ! [V4__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F),V4__S)
=> ? [V6__S_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__S_27)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__B,V6__S_27)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V6__S_27,V4__S) ) ) )
=> cTopology_2eFilters_2efilter__basis___24a3(V0__X,V1__F,V2__B) ) ) ) ) ) ).
fof('Topology.Filters.filter_basis_cond',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__F)
=> ! [V2__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V2__B)
=> ( cTopology_2eFilters_2efilter__basis___24a3(V0__X,V1__F,V2__B)
=> ! [V4__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F),V4__S)
=> ? [V6__S_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__S_27)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__B,V6__S_27)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V6__S_27,V4__S) ) ) ) ) ) ) ) ).
fof('Topology.Filters.filter_basis_elements',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__F)
=> ! [V2__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V2__B)
=> ( cTopology_2eFilters_2efilter__basis___24a3(V0__X,V1__F,V2__B)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__B,cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F)) ) ) ) ) ).
fof('Topology.Filters.filter_empty',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X)) ) ) ).
fof('Topology.Filters.filter_from_basis_basis',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__B)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X))
=> ( ! [V4__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__S1)
=> ! [V5__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V5__S2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,V4__S1)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,V5__S2)
=> ? [V8__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V8__T)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,V8__T)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V8__T,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V4__S1,V5__S2)) ) ) ) ) )
=> cTopology_2eFilters_2efilter__basis___24a3(V0__X,cTopology_2eFilters_2eBuild__Filter__from__basis___24a2(V0__X,V1__B),V1__B) ) ) ) ) ) ).
fof('Topology.Filters.filter_from_subbasis_subbasis',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__B)
=> ( ! [V2__J] :
( cType___24t(V2__J)
=> ! [V3__V] :
( c_24__type__42499___24t(V0__X,V2__J,V3__V)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V2__J)
=> ( ! [V5__j] :
( t(V5__j,V2__J)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__B,happ(V3__V,V5__j)) )
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V2__J,V0__X,V3__V)) ) ) ) )
=> cTopology_2eFilters_2efilter__subbasis___24a3(V0__X,cTopology_2eFilters_2eBuild__Filter__from__subbasis___24a2(V0__X,V1__B),V1__B) ) ) ) ).
fof('Topology.Filters.filter_full',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)) ) ) ).
fof('Topology.Filters.filter_intersection',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> ! [V2__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S1)
=> ! [V3__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),V2__S1)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),V3__S2)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__S1,V3__S2)) ) ) ) ) ) ) ).
fof('Topology.Filters.filter_subbasis_elements',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__F)
=> ! [V2__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V2__B)
=> ( cTopology_2eFilters_2efilter__subbasis___24a3(V0__X,V1__F,V2__B)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__B,cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F)) ) ) ) ) ).
fof('Topology.Filters.filter_upward_closed',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__f)
=> ! [V2__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S1)
=> ! [V3__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S2)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),V2__S1)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V2__S1,V3__S2)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__f),V3__S2) ) ) ) ) ) ) ).
fof('Topology.Filters.ultrafilter_extension',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V1__F)
=> ? [V2__U] :
( cTopology_2eFilters_2eFilter___24t(V0__X,V2__U)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFilters_2efilter__family___24a2(V0__X,V1__F),cTopology_2eFilters_2efilter__family___24a2(V0__X,V2__U))
& cTopology_2eFilters_2eultrafilter___24a2(V0__X,V2__U) ) ) ) ).
fof('Topology.FiltersAndNets.filter_cluster_point_impl_filter_to_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0)
=> cTopology_2eNets_2enet__cluster__point___24a4(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V0__X,V1__F),V0__X,cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F),V2__x0) ) ) ) ) ).
fof('Topology.FiltersAndNets.filter_limit_impl_filter_to_net_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V1__F,V2__x0)
=> cTopology_2eNets_2enet__limit___24a4(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V0__X,V1__F),V0__X,cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F),V2__x0) ) ) ) ) ).
fof('Topology.FiltersAndNets.filter_to_net_cluster_point_impl_filter_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V0__X,V1__F),V0__X,cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F),V2__x0)
=> cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,V1__F,V2__x0) ) ) ) ) ).
fof('Topology.FiltersAndNets.filter_to_net_limit_impl_filter_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V0__X,V1__F),V0__X,cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V0__X,V1__F),V2__x0)
=> cTopology_2eFilterLimits_2efilter__limit___24a3(V0__X,V1__F,V2__x0) ) ) ) ) ).
fof('Topology.FiltersAndNets.ftn_S_in_F',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__f] :
( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(V0__X,V1__F,V2__f)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eFilters_2efilter__family___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F),cTopology_2eFiltersAndNets_2eftn__S___24a3(V0__X,V1__F,V2__f)) ) ) ) ).
fof('Topology.FiltersAndNets.ftn_x_in_S',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cTopology_2eFilters_2eFilter___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__f] :
( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(V0__X,V1__F,V2__f)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eFiltersAndNets_2eftn__S___24a3(V0__X,V1__F,V2__f),cTopology_2eFiltersAndNets_2eftn__x___24a3(V0__X,V1__F,V2__f)) ) ) ) ).
fof('Topology.FiltersAndNets.tail_filter_cluster_point_impl_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__J)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__J,V0__X,V2__x)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__J))
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x0)
=> ( cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V0__X,cTopology_2eFiltersAndNets_2etail__filter___24a3(V0__X,V1__J,V2__x),V4__x0)
=> cTopology_2eNets_2enet__cluster__point___24a4(V1__J,V0__X,V2__x,V4__x0) ) ) ) ) ) ) ).
fof('Topology.FiniteIntersectionLemmas.finite_intersections_len_S_choice',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__F)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ? [V3__f] :
( c_24__type__38111___24t(V0__X,V1__F,V2__n,V3__f)
& ! [V4__U] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38116___24a3(V0__X,V1__F,V2__n),V4__U)
=> cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38116___24a3(V0__X,V1__F,V2__n),V4__U) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38120___24a3(V0__X,V1__F,V2__n),cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38120___24a3(V0__X,V1__F,V2__n)),cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38124___24a3(V0__X,V1__F,V2__n)),happ(V3__f,V4__U))),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38124___24a3(V0__X,V1__F,V2__n),cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38120___24a3(V0__X,V1__F,V2__n)),cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),c_24__lam__38124___24a3(V0__X,V1__F,V2__n)),happ(V3__f,V4__U)))) ) ) ) ) ) ).
fof('Topology.FiniteIntersectionLemmas.finite_intersections_len_S_exists',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__F)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__U)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(V0__X,V1__F,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),V2__U)
=> ? [V5__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V5__V)
& ? [V6__W] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__W)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(V0__X,V1__F,V3__n),V5__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(V0__X,V1__F,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V6__W)
& V2__U = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V5__V,V6__W) ) ) ) ) ) ) ) ).
fof('Topology.FiniteIntersectionLemmas.intersection_associative',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V1__U)
=> ! [V2__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__V)
=> ! [V3__W] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__W)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V1__U,V2__V),V3__W) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V1__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__V,V3__W)) ) ) ) ) ).
fof('Topology.FiniteIntersectionLemmas.intersection_full_set',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V1__U)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X),V1__U) = V1__U ) ) ).
fof('Topology.FiniteIntersectionLemmas.intro_fi_len_S',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__F)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__F,V2__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(V0__X,V1__F,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V2__U) ) ) ) ) ).
fof('Topology.Homeomorphisms.homeomorphic_ind',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ! [V3__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V3__f)
=> ( cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V0__X,V1__Y,V3__f)
=> p(V2__P) ) )
=> ( cTopology_2eHomeomorphisms_2ehomeomorphic___24a2(V0__X,V1__Y)
=> p(V2__P) ) ) ) ) ) ).
fof('Topology.Homeomorphisms.homeomorphism_ind',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ! [V4__g] :
( c_24__type__43805___24t(V0__X,V1__Y,V4__g)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V1__Y,V0__X,V4__g)
=> ( ! [V7__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V7__x)
=> happ(V4__g,happ(V2__f,V7__x)) = V7__x )
=> ( ! [V8__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__Y,V8__y)
=> happ(V2__f,happ(V4__g,V8__y)) = V8__y )
=> p(V3__P) ) ) ) ) )
=> ( cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V0__X,V1__Y,V2__f)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Topology.Homeomorphisms.homeomorphism_is_invertible',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V0__X,V1__Y,V2__f)
=> cZornsLemma_2eFunctionProperties_2einvertible___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f) ) ) ) ) ).
fof('Topology.Homeomorphisms.homeomorphism_is_open_map',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V0__X,V1__Y,V2__f)
=> cTopology_2eHomeomorphisms_2eopen__map___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ).
fof('Topology.Homeomorphisms.intro_homeomorphic',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V0__X,V1__Y,V2__f)
=> cTopology_2eHomeomorphisms_2ehomeomorphic___24a2(V0__X,V1__Y) ) ) ) ) ).
fof('Topology.Homeomorphisms.intro_homeomorphism',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__g] :
( c_24__type__43805___24t(V0__X,V1__Y,V3__g)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V1__Y,V0__X,V3__g)
=> ( ! [V6__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V6__x)
=> happ(V3__g,happ(V2__f,V6__x)) = V6__x )
=> ( ! [V7__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__Y,V7__y)
=> happ(V2__f,happ(V3__g,V7__y)) = V7__y )
=> cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ) ) ) ) ).
fof('Topology.Homeomorphisms.invertible_open_map_is_homeomorphism',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ( cZornsLemma_2eFunctionProperties_2einvertible___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f)
=> ( cTopology_2eContinuity_2econtinuous___24a3(V0__X,V1__Y,V2__f)
=> ( cTopology_2eHomeomorphisms_2eopen__map___24a3(V0__X,V1__Y,V2__f)
=> cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.Build_TopologicalSpace_from_closure_operator_closure',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__cl] :
( c_24__type__43878___24t(V0__X,V1__cl)
=> ( ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V2__S,happ(V1__cl,V2__S)) )
=> ( ! [V3__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S1)
=> ! [V4__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__S2)
=> happ(V1__cl,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__X,V3__S1,V4__S2)) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__X,happ(V1__cl,V3__S1),happ(V1__cl,V4__S2)) ) )
=> ( happ(V1__cl,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X)) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X)
=> ( ! [V5__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V5__S)
=> happ(V1__cl,happ(V1__cl,V5__S)) = happ(V1__cl,V5__S) )
=> ! [V6__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__closure__operator___24a2(V0__X,V1__cl)),V6__S)
=> cTopology_2eInteriorsClosures_2eclosure___24a2(cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__closure__operator___24a2(V0__X,V1__cl),V6__S) = happ(V1__cl,V6__S) ) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.Build_TopologicalSpace_from_interior_operator_interior',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__int] :
( c_24__type__43878___24t(V0__X,V1__int)
=> ( ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,happ(V1__int,V2__S),V2__S) )
=> ( ! [V3__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S1)
=> ! [V4__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__S2)
=> happ(V1__int,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V3__S1,V4__S2)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,happ(V1__int,V3__S1),happ(V1__int,V4__S2)) ) )
=> ( happ(V1__int,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)
=> ( ! [V5__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V5__S)
=> happ(V1__int,happ(V1__int,V5__S)) = happ(V1__int,V5__S) )
=> ! [V6__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__interior__operator___24a2(V0__X,V1__int)),V6__S)
=> cTopology_2eInteriorsClosures_2einterior___24a2(cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__interior__operator___24a2(V0__X,V1__int),V6__S) = happ(V1__int,V6__S) ) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.cl_increasing',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__cl] :
( c_24__type__43878___24t(V0__X,V1__cl)
=> ( ! [V2__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S1)
=> ! [V3__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S2)
=> happ(V1__cl,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__X,V2__S1,V3__S2)) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__X,happ(V1__cl,V2__S1),happ(V1__cl,V3__S2)) ) )
=> ! [V3__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S1)
=> ! [V4__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__S2)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V3__S1,V4__S2)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,happ(V1__cl,V3__S1),happ(V1__cl,V4__S2)) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.closure_closed',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.InteriorsClosures.closure_complement',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.InteriorsClosures.closure_fixes_closed',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__S)
=> cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S) = V1__S ) ) ) ).
fof('Topology.InteriorsClosures.closure_idempotent',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> cTopology_2eInteriorsClosures_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eInteriorsClosures_2eclosure___24a1(V0__X)) ) ).
fof('Topology.InteriorsClosures.closure_impl_meets_every_open_neighborhood',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V4__U)) ) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.closure_increasing',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__T)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V2__T)) ) ) ) ) ).
fof('Topology.InteriorsClosures.closure_inflationary',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.InteriorsClosures.closure_interior_idempotent',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> cTopology_2eInteriorsClosures_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__43870___24a1(V0__X)) ) ).
fof('Topology.InteriorsClosures.closure_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__T)),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V2__T))) ) ) ) ).
fof('Topology.InteriorsClosures.closure_minimal',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__F)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__F)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__F) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.closure_union',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__T)
=> cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__T)) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V2__T)) ) ) ) ).
fof('Topology.InteriorsClosures.complement_inclusion',axiom,
! [V0__Y] :
( cType___24t(V0__Y)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__Y,V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__Y,V2__T)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__Y,V1__S,V2__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__Y,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__Y,V2__T),cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__Y,V1__S)) ) ) ) ) ).
fof('Topology.InteriorsClosures.dense_meets_every_nonempty_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eInteriorsClosures_2edense___24a2(V0__X,V1__S)
=> ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V3__U)) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.int_family_union',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__int] :
( c_24__type__43878___24t(V0__X,V1__int)
=> ( ! [V2__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S1)
=> ! [V3__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S2)
=> happ(V1__int,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__S1,V3__S2)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,happ(V1__int,V2__S1),happ(V1__int,V3__S2)) ) )
=> ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S)
=> ! [V4__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V4__F)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V4__F,V3__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,happ(V1__int,V3__S),happ(V1__int,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__X,V4__F))) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.int_increasing',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__int] :
( c_24__type__43878___24t(V0__X,V1__int)
=> ( ! [V2__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__S1)
=> ! [V3__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S2)
=> happ(V1__int,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__S1,V3__S2)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,happ(V1__int,V2__S1),happ(V1__int,V3__S2)) ) )
=> ! [V3__S1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S1)
=> ! [V4__S2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__S2)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V3__S1,V4__S2)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,happ(V1__int,V3__S1),happ(V1__int,V4__S2)) ) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.interior_closure_idempotent',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> cTopology_2eInteriorsClosures_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__43872___24a1(V0__X)) ) ).
fof('Topology.InteriorsClosures.interior_complement',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.InteriorsClosures.interior_deflationary',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S),V1__S) ) ) ).
fof('Topology.InteriorsClosures.interior_fixes_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__S)
=> cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S) = V1__S ) ) ) ).
fof('Topology.InteriorsClosures.interior_idempotent',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> cTopology_2eInteriorsClosures_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),cTopology_2eInteriorsClosures_2einterior___24a1(V0__X)) ) ).
fof('Topology.InteriorsClosures.interior_increasing',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__T)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V2__T)) ) ) ) ) ).
fof('Topology.InteriorsClosures.interior_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__T)
=> cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__T)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V2__T)) ) ) ) ).
fof('Topology.InteriorsClosures.interior_maximal',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U,V1__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U,cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S)) ) ) ) ) ) ).
fof('Topology.InteriorsClosures.interior_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.InteriorsClosures.interior_union',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__S),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V2__T)),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__T))) ) ) ) ).
fof('Topology.InteriorsClosures.intersection_family_union',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V1__S)
=> ! [V2__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__F)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__F,V1__S)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V1__S,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__X,V2__F)) = V1__S ) ) ) ) ).
fof('Topology.InteriorsClosures.meets_every_nonempty_open_impl_dense',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__U)) ) ) )
=> cTopology_2eInteriorsClosures_2edense___24a2(V0__X,V1__S) ) ) ) ).
fof('Topology.InteriorsClosures.meets_every_open_neighborhood_impl_closure',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V3__U)) ) ) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x) ) ) ) ) ).
fof('Topology.MetricSpaces.MetricTopology_metrizable',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> cTopology_2eMetricSpaces_2emetrizes___24a2(cTopology_2eMetricSpaces_2eMetricTopology___24a2(V0__X,V1__d),V1__d) ) ) ) ).
fof('Topology.MetricSpaces.closer_to_S_than_T_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V4__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__S)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__S)
=> ! [V6__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__T)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__T)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),c_24__lam__44370___24a4(V0__X,V1__d,V4__S,V6__T))) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.closure_impl_dist_to_set_zero',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V4__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__S)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__S)
=> ! [V6__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V6__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V4__S),V6__x)
=> cTopology_2eMetricSpaces_2edist__to__set___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d,V4__S,V6__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.dist_to_set_triangle_inequality',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__X,V3__S)
=> ! [V5__x] :
( t(V5__x,V0__X)
=> ! [V6__y] :
( t(V6__y,V0__X)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cTopology_2eMetricSpaces_2edist__to__set___24a4(V0__X,V1__d,V3__S,V6__y),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cTopology_2eMetricSpaces_2edist__to__set___24a4(V0__X,V1__d,V3__S,V5__x),happ(happ(V1__d,V5__x),V6__y)))) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.dist_to_set_zero_impl_closure',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V4__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__S)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__S)
=> ! [V6__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V6__x)
=> ( cTopology_2eMetricSpaces_2edist__to__set___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d,V4__S,V6__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V4__S),V6__x) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.intro_metrizable',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> cTopology_2eMetricSpaces_2emetrizable___24a1(V0__X) ) ) ) ) ).
fof('Topology.MetricSpaces.intro_open_ball',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ! [V3__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V3__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a3(V0__X,V1__d,V2__x),cTopology_2eMetricSpaces_2eopen__ball___24a4(V0__X,V1__d,V2__x,V3__r)) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_nonneg',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(happ(happ(V1__d,V3__x),V4__y),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_fun_continuity',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ! [V4__dX] :
( c_24__type__44329___24t(V0__X,V1__Y,V4__dX)
=> ! [V5__dY] :
( c_24__type__44336___24t(V0__X,V1__Y,V5__dY)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V4__dX)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V1__Y,V5__dY)
=> ( ! [V8__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V8__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V8__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V10__delta] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V10__delta)
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V10__delta,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& ! [V11__x_27] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V11__x_27)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(V4__dX,V3__x),V11__x_27),V10__delta))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(V5__dY,happ(V2__f,V3__x)),happ(V2__f,V11__x_27)),V8__eps)) ) ) ) ) )
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x) ) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_fun_continuity_converse',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ! [V4__dX] :
( c_24__type__44329___24t(V0__X,V1__Y,V4__dX)
=> ! [V5__dY] :
( c_24__type__44336___24t(V0__X,V1__Y,V5__dY)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V4__dX)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V1__Y,V5__dY)
=> ( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x)
=> ! [V9__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V9__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V9__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V11__delta] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V11__delta)
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V11__delta,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& ! [V12__x_27] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V12__x_27)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(V4__dX,V3__x),V12__x_27),V11__delta))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(happ(happ(V5__dY,happ(V2__f,V3__x)),happ(V2__f,V12__x_27)),V9__eps)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( ! [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)))
=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V3__I,c_24__lam__44306___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V6__eps)) ) )
=> cTopology_2eNets_2enet__cluster__point___24a4(V3__I,V0__X,V4__x,V5__x0) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_cluster_point_converse',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V3__I,V0__X,V4__x,V5__x0)
=> ! [V7__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V7__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V3__I,c_24__lam__44321___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V7__eps)) ) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( ! [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)))
=> cTopology_2eDirectedSets_2eeventually___24a2(V3__I,c_24__lam__39212___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V6__eps)) ) )
=> cTopology_2eNets_2enet__limit___24a4(V3__I,V0__X,V4__x,V5__x0) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_space_net_limit_converse',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38499___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V1__d)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(V3__I,V0__X,V4__x,V5__x0)
=> ! [V7__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V7__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V7__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cTopology_2eDirectedSets_2eeventually___24a2(V3__I,c_24__lam__39227___24a6(V0__X,V1__d,V3__I,V4__x,V5__x0,V7__eps)) ) ) ) ) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_sym',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> happ(happ(V1__d,V3__x),V4__y) = happ(happ(V1__d,V4__y),V3__x) ) ) ) ) ) ).
fof('Topology.MetricSpaces.metric_zero',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> happ(happ(V1__d,V3__x),V3__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Topology.MetricSpaces.metrizable_impl_first_countable',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eMetricSpaces_2emetrizable___24a1(V0__X)
=> cTopology_2eCountabilityAxioms_2efirst__countable___24a1(V0__X) ) ) ).
fof('Topology.MetricSpaces.metrizable_impl_normal_sep',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eMetricSpaces_2emetrizable___24a1(V0__X)
=> cTopology_2eSeparatednessAxioms_2enormal__sep___24a1(V0__X) ) ) ).
fof('Topology.MetricSpaces.metrizable_ind',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__P] :
( cProp___24t(V1__P)
=> ( ! [V2__d] :
( c_24__type__38499___24t(V0__X,V2__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__d)
=> ( cTopology_2eMetricSpaces_2emetrizes___24a2(V0__X,V2__d)
=> p(V1__P) ) ) )
=> ( cTopology_2eMetricSpaces_2emetrizable___24a1(V0__X)
=> p(V1__P) ) ) ) ) ).
fof('Topology.MetricSpaces.triangle_inequality',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__d] :
( c_24__type__38488___24t(V0__X,V1__d)
=> ( cTopology_2eMetricSpaces_2emetric___24a2(V0__X,V1__d)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> ! [V5__z] :
( t(V5__z,V0__X)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(happ(V1__d,V3__x),V5__z),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(happ(V1__d,V3__x),V4__y),happ(happ(V1__d,V4__y),V5__z)))) ) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.Build_TopologicalSpace_from_open_neighborhood_bases_basis',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__NB] :
( c_24__type__44548___24t(V0__X,V1__NB)
=> ( ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__U)
=> ! [V3__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__V)
=> ! [V4__x] :
( t(V4__x,V0__X)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),happ(V1__NB,V4__x),V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),happ(V1__NB,V4__x),V3__V)
=> ? [V7__W] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V7__W)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),happ(V1__NB,V4__x),V7__W)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V7__W,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__U,V3__V)) ) ) ) ) ) )
=> ( ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__U)
=> ! [V4__x] :
( t(V4__x,V0__X)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),happ(V1__NB,V4__x),V3__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,V3__U,V4__x) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),happ(V1__NB,V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__X)
=> ! [V6__y] :
( t(V6__y,V0__X)
=> ! [V7__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V7__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),happ(V1__NB,V5__x),V7__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,V7__U,V6__y)
=> ? [V10__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V10__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),happ(V1__NB,V6__y),V10__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V10__V,V7__U) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__X)
=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(cTopology_2eNeighborhoodBases_2eBuild__TopologicalSpace__from__open__neighborhood__bases___24a2(V0__X,V1__NB),happ(V1__NB,V6__x),V6__x) ) ) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.Build_neighborhood_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( ! [V3__N] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__N)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V3__N)
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V3__N,V2__x) ) )
=> ( ! [V4__N] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__N)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V4__N,V2__x)
=> ? [V6__N_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__N_27)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V6__N_27)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__N_27,V4__N) ) ) )
=> cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V0__X,V1__NB,V2__x) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.Build_open_neighborhood_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V3__U)
=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V3__U,V2__x) ) )
=> ( ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V4__U,V2__x)
=> ? [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V6__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V,V4__U) ) ) )
=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,V1__NB,V2__x) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.neighborhood_basis_cond',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V0__X,V1__NB,V2__x)
=> ! [V4__N] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__N)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V4__N,V2__x)
=> ? [V6__N_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__N_27)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V6__N_27)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__N_27,V4__N) ) ) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.neighborhood_basis_elements',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V0__X,V1__NB,V2__x)
=> ! [V4__N] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__N)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V4__N)
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V4__N,V2__x) ) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.open_basis_to_open_neighborhood_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__B)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__B)
=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__44418___24a3(V0__X,V1__B,V2__x)),V2__x) ) ) ) ) ).
fof('Topology.NeighborhoodBases.open_neighborhood_bases_to_open_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( c_24__type__44420___24t(V0__X,V1__NB)
=> ( ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,happ(V1__NB,V2__x),V2__x) )
=> cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB)) ) ) ) ).
fof('Topology.NeighborhoodBases.open_neighborhood_basis_cond',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,V1__NB,V2__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V4__U,V2__x)
=> ? [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V6__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V,V4__U) ) ) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.open_neighborhood_basis_elements',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,V1__NB,V2__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__NB,V4__U)
=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V4__U,V2__x) ) ) ) ) ) ) ).
fof('Topology.NeighborhoodBases.open_neighborhood_basis_is_neighborhood_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__NB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__NB)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V0__X,V1__NB,V2__x)
=> cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V0__X,V1__NB,V2__x) ) ) ) ) ).
fof('Topology.Neighborhoods.interior_neighborhood',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__N] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__N)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__N),V2__x)
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V1__N,V2__x) ) ) ) ) ).
fof('Topology.Neighborhoods.neighborhood_interior',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__N] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__N)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V1__N,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2einterior___24a2(V0__X,V1__N),V2__x) ) ) ) ) ).
fof('Topology.Neighborhoods.open_neighborhood_is_neighborhood',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ! [V2__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x)
=> ( cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,V1__U,V2__x)
=> cTopology_2eNeighborhoods_2eneighborhood___24a3(V0__X,V1__U,V2__x) ) ) ) ) ).
fof('Topology.Nets.cluster_point_subnet_is_subnet',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V3__x0)
=> cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,cTopology_2eNets_2ecluster__point__subnet__DS___24a4(V0__X,V1__I,V2__x,V3__x0),cTopology_2eNets_2ecluster__point__subnet___24a4(V0__X,V1__I,V2__x,V3__x0)) ) ) ) ) ) ).
fof('Topology.Nets.continuous_func_preserves_net_limits',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__I)
=> ! [V4__x] :
( cTopology_2eNets_2eNet___24t(V3__I,V0__X,V4__x)
=> ! [V5__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V5__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(V3__I,V0__X,V4__x,V5__x0)
=> ( cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V5__x0)
=> cTopology_2eNets_2enet__limit___24a4(V3__I,V1__Y,c_24__lam__39252___24a5(V0__X,V1__Y,V2__f,V3__I,V4__x),happ(V2__f,V5__x0)) ) ) ) ) ) ) ) ) ).
fof('Topology.Nets.cps_U_open_neigh',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__c] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V0__X,cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c),V3__x0) ) ) ) ) ) ).
fof('Topology.Nets.cps_xi_in_U',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__c] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V0__X,V1__I,V2__x,V3__x0,V4__c)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2ecps__U___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c),happ(V2__x,cTopology_2eNets_2ecps__i___24a5(V0__X,V1__I,V2__x,V3__x0,V4__c))) ) ) ) ) ) ).
fof('Topology.Nets.func_preserving_net_limits_is_continuous',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__38915___24t(V0__X,V1__Y,V2__f)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( ! [V4__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__I)
=> ! [V5__x] :
( cTopology_2eNets_2eNet___24t(V4__I,V0__X,V5__x)
=> ( cTopology_2eNets_2enet__limit___24a4(V4__I,V0__X,V5__x,V3__x0)
=> cTopology_2eNets_2enet__limit___24a4(V4__I,V1__Y,c_24__lam__44737___24a5(V0__X,V1__Y,V2__f,V4__I,V5__x),happ(V2__f,V3__x0)) ) ) )
=> cTopology_2eContinuity_2econtinuous__at___24a4(V0__X,V1__Y,V2__f,V3__x0) ) ) ) ) ) ).
fof('Topology.Nets.intro_subnet',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V3__J)
=> ! [V4__h] :
( c_24__type__39369___24t(V0__X,V1__I,V3__J,V4__h)
=> ( ! [V5__j1] :
( cTopology_2eDirectedSets_2eDS__set___24t(V3__J,V5__j1)
=> ! [V6__j2] :
( cTopology_2eDirectedSets_2eDS__set___24t(V3__J,V6__j2)
=> ( cTopology_2eDirectedSets_2eDS__ord___24a3(V3__J,V5__j1,V6__j2)
=> cTopology_2eDirectedSets_2eDS__ord___24a3(V1__I,happ(V4__h,V5__j1),happ(V4__h,V6__j2)) ) ) )
=> ( cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V1__I,c_24__lam__39386___24a4(V0__X,V1__I,V3__J,V4__h))
=> cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V3__J,c_24__lam__39398___24a5(V0__X,V1__I,V2__x,V3__J,V4__h)) ) ) ) ) ) ) ) ).
fof('Topology.Nets.neighborhood_net_DS_set_ind',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> ! [V2__P] :
( c_24__type__44684___24t(V0__X,V1__x,V2__P)
=> ( ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ! [V4__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__y)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V1__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V4__y)
=> p(happ(V2__P,cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V0__X,V1__x,V3__U,V4__y))) ) ) ) ) )
=> ! [V4__n] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V0__X,V1__x,V4__n)
=> p(happ(V2__P,V4__n)) ) ) ) ) ) ).
fof('Topology.Nets.neighborhood_net_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V1__x)
=> cTopology_2eNets_2enet__limit___24a4(cTopology_2eNets_2eneighborhood__net__DS___24a2(V0__X,V1__x),V0__X,cTopology_2eNets_2eneighborhood__net___24a2(V0__X,V1__x),V1__x) ) ) ).
fof('Topology.Nets.net_cluster_point_impl_subnet_converges',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(cTopology_2eDirectedSets_2eDS__set___24a1(V1__I))
=> ? [V6__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V6__J)
& ? [V7__y] :
( cTopology_2eNets_2eNet___24t(V6__J,V0__X,V7__y)
& cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V6__J,V7__y)
& cTopology_2eNets_2enet__limit___24a4(V6__J,V0__X,V7__y,V3__x0) ) ) ) ) ) ) ) ) ).
fof('Topology.Nets.net_cluster_point_in_closure',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__X)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V2__S)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(V0__I,V1__X,V3__x)
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__X,V4__x0)
=> ( cTopology_2eDirectedSets_2eeventually___24a2(V0__I,c_24__lam__44587___24a4(V0__I,V1__X,V2__S,V3__x))
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V0__I,V1__X,V3__x,V4__x0)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V1__X,V2__S),V4__x0) ) ) ) ) ) ) ) ).
fof('Topology.Nets.net_limit_in_closure',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__X)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),V2__S)
=> ! [V3__x] :
( cTopology_2eNets_2eNet___24t(V0__I,V1__X,V3__x)
=> ! [V4__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__X,V4__x0)
=> ( cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V0__I,c_24__lam__44587___24a4(V0__I,V1__X,V2__S,V3__x))
=> ( cTopology_2eNets_2enet__limit___24a4(V0__I,V1__X,V3__x,V4__x0)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V1__X,V2__S),V4__x0) ) ) ) ) ) ) ) ).
fof('Topology.Nets.net_limit_is_cluster_point',axiom,
! [V0__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V0__I)
=> ! [V1__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__X)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V0__I,V1__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V1__X,V3__x0)
=> ( cTopology_2eNets_2enet__limit___24a4(V0__I,V1__X,V2__x,V3__x0)
=> cTopology_2eNets_2enet__cluster__point___24a4(V0__I,V1__X,V2__x,V3__x0) ) ) ) ) ) ).
fof('Topology.Nets.net_limits_determine_topology',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V2__x0)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__x0)
=> ? [V4__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__I)
& ? [V5__x] :
( cTopology_2eNets_2eNet___24t(V4__I,V0__X,V5__x)
& ! [V6__i] :
( cTopology_2eDirectedSets_2eDS__set___24t(V4__I,V6__i)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,happ(V5__x,V6__i)) )
& cTopology_2eNets_2enet__limit___24a4(V4__I,V0__X,V5__x,V2__x0) ) ) ) ) ) ) ).
fof('Topology.Nets.subnet_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__J)
=> ! [V5__y] :
( cTopology_2eNets_2eNet___24t(V4__J,V0__X,V5__y)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V4__J,V0__X,V5__y,V3__x0)
=> ( cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V4__J,V5__y)
=> cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V3__x0) ) ) ) ) ) ) ) ) ).
fof('Topology.Nets.subnet_limit',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__J] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__J)
=> ! [V5__y] :
( cTopology_2eNets_2eNet___24t(V4__J,V0__X,V5__y)
=> ( cTopology_2eNets_2enet__limit___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ( cTopology_2eNets_2eSubnet___24a5(V0__X,V1__I,V2__x,V4__J,V5__y)
=> cTopology_2eNets_2enet__limit___24a4(V4__J,V0__X,V5__y,V3__x0) ) ) ) ) ) ) ) ) ).
fof('Topology.OpenBases.B_open_ind',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__B)
=> ! [V2__P] :
( c_24__type__37437___24t(V0__X,V2__P)
=> ( ! [V3__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V3__F)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V3__F,V1__B)
=> p(happ(V2__P,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__X,V3__F))) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__e)
=> ( cTopology_2eOpenBases_2eB__open___24a3(V0__X,V1__B,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ) ).
fof('Topology.OpenBases.B_open_intro',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__B)
=> ! [V2__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V2__F)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V2__F,V1__B)
=> cTopology_2eOpenBases_2eB__open___24a3(V0__X,V1__B,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__X,V2__F)) ) ) ) ) ).
fof('Topology.OpenBases.Build_TopologicalSpace_from_open_basis_basis',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis__cond___24a2(V0__X,V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis__cover__cond___24a2(V0__X,V1__B)
=> cTopology_2eOpenBases_2eopen__basis___24a2(cTopology_2eOpenBases_2eBuild__TopologicalSpace__from__open__basis___24a2(V0__X,V1__B),V1__B) ) ) ) ) ).
fof('Topology.OpenBases.Build_open_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__B)
=> ( ! [V2__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__B,V2__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__V) ) )
=> ( ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V3__x)
=> ? [V7__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__B,V7__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V,V4__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V,V3__x) ) ) ) ) )
=> cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__B) ) ) ) ) ).
fof('Topology.OpenBases.coverable_by_open_basis_impl_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__B)
=> ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ( ! [V4__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V4__x)
=> ? [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__B,V6__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V,V3__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V6__V,V4__x) ) ) )
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U) ) ) ) ) ) ).
fof('Topology.OpenBases.open_basis_cover',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__B)
=> ! [V3__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x)
=> ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__U,V3__x)
=> ? [V7__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__B,V7__V)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V,V4__U)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V7__V,V3__x) ) ) ) ) ) ) ) ) ).
fof('Topology.OpenBases.open_basis_elements',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__B] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__B)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__B)
=> ! [V3__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__B,V3__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__V) ) ) ) ) ) ).
fof('Topology.OrderTopology.intro_lower_interval',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eOrderTopology_2eorder__topology__subbasis___24a2(V0__X,V1__R),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__44890___24a3(V0__X,V1__R,V2__x))) ) ) ) ).
fof('Topology.OrderTopology.intro_upper_interval',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eOrderTopology_2eorder__topology__subbasis___24a2(V0__X,V1__R),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__44894___24a3(V0__X,V1__R,V2__x))) ) ) ) ).
fof('Topology.RTopology.R_compact_subset_bounded',axiom,
! [V0__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cTopology_2eRTopology_2eRTop),V0__A)
=> ( cTopology_2eCompactness_2ecompact___24a1(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(cTopology_2eRTopology_2eRTop,V0__A))
=> cCoq_2eReals_2eRaxioms_2ebound___24a1(V0__A) ) ) ).
fof('Topology.RTopology.R_interval_open',axiom,
! [V0__p] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__q)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(cTopology_2eRTopology_2eRTop,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__45401___24a2(V0__p,V1__q))) ) ) ).
fof('Topology.SeparatednessAxioms.Hausdorff_impl_net_limit_is_unique_cluster_point',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ( cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X)
=> ( cTopology_2eNets_2enet__limit___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ! [V6__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V6__y)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V6__y)
=> V6__y = V3__x0 ) ) ) ) ) ) ) ) ).
fof('Topology.SeparatednessAxioms.Hausdorff_impl_net_limit_unique',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ( cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X)
=> cCoq_2eInit_2eLogic_2euniqueness___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2enet__limit___24a3(V1__I,V0__X,V2__x)) ) ) ) ) ).
fof('Topology.SeparatednessAxioms.T3_sep_impl_Hausdorff',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eSeparatednessAxioms_2eT3__sep___24a1(V0__X)
=> cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X) ) ) ).
fof('Topology.SeparatednessAxioms.net_limit_is_unique_cluster_point_impl_Hausdorff',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> ! [V3__x0] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V3__x0)
=> ! [V4__y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__y)
=> ( cTopology_2eNets_2enet__limit___24a4(V1__I,V0__X,V2__x,V3__x0)
=> ( cTopology_2eNets_2enet__cluster__point___24a4(V1__I,V0__X,V2__x,V4__y)
=> V4__y = V3__x0 ) ) ) ) ) )
=> cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X) ) ) ).
fof('Topology.SeparatednessAxioms.net_limit_uniqueness_impl_Hausdorff',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( ! [V1__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V1__I)
=> ! [V2__x] :
( cTopology_2eNets_2eNet___24t(V1__I,V0__X,V2__x)
=> cCoq_2eInit_2eLogic_2euniqueness___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eNets_2enet__limit___24a3(V1__I,V0__X,V2__x)) ) )
=> cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V0__X) ) ) ).
fof('Topology.SeparatednessAxioms.normal_sep_impl_T3_sep',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ( cTopology_2eSeparatednessAxioms_2enormal__sep___24a1(V0__X)
=> cTopology_2eSeparatednessAxioms_2eT3__sep___24a1(V0__X) ) ) ).
fof('Topology.Subbases.Build_TopologicalSpace_from_subbasis_subbasis',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> cTopology_2eSubbases_2esubbasis___24a2(cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis___24a2(V0__X,V1__S),V1__S) ) ) ).
fof('Topology.Subbases.Build_subbasis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__SB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__SB)
=> ( ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__SB,V2__U)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__U) ) )
=> ( ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ! [V4__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V4__x)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U)
=> ? [V7__A] :
( cType___24t(V7__A)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V7__A)
& ? [V8__V] :
( c_24__type__39698___24t(V0__X,V7__A,V8__V)
& ! [V9__a] :
( t(V9__a,V7__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__SB,happ(V8__V,V9__a)) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V7__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V8__V),V4__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V7__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V8__V),V3__U) ) ) ) ) ) )
=> cTopology_2eSubbases_2esubbasis___24a2(V0__X,V1__SB) ) ) ) ) ).
fof('Topology.Subbases.finite_intersections_of_subbasis_form_open_basis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__SB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__SB)
=> ( cTopology_2eSubbases_2esubbasis___24a2(V0__X,V1__SB)
=> cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__49387___24a2(V0__X,V1__SB))) ) ) ) ).
fof('Topology.Subbases.open_basis_is_subbasis',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__SB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__SB)
=> ( cTopology_2eOpenBases_2eopen__basis___24a2(V0__X,V1__SB)
=> cTopology_2eSubbases_2esubbasis___24a2(V0__X,V1__SB) ) ) ) ).
fof('Topology.Subbases.subbasis_cover',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__SB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__SB)
=> ( cTopology_2eSubbases_2esubbasis___24a2(V0__X,V1__SB)
=> ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ! [V4__x] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V0__X,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U,V4__x)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U)
=> ? [V7__A] :
( cType___24t(V7__A)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V7__A)
& ? [V8__V] :
( c_24__type__39698___24t(V0__X,V7__A,V8__V)
& ! [V9__a] :
( t(V9__a,V7__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__SB,happ(V8__V,V9__a)) )
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V7__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V8__V),V4__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V7__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V8__V),V3__U) ) ) ) ) ) ) ) ) ) ).
fof('Topology.Subbases.subbasis_elements',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__SB] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__SB)
=> ( cTopology_2eSubbases_2esubbasis___24a2(V0__X,V1__SB)
=> ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V3__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__SB,V3__U)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V3__U) ) ) ) ) ) ).
fof('Topology.SubspaceTopology.subspace_inc_continuous',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__A)
=> cTopology_2eContinuity_2econtinuous___24a3(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V0__X,V1__A),V0__X,cTopology_2eSubspaceTopology_2esubspace__inc___24a2(V0__X,V1__A)) ) ) ).
fof('Topology.SubspaceTopology.subspace_topology_topology',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__A)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cCoq_2eInit_2eSpecif_2esig___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),c_24__lam__39712___24a2(V0__X,V1__A)),V2__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V0__X,V1__A),V2__U)
=> ? [V4__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V4__V)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V4__V)
& V2__U = cZornsLemma_2eInverseImage_2einverse__image___24a4(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V0__X,V1__A)),cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cTopology_2eSubspaceTopology_2esubspace__inc___24a2(V0__X,V1__A),V4__V) ) ) ) ) ) ).
fof('Topology.SupInf.lt_plus_epsilon_le',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ! [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)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__y,V2__eps))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ) ) ).
fof('Topology.TopologicalSpaces.Build_TopologicalSpace_from_closed_sets_closed',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__closedP] :
( c_24__type__37437___24t(V0__X,V1__closedP)
=> ( p(happ(V1__closedP,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X)))
=> ( ! [V3__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__F)
=> ! [V4__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__G)
=> ( p(happ(V1__closedP,V3__F))
=> ( p(happ(V1__closedP,V4__G))
=> p(happ(V1__closedP,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__X,V3__F,V4__G))) ) ) ) )
=> ( ! [V4__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V4__F)
=> ( ! [V5__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V5__G)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V4__F,V5__G)
=> p(happ(V1__closedP,V5__G)) ) )
=> p(happ(V1__closedP,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__X,V4__F))) ) )
=> ! [V5__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace__from__closed__sets___24a2(V0__X,V1__closedP)),V5__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace__from__closed__sets___24a2(V0__X,V1__closedP),V5__F)
<=> p(happ(V1__closedP,V5__F)) ) ) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_complement_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U))
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__U) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_family_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ( ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__F,V2__S)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__S) ) )
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_finite_indexed_union',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V1__A)
=> ( ! [V4__a] :
( t(V4__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,happ(V2__F,V4__a)) )
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_indexed_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( ! [V3__a] :
( t(V3__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,happ(V2__F,V3__a)) )
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_intersection2',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__G)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__G)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F,V2__G)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_union2',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__G)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__G)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F,V2__G)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_empty',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))) ) ).
fof('Topology.TopologicalSpaces.open_family_union',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__F)
=> ( ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t)),V1__F,V2__S)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V2__S) ) )
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__F)) ) ) ) ).
fof('Topology.TopologicalSpaces.open_finite_indexed_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V1__A)
=> ( ! [V4__a] :
( t(V4__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,happ(V2__F,V4__a)) )
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_full',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t))) ) ).
fof('Topology.TopologicalSpaces.open_indexed_union',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( ! [V3__a] :
( t(V3__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,happ(V2__F,V3__a)) )
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_intersection2',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__U)
=> ! [V2__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V2__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V1__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V2__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__U,V2__V)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_union2',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ! [V2__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U,V2__V)) ) ) ) ) ) ).
fof('Topology.WeakTopology.intro_fa_inv_image',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__49944___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__49970___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__a] :
( t(V4__a,V1__A)
=> ! [V5__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(happ(V2__Y,V4__a)),V5__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(happ(V2__Y,V4__a),V5__V)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cTopology_2eWeakTopology_2eweak__topology__subbasis___24a4(V0__X,V1__A,V2__Y,V3__f),cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,cTopology_2eTopologicalSpaces_2epoint__set___24a1(happ(V2__Y,V4__a)),happ(V3__f,V4__a),V5__V)) ) ) ) ) ) ) ) ).
fof('Topology.WeakTopology.net_limit_in_weak_topology_impl_net_limit_in_projections',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__49944___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__50076___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__I] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V4__I)
=> ! [V5__x] :
( cTopology_2eNets_2eNet___24t(V4__I,cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),V5__x)
=> ! [V6__x0] :
( t(V6__x0,V0__X)
=> ( cTopology_2eNets_2enet__limit___24a4(V4__I,cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),V5__x,V6__x0)
=> ! [V8__a] :
( t(V8__a,V1__A)
=> cTopology_2eNets_2enet__limit___24a4(V4__I,happ(V2__Y,V8__a),c_24__lam__50093___24a7(V0__X,V1__A,V2__Y,V3__f,V4__I,V5__x,V8__a),happ(happ(V3__f,V8__a),V6__x0)) ) ) ) ) ) ) ) ) ) ).
fof('Topology.WeakTopology.weak_topology1_makes_continuous_func',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__39840___24t(V0__X,V1__Y,V2__f)
=> cTopology_2eContinuity_2econtinuous___24a3(cTopology_2eWeakTopology_2eWeakTopology1___24a3(V0__X,V1__Y,V2__f),V1__Y,V2__f) ) ) ) ).
fof('Topology.WeakTopology.weak_topology1_topology',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__39840___24t(V0__X,V1__Y,V2__f)
=> ! [V3__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(cTopology_2eWeakTopology_2eWeakTopology1___24a3(V0__X,V1__Y,V2__f),V3__U)
=> ? [V5__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V5__V)
& cTopology_2eTopologicalSpaces_2eopen___24a2(V1__Y,V5__V)
& V3__U = cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V1__Y),V2__f,V5__V) ) ) ) ) ) ) ).
fof('Topology.WeakTopology.weak_topology_is_weakest',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__49944___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__50045___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__T_27] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V4__T_27)
=> ( ! [V5__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V5__F)
=> ( ! [V6__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V5__F,V6__S)
=> p(happ(V4__T_27,V6__S)) ) )
=> p(happ(V4__T_27,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__X,V5__F))) ) )
=> ( ! [V6__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__U)
=> ! [V7__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V7__V)
=> ( p(happ(V4__T_27,V6__U))
=> ( p(happ(V4__T_27,V7__V))
=> p(happ(V4__T_27,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V6__U,V7__V))) ) ) ) )
=> ( p(happ(V4__T_27,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)))
=> ( ! [V8__a] :
( t(V8__a,V1__A)
=> cTopology_2eContinuity_2econtinuous___24a3(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(V0__X,V4__T_27),happ(V2__Y,V8__a),happ(V3__f,V8__a)) )
=> ! [V9__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V9__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),V9__U)
=> p(happ(V4__T_27,V9__U)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Topology.WeakTopology.weak_topology_makes_continuous_funcs',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__49944___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__50033___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__a] :
( t(V4__a,V1__A)
=> cTopology_2eContinuity_2econtinuous___24a3(cTopology_2eWeakTopology_2eWeakTopology___24a4(V0__X,V1__A,V2__Y,V3__f),happ(V2__Y,V4__a),happ(V3__f,V4__a)) ) ) ) ) ) ).
fof('Topology.WeakTopology.weak_topology_subbasis_ind',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__Y] :
( c_24__type__49944___24t(V1__A,V2__Y)
=> ! [V3__f] :
( c_24__type__49982___24t(V0__X,V1__A,V2__Y,V3__f)
=> ! [V4__P] :
( c_24__type__49989___24t(V0__X,V1__A,V2__Y,V4__P)
=> ( ! [V5__a] :
( t(V5__a,V1__A)
=> ! [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(happ(V2__Y,V5__a)),V6__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(happ(V2__Y,V5__a),V6__V)
=> p(happ(V4__P,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,cTopology_2eTopologicalSpaces_2epoint__set___24a1(happ(V2__Y,V5__a)),happ(V3__f,V5__a),V6__V))) ) ) )
=> ! [V6__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__e)
=> ( cTopology_2eWeakTopology_2eweak__topology__subbasis___24a5(V0__X,V1__A,V2__Y,V3__f,V6__e)
=> p(happ(V4__P,V6__e)) ) ) ) ) ) ) ) ) ).
fof('U0_in_U1',axiom,
cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cTopology_2eInteriorsClosures_2eclosure___24a2(cX,cU0),cU1) ).
fof('U0_open',axiom,
cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cU0) ).
fof('U1_open',axiom,
cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cU1) ).
fof('UrysohnsLemma.Urysohns_Lemma_construction.Un_open',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(V0__n)) ) ).
fof('ZornsLemma.CountableTypes.countable_downward_closed',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__T)
=> ( cZornsLemma_2eCountableTypes_2eCountable___24a2(V0__X,V2__T)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,V1__S,V2__T)
=> cZornsLemma_2eCountableTypes_2eCountable___24a2(V0__X,V1__S) ) ) ) ) ) ).
fof('ZornsLemma.CountableTypes.countable_img',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__S)
=> ( cZornsLemma_2eCountableTypes_2eCountable___24a2(V0__X,V3__S)
=> cZornsLemma_2eCountableTypes_2eCountable___24a2(V1__Y,cCoq_2eSets_2eImage_2eIm___24a4(V0__X,V1__Y,V3__S,V2__f)) ) ) ) ) ) ).
fof('ZornsLemma.CountableTypes.intro_nat_injection',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( c_24__type__8907___24t(V0__X,V1__f)
=> ( cZornsLemma_2eFunctionProperties_2einjective___24a3(V0__X,cCoq_2eInit_2eDatatypes_2enat,V1__f)
=> cZornsLemma_2eCountableTypes_2eCountableT___24a1(V0__X) ) ) ) ).
fof('ZornsLemma.EnsemblesSpec.intro_characteristic_sat',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__P] :
( c_24__type__8715___24t(V0__X,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P),V2__x) ) ) ) ) ).
fof('ZornsLemma.Families.empty_family_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T))) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__T) ) ).
fof('ZornsLemma.Families.empty_family_union',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T))) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__T) ) ).
fof('ZornsLemma.Families.family_intersection_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__x] :
( t(V2__x,V0__T)
=> ( ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V3__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V3__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V3__S,V2__x) ) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,V1__F),V2__x) ) ) ) ) ).
fof('ZornsLemma.Families.family_union_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V2__S)
=> ! [V3__x] :
( t(V3__x,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V2__S,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V1__F),V3__x) ) ) ) ) ) ) ).
fof('ZornsLemma.Families.subfamily_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__G] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V2__G)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__G)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,V2__G),cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,V1__F)) ) ) ) ) ).
fof('ZornsLemma.Families.subfamily_union',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__G] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V2__G)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__G)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V1__F),cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V2__G)) ) ) ) ) ).
fof('ZornsLemma.FiniteIntersections.finite_intersections_ind',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> ! [V2__P] :
( c_24__type__37437___24t(V0__X,V2__P)
=> ( p(happ(V2__P,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)))
=> ( ! [V4__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V4__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__S,V4__U)
=> p(happ(V2__P,V4__U)) ) )
=> ( ! [V5__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V5__U)
=> ! [V6__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V5__U)
=> ( p(happ(V2__P,V5__U))
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V6__V)
=> ( p(happ(V2__P,V6__V))
=> p(happ(V2__P,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V5__U,V6__V))) ) ) ) ) ) )
=> ! [V6__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V6__e)
=> ( cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a3(V0__X,V1__S,V6__e)
=> p(happ(V2__P,V6__e)) ) ) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteIntersections.intro_S',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),V1__S,V2__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V2__U) ) ) ) ) ).
fof('ZornsLemma.FiniteIntersections.intro_full',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X)) ) ) ).
fof('ZornsLemma.FiniteIntersections.intro_intersection',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__X,V1__S)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V2__U)
=> ! [V3__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V3__V)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),V3__V)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__X),cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V0__X,V1__S),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,V2__U,V3__V)) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteTypes.FiniteT_img',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V0__X)
=> ( ! [V4__y1] :
( t(V4__y1,V1__Y)
=> ! [V5__y2] :
( t(V5__y2,V1__Y)
=> ( V4__y1 = V5__y2
| V4__y1 != V5__y2 ) ) )
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V1__Y,cCoq_2eSets_2eImage_2eIm___24a4(V0__X,V1__Y,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X),V2__f)) ) ) ) ) ) ).
fof('ZornsLemma.FiniteTypes.FiniteT_ind',axiom,
! [V0__P] :
( c_24__type__28214___24t(V0__P)
=> ( p(happ(V0__P,c_24False))
=> ( ! [V2__T] :
( cType___24t(V2__T)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V2__T)
=> ( p(happ(V0__P,V2__T))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eoption___24a1(V2__T))) ) ) )
=> ( ! [V3__X] :
( cType___24t(V3__X)
=> ! [V4__Y] :
( cType___24t(V4__Y)
=> ! [V5__f] :
( c_24__type__16948___24t(V3__X,V4__Y,V5__f)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V3__X)
=> ( p(happ(V0__P,V3__X))
=> ( cZornsLemma_2eFunctionProperties_2einvertible___24a3(V3__X,V4__Y,V5__f)
=> p(happ(V0__P,V4__Y)) ) ) ) ) ) )
=> ! [V4__T] :
( cType___24t(V4__T)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V4__T)
=> p(happ(V0__P,V4__T)) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteTypes.Finite_ens_type',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__X,V1__S)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__X,V1__S)
=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eSpecif_2esig___24a2(V0__X,c_24__lam__38269___24a2(V0__X,V1__S))) ) ) ) ).
fof('ZornsLemma.FiniteTypes.True_finite',axiom,
cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(c_24True) ).
fof('ZornsLemma.FiniteTypes.add_finite',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V0__T)
=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__T)) ) ) ).
fof('ZornsLemma.FiniteTypes.bij_finite',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V0__X)
=> ( cZornsLemma_2eFunctionProperties_2einvertible___24a3(V0__X,V1__Y,V2__f)
=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V1__Y) ) ) ) ) ) ).
fof('ZornsLemma.FiniteTypes.empty_finite',axiom,
cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(c_24False) ).
fof('ZornsLemma.FiniteTypes.finite_choice',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__24818___24t(V0__A,V1__B,V2__R)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V0__A)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ? [V5__y] :
( t(V5__y,V1__B)
& p(happ(happ(V2__R,V4__x),V5__y)) ) )
=> ? [V5__f] :
( c_24__type__16948___24t(V0__A,V1__B,V5__f)
& ! [V6__x] :
( t(V6__x,V0__A)
=> p(happ(happ(V2__R,V6__x),happ(V5__f,V6__x))) ) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteTypes.inj_finite',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V1__Y)
=> ( cZornsLemma_2eFunctionProperties_2einjective___24a3(V0__X,V1__Y,V2__f)
=> ( ! [V5__y] :
( t(V5__y,V1__Y)
=> ( ? [V6__x] :
( t(V6__x,V0__X)
& happ(V2__f,V6__x) = V5__y )
| ~ ? [V6__x] :
( t(V6__x,V0__X)
& happ(V2__f,V6__x) = V5__y ) ) )
=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V0__X) ) ) ) ) ) ) ).
fof('ZornsLemma.FunctionProperties.intro_invertible',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ! [V3__g] :
( c_24__type__10973___24t(V0__X,V1__Y,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> happ(V3__g,happ(V2__f,V4__x)) = V4__x )
=> ( ! [V5__y] :
( t(V5__y,V1__Y)
=> happ(V2__f,happ(V3__g,V5__y)) = V5__y )
=> cZornsLemma_2eFunctionProperties_2einvertible___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.empty_indexed_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(c_24False,V0__T,V1__F)
=> cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(c_24False,V0__T,V1__F) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__T) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_intersection_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V0__A,V1__T,V2__F)
=> ! [V3__x] :
( t(V3__x,V1__T)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,happ(V2__F,V4__a),V3__x) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V0__A,V1__T,V2__F),V3__x) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_to_family_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,V0__T,V2__F)
=> cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__A,V0__T,V2__F) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V0__T,V1__A,V2__F)) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_to_family_union',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,V0__T,V2__F)
=> cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,V0__T,V2__F) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V0__T,V1__A,V2__F)) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_union_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V0__A,V1__T,V2__F)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__x] :
( t(V4__x,V1__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,happ(V2__F,V3__a),V4__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V0__A,V1__T,V2__F),V4__x) ) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.sub_indexed_intersection',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__T] :
( cType___24t(V2__T)
=> ! [V3__f] :
( c_24__type__16948___24t(V0__A,V1__B,V3__f)
=> ! [V4__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__B,V2__T,V4__F)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V2__T,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__B,V2__T,V4__F),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V0__A,V2__T,c_24__let__5__subF__43863___24a5(V0__A,V1__B,V2__T,V3__f,V4__F))) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.sub_indexed_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__T] :
( cType___24t(V2__T)
=> ! [V3__f] :
( c_24__type__16948___24t(V0__A,V1__B,V3__f)
=> ! [V4__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__B,V2__T,V4__F)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V2__T,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V0__A,V2__T,c_24__let__5__subF__43860___24a5(V0__A,V1__B,V2__T,V3__f,V4__F)),cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__B,V2__T,V4__F)) ) ) ) ) ) ).
fof('ZornsLemma.InfiniteTypes.finite_nat_initial_segment',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__38422___24a1(V0__n))) ) ).
fof('ZornsLemma.InverseImage.inverse_image_complement',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V1__Y,V3__T)) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T)) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_composition',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__Z] :
( cType___24t(V2__Z)
=> ! [V3__f] :
( c_24__type__16948___24t(V1__Y,V2__Z,V3__f)
=> ! [V4__g] :
( c_24__type__44249___24t(V0__X,V1__Y,V2__Z,V4__g)
=> ! [V5__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V2__Z,V5__U)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V2__Z,c_24__lam__44263___24a5(V0__X,V1__Y,V2__Z,V3__f,V4__g),V5__U) = cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V4__g,cZornsLemma_2eInverseImage_2einverse__image___24a4(V1__Y,V2__Z,V3__f,V5__U)) ) ) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_empty',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V1__Y)) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_full',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V1__Y)) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_increasing',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T1)
=> ! [V4__T2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V4__T2)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V1__Y,V3__T1,V4__T2)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T1),cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V4__T2)) ) ) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_intersection',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__16948___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T1)
=> ! [V4__T2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V4__T2)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V1__Y,V3__T1,V4__T2)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T1),cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V4__T2)) ) ) ) ) ) ).
fof('ZornsLemma.Proj1SigInjective.proj1_sig_injective',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__8715___24t(V0__A,V1__P)
=> ! [V2__a1] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,c_24__lam__45294___24a2(V0__A,V1__P),V2__a1)
=> ! [V3__a2] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,c_24__lam__45298___24a2(V0__A,V1__P),V3__a2)
=> ( cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,c_24__lam__45302___24a2(V0__A,V1__P),V2__a1) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,c_24__lam__45306___24a2(V0__A,V1__P),V3__a2)
=> V2__a1 = V3__a2 ) ) ) ) ) ).
fof('ZornsLemma.Proj1SigInjective.subset_eq_compatT',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__8715___24t(V0__U,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( p(happ(V1__P,V2__x))
=> ( p(happ(V1__P,V3__y))
=> ( V2__x = V3__y
=> cCoq_2eInit_2eSpecif_2eexist___24a3(V0__U,V1__P,V2__x) = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__U,V1__P,V3__y) ) ) ) ) ) ) ) ).
fof('ZornsLemma.ZornsLemma.sup_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__T,V1__R)
=> ! [V2__chain__sup] :
( c_24__type__50842___24t(V0__T,V1__R,V2__chain__sup)
=> ! [V3__inflation] :
( c_24__type__51101___24t(V0__T,V1__R,V3__inflation)
=> ! [V4__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V4__S)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__T,V4__S,cZornsLemma_2eZornsLemma_2etower___24a4(V0__T,V1__R,V2__chain__sup,V3__inflation))
=> ( cZornsLemma_2eZornsLemma_2echain___24a3(V0__T,V1__R,V4__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eZornsLemma_2etower___24a4(V0__T,V1__R,V2__chain__sup,V3__inflation),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__T,c_24__lam__50517___24a3(V0__T,V1__R,V4__S),happ(V2__chain__sup,V4__S))) ) ) ) ) ) ) ) ).
fof('ZornsLemma.ZornsLemma.tower_ind',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__T,V1__R)
=> ! [V2__chain__sup] :
( c_24__type__50842___24t(V0__T,V1__R,V2__chain__sup)
=> ! [V3__inflation] :
( c_24__type__51101___24t(V0__T,V1__R,V3__inflation)
=> ! [V4__P] :
( c_24__type__51405___24t(V0__T,V1__R,V4__P)
=> ( ! [V5__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V5__S)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__T,V5__S,cZornsLemma_2eZornsLemma_2etower___24a4(V0__T,V1__R,V2__chain__sup,V3__inflation))
=> ( ! [V7__x] :
( t(V7__x,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V5__S,V7__x)
=> p(happ(V4__P,V7__x)) ) )
=> ( cZornsLemma_2eZornsLemma_2echain___24a3(V0__T,V1__R,V5__S)
=> p(happ(V4__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__T,c_24__lam__50517___24a3(V0__T,V1__R,V5__S),happ(V2__chain__sup,V5__S)))) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eZornsLemma_2etower___24a4(V0__T,V1__R,V2__chain__sup,V3__inflation),V6__x)
=> ( p(happ(V4__P,V6__x))
=> p(happ(V4__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__T,c_24__lam__50608___24a3(V0__T,V1__R,V6__x),happ(V3__inflation,V6__x)))) ) ) )
=> ! [V7__t] :
( t(V7__t,V0__T)
=> ( cZornsLemma_2eZornsLemma_2etower___24a5(V0__T,V1__R,V2__chain__sup,V3__inflation,V7__t)
=> p(happ(V4__P,V7__t)) ) ) ) ) ) ) ) ) ) ).
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_Topology.OpenBases.open_basis_cover_cond_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eOpenBases_2eopen__basis__cover__cond,V_24X1),V_24X2))
<=> cTopology_2eOpenBases_2eopen__basis__cover__cond___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.Filters.ultrafilter_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eFilters_2eultrafilter,V_24X1),V_24X2))
<=> cTopology_2eFilters_2eultrafilter___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_38116_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__38116,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__38116___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_44418_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__44418,V_24X1),V_24X2),V_24X3) = c_24__lam__44418___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_44587_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__44587,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__44587___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Lists.List.seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eseq,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eseq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Singleton_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSingleton,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSingleton___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Subbases.Build_TopologicalSpace_from_subbasis_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis,V_24X1),V_24X2) = cTopology_2eSubbases_2eBuild__TopologicalSpace__from__subbasis___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_35677_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35677,V_24X1) = c_24__lam__35677___24a1(V_24X1) ).
fof('$adef_$_lam_39712_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__39712,V_24X1),V_24X2) = c_24__lam__39712___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEmul_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEmul,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_ZornsLemma.Families.FamilyUnion_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.R_dist_$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('$adef_Coq.Sets.Ensembles.Empty_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eEmpty__set,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eEmpty__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_set_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTopology_2eNets_2eneighborhood__net__DS__set__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTopology_2eNets_2eneighborhood__net__DS__set__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_lam_37275_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__37275,V_24X1),V_24X2) = c_24__lam__37275___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.Quotients.equiv_classes_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eQuotients_2eequiv__classes,V_24X1),V_24X2) = cZornsLemma_2eQuotients_2eequiv__classes___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_49387_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__49387,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__49387___24a3(V_24X1,V_24X2,V_24X3) ) ).
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_50517_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__50517,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__50517___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_Topology.Continuity.continuous_at_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eContinuity_2econtinuous__at,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eContinuity_2econtinuous__at___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_38587_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__38587,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__38587___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Sets.Cpo.Upper_Bound_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eUpper__Bound,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$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('$adef_Topology.InteriorsClosures.Build_TopologicalSpace_from_closure_operator_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__closure__operator,V_24X1),V_24X2) = cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__closure__operator___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_43870_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__43870,V_24X1),V_24X2) = c_24__lam__43870___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_35441_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35441,V_24X1),V_24X2) = c_24__prop__35441___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39212_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39212,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39212___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_ZornsLemma.FiniteTypes.FiniteT_$a1',axiom,
! [V_24X1] :
( p(happ(cZornsLemma_2eFiniteTypes_2eFiniteT,V_24X1))
<=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$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_$_let_5_subF_43863_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__5__subF__43863,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__5__subF__43863___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Topology.CountabilityAxioms.separable_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eCountabilityAxioms_2eseparable,V_24X1))
<=> cTopology_2eCountabilityAxioms_2eseparable___24a1(V_24X1) ) ).
fof('$adef_ZornsLemma.FiniteIntersections.finite_intersections_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFiniteIntersections_2efinite__intersections,V_24X1),V_24X2) = cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39398_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39398,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39398___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_ZornsLemma.Families.FamilyIntersection_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyIntersection,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_44890_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__44890,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__44890___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_38269_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38269,V_24X1),V_24X2) = c_24__lam__38269___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_let_6_lmp_1750_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__1750,V_24X1) = c_24__let__6__lmp__1750___24a1(V_24X1) ).
fof('$adef_Topology.FiltersAndNets.filter_to_net_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2efilter__to__net,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2efilter__to__net___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Topology.Nets.neighborhood_net_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eneighborhood__net,V_24X1),V_24X2) = cTopology_2eNets_2eneighborhood__net___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_44894_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__44894,V_24X1),V_24X2),V_24X3) = c_24__lam__44894___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_44890_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__44890,V_24X1),V_24X2),V_24X3) = c_24__lam__44890___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Sets.Ensembles.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_38864_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__38864,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__38864___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_2_C_41753_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__41753,V_24X1),V_24X2) = c_24__let__2__C__41753___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('$adef_$_lam_39150_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__39150,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__39150___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_43888_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__43888,V_24X1),V_24X2) = c_24__lam__43888___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35684_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35684,V_24X1),V_24X2) = c_24__prop__35684___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_41217_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__41217,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__41217___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_let_2_C_42249_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__42249,V_24X1),V_24X2) = c_24__let__2__C__42249___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.CountabilityAxioms.second_countable_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eCountabilityAxioms_2esecond__countable,V_24X1))
<=> cTopology_2eCountabilityAxioms_2esecond__countable___24a1(V_24X1) ) ).
fof('$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.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.Rle_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2eRle__dec,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons2_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.SubspaceTopology.SubspaceTopology_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eSubspaceTopology_2eSubspaceTopology,V_24X1),V_24X2) = cTopology_2eSubspaceTopology_2eSubspaceTopology___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.IndexedFamilies.ImageFamily_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eImageFamily,V_24X1),V_24X2),V_24X3) = cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Partial_Order.Definition_of_PO_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Topology.TopologicalSpaces.open_$a1',axiom,
! [V_24X1] : happ(cTopology_2eTopologicalSpaces_2eopen,V_24X1) = cTopology_2eTopologicalSpaces_2eopen___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Specif.sig$51063_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esig_2451063,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eSpecif_2esig_2451063___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_41013_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__41013,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__41013___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_2_C_41463_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__41463,V_24X1),V_24X2) = c_24__let__2__C__41463___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Directed_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eDirected,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eDirected___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.TopologicalSpaces.closed_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eTopologicalSpaces_2eclosed,V_24X1),V_24X2))
<=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Partial_Order.Carrier_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eCarrier__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$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_39350_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39350,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39350___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Sets.Ensembles.Subtract_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSubtract,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Couple_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eCouple,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eCouple___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.Filters.Build_Filter_from_subbasis_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilters_2eBuild__Filter__from__subbasis,V_24X1),V_24X2) = cTopology_2eFilters_2eBuild__Filter__from__subbasis___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Powerset.Inclusion_is_an_order_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePowerset_2eInclusion__is__an__order,V_24X1) = cCoq_2eSets_2ePowerset_2eInclusion__is__an__order___24a1(V_24X1) ).
fof('$adef_$_let_2_C_41607_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__41607,V_24X1),V_24X2) = c_24__let__2__C__41607___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1) = cCoq_2eVectors_2eVectorDef_2econs___24a1(V_24X1) ).
fof('$adef_$_lam_50608_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__50608,V_24X1),V_24X2),V_24X3) = c_24__lam__50608___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Empty_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEmpty__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V_24X1) ).
fof('$adef_$_prop_35440_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35440,V_24X1),V_24X2) = c_24__prop__35440___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_44263_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__44263,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__44263___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Ensembles.Complement_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Powerset.Power_set_Inhabited_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePowerset_2ePower__set__Inhabited,V_24X1),V_24X2) = cCoq_2eSets_2ePowerset_2ePower__set__Inhabited___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_52139_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__52139,V_24X1),V_24X2))
<=> c_24__lam__52139___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
fof('$adef_Topology.Neighborhoods.neighborhood_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoods_2eneighborhood,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoods_2eneighborhood___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('$adef_ZornsLemma.InverseImage.inverse_image_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cZornsLemma_2eInverseImage_2einverse__image,V_24X1),V_24X2),V_24X3),V_24X4) = cZornsLemma_2eInverseImage_2einverse__image___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_39350_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__39350,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__39350___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Sets.Cpo.Directed_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eDirected__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eCpo_2eDirected__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_38507_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__38507,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__38507___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Topology.Nets.Subnet_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cTopology_2eNets_2eSubnet,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cTopology_2eNets_2eSubnet___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_51609_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__51609,V_24X1),V_24X2) = c_24__lam__51609___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39336_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__39336,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__39336___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_41148_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__41148,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__41148___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.RiemannInt_SF.mkStepFun_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2emkStepFun,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eReals_2eRiemannInt__SF_2emkStepFun___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Topology.Nets.cluster_point_subnet_DS_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet__DS___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.MetricSpaces.metric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eMetricSpaces_2emetric,V_24X1),V_24X2))
<=> cTopology_2eMetricSpaces_2emetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_45401_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__45401,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__45401___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.SeqProp.Un_decreasing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eSeqProp_2eUn__decreasing,V_24X1))
<=> cCoq_2eReals_2eSeqProp_2eUn__decreasing___24a1(V_24X1) ) ).
fof('$adef_$_lam_38900_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__38900,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__38900___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eneighborhood__net__DS__set,V_24X1),V_24X2) = cTopology_2eNets_2eneighborhood__net__DS__set___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_$_let_5_subF_43860_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__5__subF__43860,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__5__subF__43860___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_$_lam_37373_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__37373,V_24X1),V_24X2) = c_24__lam__37373___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_45132_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__45132,V_24X1),V_24X2),V_24X3) = c_24__lam__45132___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.InteriorsClosures.Build_TopologicalSpace_from_interior_operator_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__interior__operator,V_24X1),V_24X2) = cTopology_2eInteriorsClosures_2eBuild__TopologicalSpace__from__interior__operator___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_41027_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__41027,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__41027___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_ZornsLemma.ZornsLemma.chains_ord_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cZornsLemma_2eZornsLemma_2echains__ord,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cZornsLemma_2eZornsLemma_2echains__ord___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Ensembles.Singleton_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eSingleton,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Complement_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eComplement___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_lam_39043_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__39043,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__39043___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_45302_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__45302,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__45302___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_var_var_13_y_11472_11475_11538_$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__11472__11475__11538,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__11472__11475__11538___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_lam_44306_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__44306,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__44306___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_45144_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__45144,V_24X1),V_24X2),V_24X3) = c_24__lam__45144___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_ZornsLemma.CountableTypes.Countable_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cZornsLemma_2eCountableTypes_2eCountable,V_24X1),V_24X2))
<=> cZornsLemma_2eCountableTypes_2eCountable___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalDependentChoice_on_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on,V_24X1))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Partial_Order.Rel_of_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eRel__of,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Ensembles.Strict_Included_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eStrict__Included,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.DirectedSets.exists_arbitrarily_large_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eDirectedSets_2eexists__arbitrarily__large,V_24X1),V_24X2))
<=> cTopology_2eDirectedSets_2eexists__arbitrarily__large___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_2_C_41956_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__41956,V_24X1),V_24X2) = c_24__let__2__C__41956___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_18344_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__18344,V_24X1),V_24X2) = c_24__prop__18344___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.BFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eTauto_2eBFormula,V_24X1) = cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.id_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_42592_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__42592,V_24X1),V_24X2),V_24X3) = c_24__lam__42592___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_41198_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__41198,V_24X1),V_24X2) = c_24__lam__41198___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEadd_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_37771_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__37771,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__37771___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_45651_$a1',axiom,
! [V_24X1] : happ(c_24__lam__45651,V_24X1) = c_24__lam__45651___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_$_lam_49784_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__49784,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> c_24__lam__49784___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_let_17_mkopp_pow_12389_$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__12389,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__12389___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Topology.MetricSpaces.metric_topology_neighborhood_basis_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_39227_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__39227,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__39227___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_lam_45314_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__45314,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__45314___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_43888_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__43888,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__43888___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_3_R_41754_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__41754,V_24X1),V_24X2) = c_24__let__3__R__41754___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_2_C_42115_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__42115,V_24X1),V_24X2) = c_24__let__2__C__42115___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_14_s1_11510_11514_11560_$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__11510__11514__11560,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__11510__11514__11560___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Init.Datatypes.inl_$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('$adef_Topology.FiltersAndNets.tail_filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2etail__filter,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2etail__filter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_37275_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__37275,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__37275___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_49784_$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__lam__49784,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__49784___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Topology.Filters.filter_subbasis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eFilters_2efilter__subbasis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eFilters_2efilter__subbasis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Nets.cluster_point_subnet_DS_set_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS__set,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet__DS__set___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_38422_$a1',axiom,
! [V_24X1] : happ(c_24__lam__38422,V_24X1) = c_24__lam__38422___24a1(V_24X1) ).
fof('$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.Sets.Ensembles.Union_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eUnion,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eUnion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Strings.String.length_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2elength,V_24X1) = cCoq_2eStrings_2eString_2elength___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Conditionally_complete_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_37771_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__37771,V_24X1),V_24X2) = c_24__lam__37771___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_50608_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__50608,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__50608___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.SeparatednessAxioms.T1_sep_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eSeparatednessAxioms_2eT1__sep,V_24X1))
<=> cTopology_2eSeparatednessAxioms_2eT1__sep___24a1(V_24X1) ) ).
fof('$adef_Topology.NeighborhoodBases.neighborhood_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoodBases_2eneighborhood__basis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoodBases_2eneighborhood__basis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_41963_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__41963,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__41963___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_ZornsLemma.Families.FamilyUnion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFamilies_2eFamilyUnion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_var_var_13_y_11485_11489_11547_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__11485__11489__11547,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__11485__11489__11547___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Topology.InteriorsClosures.interior_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eInteriorsClosures_2einterior,V_24X1),V_24X2) = cTopology_2eInteriorsClosures_2einterior___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38124_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38124,V_24X1),V_24X2),V_24X3) = c_24__lam__38124___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Couple_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eCouple,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eCouple___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Topology.Subbases.subbasis_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eSubbases_2esubbasis,V_24X1),V_24X2))
<=> cTopology_2eSubbases_2esubbasis___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_39032_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__39032,V_24X1),V_24X2) = c_24__lam__39032___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.net_limit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eNets_2enet__limit,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eNets_2enet__limit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Topology.InteriorsClosures.closure_$a1',axiom,
! [V_24X1] : happ(cTopology_2eInteriorsClosures_2eclosure,V_24X1) = cTopology_2eInteriorsClosures_2eclosure___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Relations_1.Antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eAntisymmetric,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.TopologicalSpaces.open_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eTopologicalSpaces_2eopen,V_24X1),V_24X2))
<=> cTopology_2eTopologicalSpaces_2eopen___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Ensembles.Setminus_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSetminus,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eSetminus___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_37373_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__37373,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__37373___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.AltSeries.tg_alt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eAltSeries_2etg__alt,V_24X1),V_24X2) = cCoq_2eReals_2eAltSeries_2etg__alt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Finite_sets.cardinal_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eFinite__sets_2ecardinal,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_lam_45144_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45144,V_24X1),V_24X2) = c_24__lam__45144___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_41148_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__41148,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__41148___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_lam_44370_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__44370,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__44370___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_38484_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__38484,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__38484___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Topology.MetricSpaces.open_ball_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eMetricSpaces_2eopen__ball,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eMetricSpaces_2eopen__ball___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_39252_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39252,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39252___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_Topology.InteriorsClosures.dense_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eInteriorsClosures_2edense,V_24X1),V_24X2))
<=> cTopology_2eInteriorsClosures_2edense___24a2(V_24X1,V_24X2) ) ).
fof('$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.Init.Nat.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_44321_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__44321,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__44321___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_$_lam_45294_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__45294,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__45294___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Partial_Order.covers_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2ecovers,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.OpenBases.open_basis_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eOpenBases_2eopen__basis,V_24X1),V_24X2))
<=> cTopology_2eOpenBases_2eopen__basis___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Reals.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_Topology.FiniteIntersectionLemmas.finite_intersections_len_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len,V_24X1),V_24X2),V_24X3) = cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_37632_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__37632,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__37632___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Ranalysis1.continuity_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRanalysis1_2econtinuity,V_24X1))
<=> cCoq_2eReals_2eRanalysis1_2econtinuity___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Inhabited_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eInhabited,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Cpo.Lower_Bound_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLower__Bound,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_let_var_var_15_s2_11511_11515_11561_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__15__s2__11511__11515__11561,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__15__s2__11511__11515__11561___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Reals.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.Reals.RList.ordered_Rlist_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRList_2eordered__Rlist,V_24X1))
<=> cCoq_2eReals_2eRList_2eordered__Rlist___24a1(V_24X1) ) ).
fof('$adef_Topology.SupInf.inf_$a1',axiom,
! [V_24X1] : happ(cTopology_2eSupInf_2einf,V_24X1) = cTopology_2eSupInf_2einf___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eltb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eltb___24a2(V_24X1,V_24X2) ).
fof('$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.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_$_lam_41181_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__41181,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__41181___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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_44418_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__44418,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__44418___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.SubspaceTopology.subspace_inc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eSubspaceTopology_2esubspace__inc,V_24X1),V_24X2) = cTopology_2eSubspaceTopology_2esubspace__inc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rseries.Rmax_N_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRseries_2eRmax__N,V_24X1),V_24X2) = cCoq_2eReals_2eRseries_2eRmax__N___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedUnion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedUnion,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.Un_cv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRseries_2eUn__cv,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRseries_2eUn__cv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_var_var_13_y_11509_11513_11559_$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__11509__11513__11559,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__11509__11513__11559___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_set_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eNets_2eneighborhood__net__DS__set__rec,V_24X1),V_24X2),V_24X3) = cTopology_2eNets_2eneighborhood__net__DS__set__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_50093_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__50093,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__50093___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Topology.InteriorsClosures.interior_$a1',axiom,
! [V_24X1] : happ(cTopology_2eInteriorsClosures_2einterior,V_24X1) = cTopology_2eInteriorsClosures_2einterior___24a1(V_24X1) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedUnion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedUnion,V_24X1),V_24X2),V_24X3) = cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.Nets.net_cluster_point_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eNets_2enet__cluster__point,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eNets_2enet__cluster__point___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_let_3_R_42250_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__42250,V_24X1),V_24X2) = c_24__let__3__R__42250___24a2(V_24X1,V_24X2) ).
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('$adef_Topology.OpenBases.open_basis_cond_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eOpenBases_2eopen__basis__cond,V_24X1),V_24X2))
<=> cTopology_2eOpenBases_2eopen__basis__cond___24a2(V_24X1,V_24X2) ) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.MetricSpaces.metrizes_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eMetricSpaces_2emetrizes,V_24X1),V_24X2))
<=> cTopology_2eMetricSpaces_2emetrizes___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.DirectedSets.eventually_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eDirectedSets_2eeventually,V_24X1),V_24X2))
<=> cTopology_2eDirectedSets_2eeventually___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.cluster_point_subnet_DS_ord_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS__ord,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_44737_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__44737,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__44737___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Sets.Ensembles.Included_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIncluded,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.Init.Nat.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Cpo.Conditionally_complete_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$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_Topology.Nets.neighborhood_net_DS_ord_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eneighborhood__net__DS__ord,V_24X1),V_24X2) = cTopology_2eNets_2eneighborhood__net__DS__ord___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.DirectedSets.Build_DirectedSet_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eDirectedSets_2eBuild__DirectedSet,V_24X1),V_24X2) = cTopology_2eDirectedSets_2eBuild__DirectedSet___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rseries.Un_growing_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRseries_2eUn__growing,V_24X1))
<=> cCoq_2eReals_2eRseries_2eUn__growing___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_Topology.OrderTopology.order_topology_subbasis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eOrderTopology_2eorder__topology__subbasis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eOrderTopology_2eorder__topology__subbasis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_lam_39741_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__39741,V_24X1),V_24X2))
<=> c_24__lam__39741___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_43870_$a1',axiom,
! [V_24X1] : happ(c_24__lam__43870,V_24X1) = c_24__lam__43870___24a1(V_24X1) ).
fof('$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_Topology.Filters.Build_Filter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilters_2eBuild__Filter,V_24X1),V_24X2) = cTopology_2eFilters_2eBuild__Filter___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_42253_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__42253,V_24X1),V_24X2),V_24X3) = c_24__lam__42253___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_ZornsLemma.Families.Family_$a1',axiom,
! [V_24X1] : happ(cZornsLemma_2eFamilies_2eFamily,V_24X1) = cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1) ).
fof('$adef_$_lam_45298_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45298,V_24X1),V_24X2) = c_24__lam__45298___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_44370_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__44370,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__44370___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_2297_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__2297,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__2297___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.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_Topology.FiltersAndNets.Build_filter_to_net_DS_set_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eFiltersAndNets_2eBuild__filter__to__net__DS__set___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Relations_1.Order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eOrder,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.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.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.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.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_Topology.FiltersAndNets.filter_to_net_DS_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2efilter__to__net__DS__set,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24a2(V_24X1,V_24X2) ).
fof('$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_$_let_var_var_12_x_11508_11512_11558_$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__11508__11512__11558,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__11508__11512__11558___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Reals.Ranalysis1.plus_fct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRanalysis1_2eplus__fct,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRanalysis1_2eplus__fct___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.fst_$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('$adef_$_lam_2297_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__2297,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__2297___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.Init.Nat.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2esqrt,V_24X1) = cCoq_2eInit_2eNat_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Topology.Nets.cps_i_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTopology_2eNets_2ecps__i,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTopology_2eNets_2ecps__i___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Ensembles.Intersection_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Sets.Cpo.Lub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLub,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eLub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_ZornsLemma.FunctionProperties.surjective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFunctionProperties_2esurjective,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFunctionProperties_2esurjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.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_Topology.FiltersAndNets.ftn_S_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2eftn__S,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2eftn__S___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.FilterLimits.filter_cluster_point_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eFilterLimits_2efilter__cluster__point,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eFilterLimits_2efilter__cluster__point___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedIntersection_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedIntersection,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39252_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__39252,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__39252___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_lam_38120_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__38120,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__38120___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$adef_$_lam_38900_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38900,V_24X1),V_24X2),V_24X3) = c_24__lam__38900___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Intersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
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('$adef_ZornsLemma.ZornsLemma.chains_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eZornsLemma_2echains,V_24X1),V_24X2) = cZornsLemma_2eZornsLemma_2echains___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('$adef_Topology.SeparatednessAxioms.T3_sep_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eSeparatednessAxioms_2eT3__sep,V_24X1))
<=> cTopology_2eSeparatednessAxioms_2eT3__sep___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.RiemannInt_SF.open_interval_$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('$adef_Topology.Completeness.complete_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eCompleteness_2ecomplete,V_24X1),V_24X2))
<=> cTopology_2eCompleteness_2ecomplete___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.OpenBases.Build_TopologicalSpace_from_open_basis_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eOpenBases_2eBuild__TopologicalSpace__from__open__basis,V_24X1),V_24X2) = cTopology_2eOpenBases_2eBuild__TopologicalSpace__from__open__basis___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.ZornsLemma.chain_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eZornsLemma_2echain,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eZornsLemma_2echain___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.TopologicalSpaces.point_set_$a1',axiom,
! [V_24X1] : happ(cTopology_2eTopologicalSpaces_2epoint__set,V_24X1) = cTopology_2eTopologicalSpaces_2epoint__set___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('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_$_lam_44886_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__44886,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__44886___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RiemannInt_SF.fe_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2efe,V_24X1),V_24X2),V_24X3) = cCoq_2eReals_2eRiemannInt__SF_2efe___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Topology.Completeness.d_restriction_metric_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eCompleteness_2ed__restriction__metric,V_24X1),V_24X2),V_24X3) = cTopology_2eCompleteness_2ed__restriction__metric___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_45314_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45314,V_24X1),V_24X2) = c_24__lam__45314___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_5_subF_43863_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__5__subF__43863,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__5__subF__43863___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_$_lam_43872_$a1',axiom,
! [V_24X1] : happ(c_24__lam__43872,V_24X1) = c_24__lam__43872___24a1(V_24X1) ).
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('$adef_$_let_17_mkopp_pow_12389_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__12389,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__12389___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$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_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.Sets.Ensembles.Setminus_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSetminus,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Full_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eFull__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.FiltersAndNets.ftn_x_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2eftn__x,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2eftn__x___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.WeakTopology.weak_topology_subbasis_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cTopology_2eWeakTopology_2eweak__topology__subbasis,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cTopology_2eWeakTopology_2eweak__topology__subbasis___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Topology.Filters.filter_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eFilters_2efilter__basis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eFilters_2efilter__basis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_var_var_12_x_11484_11488_11546_$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__11484__11488__11546,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__11484__11488__11546___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Sets.Relations_1.contains_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eRelations__1_2econtains,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eRelations__1_2econtains___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Topology.Homeomorphisms.topological_property_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eHomeomorphisms_2etopological__property,V_24X1))
<=> cTopology_2eHomeomorphisms_2etopological__property___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('$adef_Topology.TopologicalSpaces.Build_TopologicalSpace_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace,V_24X1),V_24X2) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___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('$adef_Topology.Continuity.continuous_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eContinuity_2econtinuous,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eContinuity_2econtinuous___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_var_11_x_11500_11550_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__11500__11550,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__11500__11550___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_44306_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__44306,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__44306___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_lam_39386_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__39386,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__39386___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_16_mkpow_12388_$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__12388,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__12388___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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_50517_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__50517,V_24X1),V_24X2),V_24X3) = c_24__lam__50517___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Partial_Order.Strict_Rel_of_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.Homeomorphisms.homeomorphic_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eHomeomorphisms_2ehomeomorphic,V_24X1),V_24X2))
<=> cTopology_2eHomeomorphisms_2ehomeomorphic___24a2(V_24X1,V_24X2) ) ).
fof('$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_ZornsLemma.ZornsLemma.tower_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cZornsLemma_2eZornsLemma_2etower,V_24X1),V_24X2),V_24X3),V_24X4) = cZornsLemma_2eZornsLemma_2etower___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eneighborhood__net__DS,V_24X1),V_24X2) = cTopology_2eNets_2eneighborhood__net__DS___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.ZornsLemma.tower_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cZornsLemma_2eZornsLemma_2etower,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cZornsLemma_2eZornsLemma_2etower___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Topology.OrderTopology.OrderTopology_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eOrderTopology_2eOrderTopology,V_24X1),V_24X2) = cTopology_2eOrderTopology_2eOrderTopology___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_11_subst_l_2225_$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__2225,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__2225___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.FiniteIntersectionLemmas.finite_intersections_len_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eFiniteIntersectionLemmas_2efinite__intersections__len___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.MetricSpaces.dist_to_set_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eMetricSpaces_2edist__to__set,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eMetricSpaces_2edist__to__set___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.NeighborhoodBases.Build_TopologicalSpace_from_open_neighborhood_bases_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNeighborhoodBases_2eBuild__TopologicalSpace__from__open__neighborhood__bases,V_24X1),V_24X2) = cTopology_2eNeighborhoodBases_2eBuild__TopologicalSpace__from__open__neighborhood__bases___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.FiltersAndNets.filter_to_net_DS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFiltersAndNets_2efilter__to__net__DS,V_24X1),V_24X2) = cTopology_2eFiltersAndNets_2efilter__to__net__DS___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.InteriorsClosures.idempotent_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eInteriorsClosures_2eidempotent,V_24X1),V_24X2))
<=> cTopology_2eInteriorsClosures_2eidempotent___24a2(V_24X1,V_24X2) ) ).
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('$adef_$_lam_45294_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45294,V_24X1),V_24X2) = c_24__lam__45294___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.TopologicalSpaces.Build_TopologicalSpace_from_closed_sets_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace__from__closed__sets,V_24X1),V_24X2) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace__from__closed__sets___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Powerset.Power_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePowerset_2ePower__set,V_24X1),V_24X2) = cCoq_2eSets_2ePowerset_2ePower__set___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_50093_$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__lam__50093,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__50093___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_lam_39212_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__39212,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__39212___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2egcd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.WeakTopology.WeakTopology_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eWeakTopology_2eWeakTopology,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eWeakTopology_2eWeakTopology___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.SupInf.is_lower_bound_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eSupInf_2eis__lower__bound,V_24X1),V_24X2))
<=> cTopology_2eSupInf_2eis__lower__bound___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Ranalysis1.continuity_pt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRanalysis1_2econtinuity__pt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRanalysis1_2econtinuity__pt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eSpecif_2esig__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_41217_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__41217,V_24X1),V_24X2),V_24X3) = c_24__lam__41217___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_18_mkmult_pow_12390_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__12390,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__12390___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Sets.Partial_Order.Definition_of_PO_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_var_12_x_11525_11527_11562_$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__11525__11527__11562,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__11525__11527__11562___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_$_lam_38120_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38120,V_24X1),V_24X2),V_24X3) = c_24__lam__38120___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedIntersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedIntersection,V_24X1),V_24X2),V_24X3) = cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.Nets.cluster_point_subnet_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTopology_2eNets_2ecluster__point__subnet___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_38587_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__38587,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__38587___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_42592_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__42592,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__42592___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Sets.Cpo.Conditionally_complete_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eConditionally__complete__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.DirectedSets.DS_ord_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eDirectedSets_2eDS__ord,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eDirectedSets_2eDS__ord___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Relations_1.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_var_var_14_s_11473_11476_11539_$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__11473__11476__11539,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__11473__11476__11539___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_39032_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__39032,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__39032___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.WeakTopology.WeakTopology1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eWeakTopology_2eWeakTopology1,V_24X1),V_24X2),V_24X3) = cTopology_2eWeakTopology_2eWeakTopology1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.MetricSpaces.metric_topology_neighborhood_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis,V_24X1),V_24X2),V_24X3) = cTopology_2eMetricSpaces_2emetric__topology__neighborhood__basis___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.NeighborhoodBases.open_neighborhood_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoodBases_2eopen__neighborhood__basis___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.Sets.Finite_sets.Finite_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eFinite__sets_2eFinite,V_24X1),V_24X2))
<=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.Even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eEven,V_24X1))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rec___24a1(V_24X1) ).
fof('$adef_$_lam_39398_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__39398,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__39398___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_44587_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__44587,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__44587___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.DirectedSets.DS_set_$a1',axiom,
! [V_24X1] : happ(cTopology_2eDirectedSets_2eDS__set,V_24X1) = cTopology_2eDirectedSets_2eDS__set___24a1(V_24X1) ).
fof('$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_$_let_var_var_14_s1_11486_11490_11548_$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__11486__11490__11548,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__11486__11490__11548___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_39150_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__39150,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__39150___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_ZornsLemma.FunctionProperties.injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFunctionProperties_2einjective,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFunctionProperties_2einjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Nets.cluster_point_subnet_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Image.Im_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eImage_2eIm,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eImage_2eIm___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Powerset.Power_set_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2ePowerset_2ePower__set,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2ePowerset_2ePower__set___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Nets.net_limit_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eNets_2enet__limit,V_24X1),V_24X2),V_24X3) = cTopology_2eNets_2enet__limit___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_let_var_var_14_s_11460_11463_11533_$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__11460__11463__11533,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__11460__11463__11533___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_43872_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__43872,V_24X1),V_24X2) = c_24__lam__43872___24a2(V_24X1,V_24X2) ).
fof('$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_UrysohnsLemma.Urysohns_Lemma_construction.Un_$a1',axiom,
! [V_24X1] : happ(cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn,V_24X1) = cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(V_24X1) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.FiltersAndNets.tail_filter_basis_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2etail__filter__basis,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2etail__filter__basis___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_$_prop_18281_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__18281,V_24X1),V_24X2) = c_24__prop__18281___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38864_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38864,V_24X1),V_24X2),V_24X3) = c_24__lam__38864___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_35703_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__35703,V_24X1),V_24X2))
<=> c_24__lam__35703___24a2(V_24X1,V_24X2) ) ).
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('$adef_$_lam_45401_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45401,V_24X1),V_24X2) = c_24__lam__45401___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_35703_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35703,V_24X1) = c_24__lam__35703___24a1(V_24X1) ).
fof('$adef_ZornsLemma.Families.FamilyIntersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFamilies_2eFamilyIntersection,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFamilies_2eFamilyIntersection___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_41198_$a1',axiom,
! [V_24X1] : happ(c_24__lam__41198,V_24X1) = c_24__lam__41198___24a1(V_24X1) ).
fof('$adef_$_lam_38422_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__38422,V_24X1),V_24X2))
<=> c_24__lam__38422___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_41614_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__41614,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__41614___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.Filters.Build_Filter_from_basis_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilters_2eBuild__Filter__from__basis,V_24X1),V_24X2) = cTopology_2eFilters_2eBuild__Filter__from__basis___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_$_lam_41614_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__41614,V_24X1),V_24X2) = c_24__lam__41614___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.Quotients.quotient_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eQuotients_2equotient,V_24X1),V_24X2) = cZornsLemma_2eQuotients_2equotient___24a2(V_24X1,V_24X2) ).
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_44879_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__44879,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__44879___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.FilterLimits.neighborhood_filter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilterLimits_2eneighborhood__filter,V_24X1),V_24X2) = cTopology_2eFilterLimits_2eneighborhood__filter___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.InteriorsClosures.closure_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eInteriorsClosures_2eclosure,V_24X1),V_24X2) = cTopology_2eInteriorsClosures_2eclosure___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.SupInf.is_glb_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eSupInf_2eis__glb,V_24X1),V_24X2))
<=> cTopology_2eSupInf_2eis__glb___24a2(V_24X1,V_24X2) ) ).
fof('$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_Topology.Filters.filter_direct_image_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eFilters_2efilter__direct__image,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eFilters_2efilter__direct__image___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.SeparatednessAxioms.T0_sep_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eSeparatednessAxioms_2eT0__sep,V_24X1))
<=> cTopology_2eSeparatednessAxioms_2eT0__sep___24a1(V_24X1) ) ).
fof('$adef_Topology.FiltersAndNets.ftn_x_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2eftn__x,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2eftn__x___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_39712_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__39712,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__39712___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Topology.SeparatednessAxioms.normal_sep_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eSeparatednessAxioms_2enormal__sep,V_24X1))
<=> cTopology_2eSeparatednessAxioms_2enormal__sep___24a1(V_24X1) ) ).
fof('$adef_$_case_Coq.Init.Specif.sig$50774_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esig_2450774,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eSpecif_2esig_2450774___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_ZornsLemma.FunctionProperties.invertible_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFunctionProperties_2einvertible,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFunctionProperties_2einvertible___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.MetricSpaces.MetricTopology_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eMetricSpaces_2eMetricTopology,V_24X1),V_24X2) = cTopology_2eMetricSpaces_2eMetricTopology___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_44879_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__44879,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__44879___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_38269_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__38269,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__38269___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_18345_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__18345,V_24X1),V_24X2) = c_24__prop__18345___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedFamily_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedFamily,V_24X1),V_24X2) = cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_$_case_Topology.TopologicalSpaces.TopologicalSpace$49888_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2449888,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Topology_2eTopologicalSpaces_2eTopologicalSpace_2449888___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Logic.uniqueness_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eLogic_2euniqueness,V_24X1),V_24X2))
<=> cCoq_2eInit_2eLogic_2euniqueness___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.Nets.Build_cluster_point_subnet_DS_set_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cTopology_2eNets_2eBuild__cluster__point__subnet__DS__set___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_lam_38116_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38116,V_24X1),V_24X2),V_24X3) = c_24__lam__38116___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_39043_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__39043,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__39043___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_$_lam_38484_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__38484,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__38484___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Powerset.Power_set_PO_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePowerset_2ePower__set__PO,V_24X1),V_24X2) = cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_45132_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45132,V_24X1),V_24X2) = c_24__lam__45132___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.inhabited_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic_2einhabited,V_24X1))
<=> cCoq_2eInit_2eLogic_2einhabited___24a1(V_24X1) ) ).
fof('$adef_Coq.Sets.Ensembles.Union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eUnion,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Sets.Relations_1.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Completeness.cauchy_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eCompleteness_2ecauchy,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eCompleteness_2ecauchy___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$38069_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2438069,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2438069___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Topology.Compactness.compact_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eCompactness_2ecompact,V_24X1))
<=> cTopology_2eCompactness_2ecompact___24a1(V_24X1) ) ).
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('$adef_$_let_var_var_12_x_11458_11461_11531_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__11458__11461__11531,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__11458__11461__11531___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Topology.Nets.cps_U_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cTopology_2eNets_2ecps__U,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cTopology_2eNets_2ecps__U___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Ensembles.Same_set_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSame__set,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Topology.Nets.neighborhood_net_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eNets_2eneighborhood__net,V_24X1),V_24X2),V_24X3) = cTopology_2eNets_2eneighborhood__net___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_set_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eNets_2eneighborhood__net__DS__set__rect,V_24X1),V_24X2),V_24X3) = cTopology_2eNets_2eneighborhood__net__DS__set__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_fix_38095_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__38095__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__38095__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Reals.Rfunctions.sum_nat_f_O_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2esum__nat__f__O,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.lt_alt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2elt__alt,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2elt__alt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.inleft_$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('$adef_Topology.Homeomorphisms.open_map_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eHomeomorphisms_2eopen__map,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eHomeomorphisms_2eopen__map___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.micromega.RingMicromega.PsatzSquare_$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('$adef_Topology.Completeness.complete_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eCompleteness_2ecomplete,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eCompleteness_2ecomplete___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_lam_45298_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__45298,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__45298___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Cpo.Glb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eGlb,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eGlb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Topology.Nets.intro_neighborhood_net_DS_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2eintro__neighborhood__net__DS,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2eintro__neighborhood__net__DS___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_44894_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__44894,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__44894___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Ensembles.Full_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Add_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eAdd,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.sqrt_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2esqrt__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_39741_$a1',axiom,
! [V_24X1] : happ(c_24__lam__39741,V_24X1) = c_24__lam__39741___24a1(V_24X1) ).
fof('$adef_Topology.OrderTopology.order_topology_subbasis_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eOrderTopology_2eorder__topology__subbasis,V_24X1),V_24X2) = cTopology_2eOrderTopology_2eorder__topology__subbasis___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39386_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__39386,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__39386___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_Coq.Init.Datatypes.Some_$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('$adef_$_let_5_subF_43860_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__5__subF__43860,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__5__subF__43860___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_$_lam_41963_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__41963,V_24X1),V_24X2) = c_24__lam__41963___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Sets.Partial_Order.Rel_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eRel__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Topology.FiltersAndNets.net_tail_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eFiltersAndNets_2enet__tail,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eFiltersAndNets_2enet__tail___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RiemannInt_SF.co_interval_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eco__interval,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eReals_2eRiemannInt__SF_2eco__interval___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_lam_44886_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__44886,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__44886___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_let_var_var_12_x_11471_11474_11537_$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__11471__11474__11537,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__11471__11474__11537___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_18_mkmult_pow_12390_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__12390,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__12390___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_prop_42312_$a1',axiom,
! [V_24X1] : happ(c_24__prop__42312,V_24X1) = c_24__prop__42312___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Conditionally_complete_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete,V_24X1),V_24X2))
<=> cCoq_2eSets_2eCpo_2eConditionally__complete___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('$adef_$_let_3_R_42116_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__42116,V_24X1),V_24X2) = c_24__let__3__R__42116___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_42253_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__42253,V_24X1),V_24X2) = c_24__lam__42253___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eTotally__ordered__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_45302_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45302,V_24X1),V_24X2) = c_24__lam__45302___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Filters.filter_family_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eFilters_2efilter__family,V_24X1),V_24X2) = cTopology_2eFilters_2efilter__family___24a2(V_24X1,V_24X2) ).
fof('$adef_Topology.Nets.neighborhood_net_DS_ord_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cTopology_2eNets_2eneighborhood__net__DS__ord,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cTopology_2eNets_2eneighborhood__net__DS__ord___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Logic.True_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eTrue__rect,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eTrue__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_37632_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__37632,V_24X1),V_24X2) = c_24__lam__37632___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_3_R_41608_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__41608,V_24X1),V_24X2) = c_24__let__3__R__41608___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_15_s2_11487_11491_11549_$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__11487__11491__11549,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__11487__11491__11549___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_41027_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__41027,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__41027___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_52139_$a1',axiom,
! [V_24X1] : happ(c_24__lam__52139,V_24X1) = c_24__lam__52139___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.nb_digits_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enb__digits,V_24X1) = cCoq_2eInit_2eDecimal_2enb__digits___24a1(V_24X1) ).
fof('$adef_$_let_3_R_41957_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__41957,V_24X1),V_24X2) = c_24__let__3__R__41957___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
fof('$adef_$_lam_41013_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__41013,V_24X1),V_24X2),V_24X3) = c_24__lam__41013___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Included_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eIncluded,V_24X1) = cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rabs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRabs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V_24X1) ).
fof('$adef_Topology.CountabilityAxioms.first_countable_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eCountabilityAxioms_2efirst__countable,V_24X1))
<=> cTopology_2eCountabilityAxioms_2efirst__countable___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('$adef_Topology.WeakTopology.weak_topology_subbasis_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eWeakTopology_2eweak__topology__subbasis,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eWeakTopology_2eweak__topology__subbasis___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Cpo.Directed_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eDirected__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eDirected__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_45306_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__45306,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__45306___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_Topology.Homeomorphisms.homeomorphism_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eHomeomorphisms_2ehomeomorphism,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eHomeomorphisms_2ehomeomorphism___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_39227_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39227,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39227___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_44321_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__44321,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__44321___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$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_Topology.SeparatednessAxioms.Hausdorff_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eSeparatednessAxioms_2eHausdorff,V_24X1))
<=> cTopology_2eSeparatednessAxioms_2eHausdorff___24a1(V_24X1) ) ).
fof('$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_Topology.Neighborhoods.open_neighborhood_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eNeighborhoods_2eopen__neighborhood,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eNeighborhoods_2eopen__neighborhood___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_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.setoid_ring.Field_theory.PCond_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eField__theory_2ePCond___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_$_lam_51609_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__51609,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__51609___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.CountabilityAxioms.Lindelof_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eCountabilityAxioms_2eLindelof,V_24X1))
<=> cTopology_2eCountabilityAxioms_2eLindelof___24a1(V_24X1) ) ).
fof('$adef_Topology.Nets.Net_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eNets_2eNet,V_24X1),V_24X2) = cTopology_2eNets_2eNet___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_bf_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__bf,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_Topology.DirectedSets.DS_ord_$a1',axiom,
! [V_24X1] : happ(cTopology_2eDirectedSets_2eDS__ord,V_24X1) = cTopology_2eDirectedSets_2eDS__ord___24a1(V_24X1) ).
fof('$adef_ZornsLemma.CountableTypes.CountableT_$a1',axiom,
! [V_24X1] :
( p(happ(cZornsLemma_2eCountableTypes_2eCountableT,V_24X1))
<=> cZornsLemma_2eCountableTypes_2eCountableT___24a1(V_24X1) ) ).
fof('$adef_Topology.SupInf.lower_bound_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eSupInf_2elower__bound,V_24X1))
<=> cTopology_2eSupInf_2elower__bound___24a1(V_24X1) ) ).
fof('$adef_Topology.Connectedness.connected_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eConnectedness_2econnected,V_24X1))
<=> cTopology_2eConnectedness_2econnected___24a1(V_24X1) ) ).
fof('$adef_Coq.Sets.Cpo.Directed_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eDirected__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eDirected__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_49387_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__49387,V_24X1),V_24X2) = c_24__lam__49387___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39336_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39336,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39336___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_$_let_var_11_x_11503_11551_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__11503__11551,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__11503__11551___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_lam_44263_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__44263,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__44263___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_50156_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__50156,V_24X1),V_24X2) = c_24__lam__50156___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.Reals.RiemannInt_SF.Nbound_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eReals_2eRiemannInt__SF_2eNbound,V_24X1))
<=> cCoq_2eReals_2eRiemannInt__SF_2eNbound___24a1(V_24X1) ) ).
fof('$adef_Topology.Filters.Filter_$a1',axiom,
! [V_24X1] : happ(cTopology_2eFilters_2eFilter,V_24X1) = cTopology_2eFilters_2eFilter___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Topology.FiltersAndNets.net_tail_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cTopology_2eFiltersAndNets_2enet__tail,V_24X1),V_24X2),V_24X3) = cTopology_2eFiltersAndNets_2enet__tail___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_44737_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__44737,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__44737___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Topology.Nets.cluster_point_subnet_DS_ord_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cTopology_2eNets_2ecluster__point__subnet__DS__ord,V_24X1),V_24X2),V_24X3),V_24X4) = cTopology_2eNets_2ecluster__point__subnet__DS__ord___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_var_var_13_y_11459_11462_11532_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__11459__11462__11532,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__11459__11462__11532___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_lam_45306_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__45306,V_24X1),V_24X2) = c_24__lam__45306___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Factorial.fact_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2eFactorial_2efact,V_24X1) = cCoq_2eArith_2eFactorial_2efact___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sigT_$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('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_Topology.OpenBases.B_open_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eOpenBases_2eB__open,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eOpenBases_2eB__open___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.Connectedness.clopen_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eConnectedness_2eclopen,V_24X1),V_24X2))
<=> cTopology_2eConnectedness_2eclopen___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('$adef_Coq.micromega.EnvRing.PX_$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('$adef_$_let_3_R_41464_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__41464,V_24X1),V_24X2) = c_24__let__3__R__41464___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_38124_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__38124,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__38124___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_ZornsLemma.FiniteIntersections.finite_intersections_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFiniteIntersections_2efinite__intersections,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFiniteIntersections_2efinite__intersections___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Image.Im_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eSets_2eImage_2eIm,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eSets_2eImage_2eIm___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Sets.Partial_Order.PO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePartial__Order_2ePO,V_24X1) = cCoq_2eSets_2ePartial__Order_2ePO___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('$adef_Topology.MetricSpaces.metrizable_$a1',axiom,
! [V_24X1] :
( p(happ(cTopology_2eMetricSpaces_2emetrizable,V_24X1))
<=> cTopology_2eMetricSpaces_2emetrizable___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.RiemannInt_SF.StepFun_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRiemannInt__SF_2eStepFun,V_24X1),V_24X2) = cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.Field_theory.denum_$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('$adef_$_let_16_mkpow_12388_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__12388,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__12388___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Ensembles.Ensemble_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEnsemble,V_24X1) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1) ).
fof('$adef_$_lam_41181_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__41181,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__41181___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.divmod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2edivmod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2edivmod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Topology.FilterLimits.filter_limit_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cTopology_2eFilterLimits_2efilter__limit,V_24X1),V_24X2),V_24X3))
<=> cTopology_2eFilterLimits_2efilter__limit___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_38507_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__38507,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__38507___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_type_16040',axiom,
! [V_24Y] :
( c_24__type__16040___24t(V_24Y)
<=> t(V_24Y,c_24__type__16040) ) ).
fof('$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_37759',axiom,
! [V_24Y] :
( c_24__type__37759___24t(V_24Y)
<=> t(V_24Y,c_24__type__37759) ) ).
fof('$tdef_$_type_42223',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42223___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42223___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_16069',axiom,
! [V_24Y] :
( c_24__type__16069___24t(V_24Y)
<=> t(V_24Y,c_24__type__16069) ) ).
fof('$tdef_$_type_44680',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__44680___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__44680___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1244',axiom,
! [V_24Y] :
( c_24__type__1244___24t(V_24Y)
<=> t(V_24Y,c_24__type__1244) ) ).
fof('$tdef_$_type_38499',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38499___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38499___24a1(V_24X1)) ) ).
fof('$tdef_Topology.DirectedSets.DS_set',axiom,
! [V_24X1,V_24Y] :
( cTopology_2eDirectedSets_2eDS__set___24t(V_24X1,V_24Y)
<=> t(V_24Y,cTopology_2eDirectedSets_2eDS__set___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4476',axiom,
! [V_24Y] :
( c_24__type__4476___24t(V_24Y)
<=> t(V_24Y,c_24__type__4476) ) ).
fof('$tdef_$_type_531',axiom,
! [V_24Y] :
( c_24__type__531___24t(V_24Y)
<=> t(V_24Y,c_24__type__531) ) ).
fof('$tdef_$_type_45380',axiom,
! [V_24Y] :
( c_24__type__45380___24t(V_24Y)
<=> t(V_24Y,c_24__type__45380) ) ).
fof('$tdef_$_type_44329',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44329___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44329___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38111',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__38111___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__38111___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_410',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__410___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__410___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_11237',axiom,
! [V_24Y] :
( c_24__type__11237___24t(V_24Y)
<=> t(V_24Y,c_24__type__11237) ) ).
fof('$tdef_$_type_43790',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__43790___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__43790___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24307',axiom,
! [V_24Y] :
( c_24__type__24307___24t(V_24Y)
<=> t(V_24Y,c_24__type__24307) ) ).
fof('$tdef_$_type_50588',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__50588___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__50588___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_41106',axiom,
! [V_24Y] :
( c_24__type__41106___24t(V_24Y)
<=> t(V_24Y,c_24__type__41106) ) ).
fof('$tdef_$_type_529',axiom,
! [V_24X1,V_24Y] :
( c_24__type__529___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__529___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38182',axiom,
! [V_24Y] :
( c_24__type__38182___24t(V_24Y)
<=> t(V_24Y,c_24__type__38182) ) ).
fof('$tdef_$_type_10978',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10978___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10978___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24641',axiom,
! [V_24Y] :
( c_24__type__24641___24t(V_24Y)
<=> t(V_24Y,c_24__type__24641) ) ).
fof('$tdef_$_type_49417',axiom,
! [V_24Y] :
( c_24__type__49417___24t(V_24Y)
<=> t(V_24Y,c_24__type__49417) ) ).
fof('$tdef_$_type_42688',axiom,
! [V_24Y] :
( c_24__type__42688___24t(V_24Y)
<=> t(V_24Y,c_24__type__42688) ) ).
fof('$tdef_$_type_32584',axiom,
! [V_24Y] :
( c_24__type__32584___24t(V_24Y)
<=> t(V_24Y,c_24__type__32584) ) ).
fof('$tdef_$_type_42640',axiom,
! [V_24Y] :
( c_24__type__42640___24t(V_24Y)
<=> t(V_24Y,c_24__type__42640) ) ).
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_$_type_50173',axiom,
! [V_24Y] :
( c_24__type__50173___24t(V_24Y)
<=> t(V_24Y,c_24__type__50173) ) ).
fof('$tdef_$_type_45206',axiom,
! [V_24Y] :
( c_24__type__45206___24t(V_24Y)
<=> t(V_24Y,c_24__type__45206) ) ).
fof('$tdef_$_type_38644',axiom,
! [V_24Y] :
( c_24__type__38644___24t(V_24Y)
<=> t(V_24Y,c_24__type__38644) ) ).
fof('$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_38529',axiom,
! [V_24Y] :
( c_24__type__38529___24t(V_24Y)
<=> t(V_24Y,c_24__type__38529) ) ).
fof('$tdef_$_type_44871',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__44871___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__44871___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_Coq.Reals.RiemannInt_SF.StepFun',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt__SF_2eStepFun___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1161',axiom,
! [V_24Y] :
( c_24__type__1161___24t(V_24Y)
<=> t(V_24Y,c_24__type__1161) ) ).
fof('$tdef_$_type_32071',axiom,
! [V_24Y] :
( c_24__type__32071___24t(V_24Y)
<=> t(V_24Y,c_24__type__32071) ) ).
fof('$tdef_$_type_1584',axiom,
! [V_24Y] :
( c_24__type__1584___24t(V_24Y)
<=> t(V_24Y,c_24__type__1584) ) ).
fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).
fof('$tdef_$_type_49989',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__49989___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__49989___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1688',axiom,
! [V_24Y] :
( c_24__type__1688___24t(V_24Y)
<=> t(V_24Y,c_24__type__1688) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_589',axiom,
! [V_24Y] :
( c_24__type__589___24t(V_24Y)
<=> t(V_24Y,c_24__type__589) ) ).
fof('$tdef_$_type_4406',axiom,
! [V_24Y] :
( c_24__type__4406___24t(V_24Y)
<=> t(V_24Y,c_24__type__4406) ) ).
fof('$tdef_$_type_11790',axiom,
! [V_24Y] :
( c_24__type__11790___24t(V_24Y)
<=> t(V_24Y,c_24__type__11790) ) ).
fof('$tdef_Topology.Nets.neighborhood_net_DS_set',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cTopology_2eNets_2eneighborhood__net__DS__set___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cTopology_2eNets_2eneighborhood__net__DS__set___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_42381',axiom,
! [V_24Y] :
( c_24__type__42381___24t(V_24Y)
<=> t(V_24Y,c_24__type__42381) ) ).
fof('$tdef_$_type_36107',axiom,
! [V_24Y] :
( c_24__type__36107___24t(V_24Y)
<=> t(V_24Y,c_24__type__36107) ) ).
fof('$tdef_$_type_18622',axiom,
! [V_24Y] :
( c_24__type__18622___24t(V_24Y)
<=> t(V_24Y,c_24__type__18622) ) ).
fof('$tdef_$_type_49602',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__49602___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__49602___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2451',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2451___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2451___24a1(V_24X1)) ) ).
fof('$tdef_$_type_45522',axiom,
! [V_24Y] :
( c_24__type__45522___24t(V_24Y)
<=> t(V_24Y,c_24__type__45522) ) ).
fof('$tdef_$_type_45221',axiom,
! [V_24Y] :
( c_24__type__45221___24t(V_24Y)
<=> t(V_24Y,c_24__type__45221) ) ).
fof('$tdef_$_type_41134',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__41134___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__41134___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_64980',axiom,
! [V_24Y] :
( c_24__type__64980___24t(V_24Y)
<=> t(V_24Y,c_24__type__64980) ) ).
fof('$tdef_$_type_44647',axiom,
! [V_24Y] :
( c_24__type__44647___24t(V_24Y)
<=> t(V_24Y,c_24__type__44647) ) ).
fof('$tdef_$_type_39433',axiom,
! [V_24Y] :
( c_24__type__39433___24t(V_24Y)
<=> t(V_24Y,c_24__type__39433) ) ).
fof('$tdef_$_type_41929',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41929___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41929___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_37643',axiom,
! [V_24Y] :
( c_24__type__37643___24t(V_24Y)
<=> t(V_24Y,c_24__type__37643) ) ).
fof('$tdef_$_type_2907',axiom,
! [V_24Y] :
( c_24__type__2907___24t(V_24Y)
<=> t(V_24Y,c_24__type__2907) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).
fof('$tdef_$_type_11647',axiom,
! [V_24Y] :
( c_24__type__11647___24t(V_24Y)
<=> t(V_24Y,c_24__type__11647) ) ).
fof('$tdef_$_type_50045',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__50045___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__50045___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4488',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4488___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4488___24a1(V_24X1)) ) ).
fof('$tdef_$_type_41094',axiom,
! [V_24Y] :
( c_24__type__41094___24t(V_24Y)
<=> t(V_24Y,c_24__type__41094) ) ).
fof('$tdef_$_type_2915',axiom,
! [V_24Y] :
( c_24__type__2915___24t(V_24Y)
<=> t(V_24Y,c_24__type__2915) ) ).
fof('$tdef_$_type_2443',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2443___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2443___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37285',axiom,
! [V_24Y] :
( c_24__type__37285___24t(V_24Y)
<=> t(V_24Y,c_24__type__37285) ) ).
fof('$tdef_$_type_1961',axiom,
! [V_24Y] :
( c_24__type__1961___24t(V_24Y)
<=> t(V_24Y,c_24__type__1961) ) ).
fof('$tdef_$_type_4403',axiom,
! [V_24Y] :
( c_24__type__4403___24t(V_24Y)
<=> t(V_24Y,c_24__type__4403) ) ).
fof('$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_$_type_536',axiom,
! [V_24Y] :
( c_24__type__536___24t(V_24Y)
<=> t(V_24Y,c_24__type__536) ) ).
fof('$tdef_$_type_44843',axiom,
! [V_24Y] :
( c_24__type__44843___24t(V_24Y)
<=> t(V_24Y,c_24__type__44843) ) ).
fof('$tdef_$_type_35699',axiom,
! [V_24Y] :
( c_24__type__35699___24t(V_24Y)
<=> t(V_24Y,c_24__type__35699) ) ).
fof('$tdef_$_type_39517',axiom,
! [V_24Y] :
( c_24__type__39517___24t(V_24Y)
<=> t(V_24Y,c_24__type__39517) ) ).
fof('$tdef_$_type_39028',axiom,
! [V_24Y] :
( c_24__type__39028___24t(V_24Y)
<=> t(V_24Y,c_24__type__39028) ) ).
fof('$tdef_$_type_32524',axiom,
! [V_24Y] :
( c_24__type__32524___24t(V_24Y)
<=> t(V_24Y,c_24__type__32524) ) ).
fof('$tdef_$_type_9027',axiom,
! [V_24Y] :
( c_24__type__9027___24t(V_24Y)
<=> t(V_24Y,c_24__type__9027) ) ).
fof('$tdef_$_type_38346',axiom,
! [V_24Y] :
( c_24__type__38346___24t(V_24Y)
<=> t(V_24Y,c_24__type__38346) ) ).
fof('$tdef_$_type_38175',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__38175___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__38175___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Sets.Ensembles.Ensemble',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1950',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1950___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1950___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_38594',axiom,
! [V_24Y] :
( c_24__type__38594___24t(V_24Y)
<=> t(V_24Y,c_24__type__38594) ) ).
fof('$tdef_$_type_50021',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__50021___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__50021___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_39052',axiom,
! [V_24Y] :
( c_24__type__39052___24t(V_24Y)
<=> t(V_24Y,c_24__type__39052) ) ).
fof('$tdef_$_type_45825',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45825___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45825___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_39479',axiom,
! [V_24Y] :
( c_24__type__39479___24t(V_24Y)
<=> t(V_24Y,c_24__type__39479) ) ).
fof('$tdef_$_type_39125',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39125___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39125___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32609',axiom,
! [V_24Y] :
( c_24__type__32609___24t(V_24Y)
<=> t(V_24Y,c_24__type__32609) ) ).
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_$_type_487',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__487___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__487___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Topology.Nets.Net',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cTopology_2eNets_2eNet___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cTopology_2eNets_2eNet___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28244',axiom,
! [V_24Y] :
( c_24__type__28244___24t(V_24Y)
<=> t(V_24Y,c_24__type__28244) ) ).
fof('$tdef_$_type_42489',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__42489___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__42489___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_type_45287',axiom,
! [V_24Y] :
( c_24__type__45287___24t(V_24Y)
<=> t(V_24Y,c_24__type__45287) ) ).
fof('$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_64956',axiom,
! [V_24Y] :
( c_24__type__64956___24t(V_24Y)
<=> t(V_24Y,c_24__type__64956) ) ).
fof('$tdef_$_type_524',axiom,
! [V_24Y] :
( c_24__type__524___24t(V_24Y)
<=> t(V_24Y,c_24__type__524) ) ).
fof('$tdef_$_type_4535',axiom,
! [V_24Y] :
( c_24__type__4535___24t(V_24Y)
<=> t(V_24Y,c_24__type__4535) ) ).
fof('$tdef_$_type_14',axiom,
! [V_24Y] :
( c_24__type__14___24t(V_24Y)
<=> t(V_24Y,c_24__type__14) ) ).
fof('$tdef_$_type_1142',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1142___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1142___24a1(V_24X1)) ) ).
fof('$tdef_$_type_45424',axiom,
! [V_24Y] :
( c_24__type__45424___24t(V_24Y)
<=> t(V_24Y,c_24__type__45424) ) ).
fof('$tdef_$_type_35841',axiom,
! [V_24Y] :
( c_24__type__35841___24t(V_24Y)
<=> t(V_24Y,c_24__type__35841) ) ).
fof('$tdef_$_type_3165',axiom,
! [V_24Y] :
( c_24__type__3165___24t(V_24Y)
<=> t(V_24Y,c_24__type__3165) ) ).
fof('$tdef_$_type_45416',axiom,
! [V_24Y] :
( c_24__type__45416___24t(V_24Y)
<=> t(V_24Y,c_24__type__45416) ) ).
fof('$tdef_$_type_39160',axiom,
! [V_24Y] :
( c_24__type__39160___24t(V_24Y)
<=> t(V_24Y,c_24__type__39160) ) ).
fof('$tdef_$_type_11999',axiom,
! [V_24Y] :
( c_24__type__11999___24t(V_24Y)
<=> t(V_24Y,c_24__type__11999) ) ).
fof('$tdef_$_type_24818',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24818___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24818___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12668',axiom,
! [V_24Y] :
( c_24__type__12668___24t(V_24Y)
<=> t(V_24Y,c_24__type__12668) ) ).
fof('$tdef_$_type_49393',axiom,
! [V_24Y] :
( c_24__type__49393___24t(V_24Y)
<=> t(V_24Y,c_24__type__49393) ) ).
fof('$tdef_$_type_1159',axiom,
! [V_24Y] :
( c_24__type__1159___24t(V_24Y)
<=> t(V_24Y,c_24__type__1159) ) ).
fof('$tdef_$_type_51621',axiom,
! [V_24Y] :
( c_24__type__51621___24t(V_24Y)
<=> t(V_24Y,c_24__type__51621) ) ).
fof('$tdef_$_type_38256',axiom,
! [V_24Y] :
( c_24__type__38256___24t(V_24Y)
<=> t(V_24Y,c_24__type__38256) ) ).
fof('$tdef_$_type_4372',axiom,
! [V_24Y] :
( c_24__type__4372___24t(V_24Y)
<=> t(V_24Y,c_24__type__4372) ) ).
fof('$tdef_$_type_52130',axiom,
! [V_24Y] :
( c_24__type__52130___24t(V_24Y)
<=> t(V_24Y,c_24__type__52130) ) ).
fof('$tdef_$_type_710',axiom,
! [V_24Y] :
( c_24__type__710___24t(V_24Y)
<=> t(V_24Y,c_24__type__710) ) ).
fof('$tdef_$_type_16196',axiom,
! [V_24Y] :
( c_24__type__16196___24t(V_24Y)
<=> t(V_24Y,c_24__type__16196) ) ).
fof('$tdef_$_type_50076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__50076___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__50076___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32612',axiom,
! [V_24Y] :
( c_24__type__32612___24t(V_24Y)
<=> t(V_24Y,c_24__type__32612) ) ).
fof('$tdef_$_type_42929',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42929___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42929___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Topology.TopologicalSpaces.TopologicalSpace',axiom,
! [V_24Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V_24Y)
<=> t(V_24Y,cTopology_2eTopologicalSpaces_2eTopologicalSpace) ) ).
fof('$tdef_$_type_38578',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38578___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38578___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_39369',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__39369___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__39369___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_38383',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38383___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38383___24a1(V_24X1)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_45634',axiom,
! [V_24Y] :
( c_24__type__45634___24t(V_24Y)
<=> t(V_24Y,c_24__type__45634) ) ).
fof('$tdef_$_type_9380',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9380___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9380___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18617',axiom,
! [V_24Y] :
( c_24__type__18617___24t(V_24Y)
<=> t(V_24Y,c_24__type__18617) ) ).
fof('$tdef_$_type_39313',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__39313___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__39313___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_Topology.TopologicalSpaces.point_set',axiom,
! [V_24X1,V_24Y] :
( cTopology_2eTopologicalSpaces_2epoint__set___24t(V_24X1,V_24Y)
<=> t(V_24Y,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38720',axiom,
! [V_24Y] :
( c_24__type__38720___24t(V_24Y)
<=> t(V_24Y,c_24__type__38720) ) ).
fof('$tdef_$_type_2644',axiom,
! [V_24Y] :
( c_24__type__2644___24t(V_24Y)
<=> t(V_24Y,c_24__type__2644) ) ).
fof('$tdef_$_type_8715',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8715___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8715___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16051',axiom,
! [V_24Y] :
( c_24__type__16051___24t(V_24Y)
<=> t(V_24Y,c_24__type__16051) ) ).
fof('$tdef_$_type_38271',axiom,
! [V_24Y] :
( c_24__type__38271___24t(V_24Y)
<=> t(V_24Y,c_24__type__38271) ) ).
fof('$tdef_$_type_49448',axiom,
! [V_24Y] :
( c_24__type__49448___24t(V_24Y)
<=> t(V_24Y,c_24__type__49448) ) ).
fof('$tdef_$_type_41554',axiom,
! [V_24Y] :
( c_24__type__41554___24t(V_24Y)
<=> t(V_24Y,c_24__type__41554) ) ).
fof('$tdef_$_type_45364',axiom,
! [V_24Y] :
( c_24__type__45364___24t(V_24Y)
<=> t(V_24Y,c_24__type__45364) ) ).
fof('$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_1191',axiom,
! [V_24Y] :
( c_24__type__1191___24t(V_24Y)
<=> t(V_24Y,c_24__type__1191) ) ).
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_Coq.Sets.Partial_Order.PO',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2ePartial__Order_2ePO___24a1(V_24X1)) ) ).
fof('$tdef_$_type_41882',axiom,
! [V_24Y] :
( c_24__type__41882___24t(V_24Y)
<=> t(V_24Y,c_24__type__41882) ) ).
fof('$tdef_$_type_3185',axiom,
! [V_24Y] :
( c_24__type__3185___24t(V_24Y)
<=> t(V_24Y,c_24__type__3185) ) ).
fof('$tdef_$_type_11788',axiom,
! [V_24Y] :
( c_24__type__11788___24t(V_24Y)
<=> t(V_24Y,c_24__type__11788) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_44420',axiom,
! [V_24X1,V_24Y] :
( c_24__type__44420___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__44420___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18279',axiom,
! [V_24Y] :
( c_24__type__18279___24t(V_24Y)
<=> t(V_24Y,c_24__type__18279) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_2672',axiom,
! [V_24Y] :
( c_24__type__2672___24t(V_24Y)
<=> t(V_24Y,c_24__type__2672) ) ).
fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_52005',axiom,
! [V_24Y] :
( c_24__type__52005___24t(V_24Y)
<=> t(V_24Y,c_24__type__52005) ) ).
fof('$tdef_$_type_50164',axiom,
! [V_24Y] :
( c_24__type__50164___24t(V_24Y)
<=> t(V_24Y,c_24__type__50164) ) ).
fof('$tdef_$_type_65007',axiom,
! [V_24Y] :
( c_24__type__65007___24t(V_24Y)
<=> t(V_24Y,c_24__type__65007) ) ).
fof('$tdef_Topology.Nets.cluster_point_subnet_DS_set',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cTopology_2eNets_2ecluster__point__subnet__DS__set___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cTopology_2eNets_2ecluster__point__subnet__DS__set___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_44249',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__44249___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__44249___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_45777',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45777___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45777___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_52090',axiom,
! [V_24Y] :
( c_24__type__52090___24t(V_24Y)
<=> t(V_24Y,c_24__type__52090) ) ).
fof('$tdef_$_type_39578',axiom,
! [V_24Y] :
( c_24__type__39578___24t(V_24Y)
<=> t(V_24Y,c_24__type__39578) ) ).
fof('$tdef_$_type_37378',axiom,
! [V_24Y] :
( c_24__type__37378___24t(V_24Y)
<=> t(V_24Y,c_24__type__37378) ) ).
fof('$tdef_$_type_3172',axiom,
! [V_24Y] :
( c_24__type__3172___24t(V_24Y)
<=> t(V_24Y,c_24__type__3172) ) ).
fof('$tdef_$_type_1757',axiom,
! [V_24Y] :
( c_24__type__1757___24t(V_24Y)
<=> t(V_24Y,c_24__type__1757) ) ).
fof('$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_44336',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44336___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44336___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_42310',axiom,
! [V_24Y] :
( c_24__type__42310___24t(V_24Y)
<=> t(V_24Y,c_24__type__42310) ) ).
fof('$tdef_Coq.Init.Decimal.uint',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_3162',axiom,
! [V_24Y] :
( c_24__type__3162___24t(V_24Y)
<=> t(V_24Y,c_24__type__3162) ) ).
fof('$tdef_$_type_10987',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10987___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10987___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24658',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24658___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24658___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_37993',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__37993___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__37993___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_45813',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__45813___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__45813___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45432',axiom,
! [V_24Y] :
( c_24__type__45432___24t(V_24Y)
<=> t(V_24Y,c_24__type__45432) ) ).
fof('$tdef_$_type_37524',axiom,
! [V_24Y] :
( c_24__type__37524___24t(V_24Y)
<=> t(V_24Y,c_24__type__37524) ) ).
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_$_type_1737',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1737___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1737___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38807',axiom,
! [V_24Y] :
( c_24__type__38807___24t(V_24Y)
<=> t(V_24Y,c_24__type__38807) ) ).
fof('$tdef_$_type_37816',axiom,
! [V_24Y] :
( c_24__type__37816___24t(V_24Y)
<=> t(V_24Y,c_24__type__37816) ) ).
fof('$tdef_$_type_32558',axiom,
! [V_24Y] :
( c_24__type__32558___24t(V_24Y)
<=> t(V_24Y,c_24__type__32558) ) ).
fof('$tdef_$_type_45482',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__45482___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__45482___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_42365',axiom,
! [V_24Y] :
( c_24__type__42365___24t(V_24Y)
<=> t(V_24Y,c_24__type__42365) ) ).
fof('$tdef_$_type_37329',axiom,
! [V_24Y] :
( c_24__type__37329___24t(V_24Y)
<=> t(V_24Y,c_24__type__37329) ) ).
fof('$tdef_$_type_37299',axiom,
! [V_24Y] :
( c_24__type__37299___24t(V_24Y)
<=> t(V_24Y,c_24__type__37299) ) ).
fof('$tdef_$_type_2728',axiom,
! [V_24Y] :
( c_24__type__2728___24t(V_24Y)
<=> t(V_24Y,c_24__type__2728) ) ).
fof('$tdef_$_type_15187',axiom,
! [V_24Y] :
( c_24__type__15187___24t(V_24Y)
<=> t(V_24Y,c_24__type__15187) ) ).
fof('$tdef_$_type_3119',axiom,
! [V_24Y] :
( c_24__type__3119___24t(V_24Y)
<=> t(V_24Y,c_24__type__3119) ) ).
fof('$tdef_$_type_2218',axiom,
! [V_24Y] :
( c_24__type__2218___24t(V_24Y)
<=> t(V_24Y,c_24__type__2218) ) ).
fof('$tdef_$_type_42599',axiom,
! [V_24Y] :
( c_24__type__42599___24t(V_24Y)
<=> t(V_24Y,c_24__type__42599) ) ).
fof('$tdef_$_type_17',axiom,
! [V_24Y] :
( c_24__type__17___24t(V_24Y)
<=> t(V_24Y,c_24__type__17) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_45328',axiom,
! [V_24Y] :
( c_24__type__45328___24t(V_24Y)
<=> t(V_24Y,c_24__type__45328) ) ).
fof('$tdef_$_type_37280',axiom,
! [V_24Y] :
( c_24__type__37280___24t(V_24Y)
<=> t(V_24Y,c_24__type__37280) ) ).
fof('$tdef_$_type_15246',axiom,
! [V_24Y] :
( c_24__type__15246___24t(V_24Y)
<=> t(V_24Y,c_24__type__15246) ) ).
fof('$tdef_$_type_18306',axiom,
! [V_24Y] :
( c_24__type__18306___24t(V_24Y)
<=> t(V_24Y,c_24__type__18306) ) ).
fof('$tdef_$_type_38313',axiom,
! [V_24Y] :
( c_24__type__38313___24t(V_24Y)
<=> t(V_24Y,c_24__type__38313) ) ).
fof('$tdef_$_type_31982',axiom,
! [V_24Y] :
( c_24__type__31982___24t(V_24Y)
<=> t(V_24Y,c_24__type__31982) ) ).
fof('$tdef_$_type_35682',axiom,
! [V_24Y] :
( c_24__type__35682___24t(V_24Y)
<=> t(V_24Y,c_24__type__35682) ) ).
fof('$tdef_$_type_16035',axiom,
! [V_24Y] :
( c_24__type__16035___24t(V_24Y)
<=> t(V_24Y,c_24__type__16035) ) ).
fof('$tdef_$_type_50842',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__50842___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__50842___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39723',axiom,
! [V_24Y] :
( c_24__type__39723___24t(V_24Y)
<=> t(V_24Y,c_24__type__39723) ) ).
fof('$tdef_$_type_35679',axiom,
! [V_24Y] :
( c_24__type__35679___24t(V_24Y)
<=> t(V_24Y,c_24__type__35679) ) ).
fof('$tdef_$_type_42834',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42834___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42834___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_49558',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__49558___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__49558___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2213',axiom,
! [V_24Y] :
( c_24__type__2213___24t(V_24Y)
<=> t(V_24Y,c_24__type__2213) ) ).
fof('$tdef_$_type_43856',axiom,
! [V_24Y] :
( c_24__type__43856___24t(V_24Y)
<=> t(V_24Y,c_24__type__43856) ) ).
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_$_type_45239',axiom,
! [V_24Y] :
( c_24__type__45239___24t(V_24Y)
<=> t(V_24Y,c_24__type__45239) ) ).
fof('$tdef_$_type_18296',axiom,
! [V_24Y] :
( c_24__type__18296___24t(V_24Y)
<=> t(V_24Y,c_24__type__18296) ) ).
fof('$tdef_$_type_42936',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42936___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42936___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_64978',axiom,
! [V_24Y] :
( c_24__type__64978___24t(V_24Y)
<=> t(V_24Y,c_24__type__64978) ) ).
fof('$tdef_$_type_1781',axiom,
! [V_24Y] :
( c_24__type__1781___24t(V_24Y)
<=> t(V_24Y,c_24__type__1781) ) ).
fof('$tdef_$_type_38725',axiom,
! [V_24Y] :
( c_24__type__38725___24t(V_24Y)
<=> t(V_24Y,c_24__type__38725) ) ).
fof('$tdef_$_type_38380',axiom,
! [V_24Y] :
( c_24__type__38380___24t(V_24Y)
<=> t(V_24Y,c_24__type__38380) ) ).
fof('$tdef_$_type_35686',axiom,
! [V_24Y] :
( c_24__type__35686___24t(V_24Y)
<=> t(V_24Y,c_24__type__35686) ) ).
fof('$tdef_$_type_30513',axiom,
! [V_24Y] :
( c_24__type__30513___24t(V_24Y)
<=> t(V_24Y,c_24__type__30513) ) ).
fof('$tdef_$_type_27584',axiom,
! [V_24Y] :
( c_24__type__27584___24t(V_24Y)
<=> t(V_24Y,c_24__type__27584) ) ).
fof('$tdef_$_type_16948',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16948___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16948___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1232',axiom,
! [V_24Y] :
( c_24__type__1232___24t(V_24Y)
<=> t(V_24Y,c_24__type__1232) ) ).
fof('$tdef_$_type_2210',axiom,
! [V_24Y] :
( c_24__type__2210___24t(V_24Y)
<=> t(V_24Y,c_24__type__2210) ) ).
fof('$tdef_$_type_39698',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39698___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39698___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8907',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8907___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8907___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1137',axiom,
! [V_24Y] :
( c_24__type__1137___24t(V_24Y)
<=> t(V_24Y,c_24__type__1137) ) ).
fof('$tdef_$_type_43797',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__43797___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__43797___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_38915',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38915___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38915___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_43878',axiom,
! [V_24X1,V_24Y] :
( c_24__type__43878___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__43878___24a1(V_24X1)) ) ).
fof('$tdef_$_type_45392',axiom,
! [V_24Y] :
( c_24__type__45392___24t(V_24Y)
<=> t(V_24Y,c_24__type__45392) ) ).
fof('$tdef_$_type_51101',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__51101___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__51101___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30510',axiom,
! [V_24Y] :
( c_24__type__30510___24t(V_24Y)
<=> t(V_24Y,c_24__type__30510) ) ).
fof('$tdef_$_type_38400',axiom,
! [V_24Y] :
( c_24__type__38400___24t(V_24Y)
<=> t(V_24Y,c_24__type__38400) ) ).
fof('$tdef_$_type_11018',axiom,
! [V_24Y] :
( c_24__type__11018___24t(V_24Y)
<=> t(V_24Y,c_24__type__11018) ) ).
fof('$tdef_$_type_51813',axiom,
! [V_24Y] :
( c_24__type__51813___24t(V_24Y)
<=> t(V_24Y,c_24__type__51813) ) ).
fof('$tdef_$_type_38983',axiom,
! [V_24Y] :
( c_24__type__38983___24t(V_24Y)
<=> t(V_24Y,c_24__type__38983) ) ).
fof('$tdef_$_type_38581',axiom,
! [V_24Y] :
( c_24__type__38581___24t(V_24Y)
<=> t(V_24Y,c_24__type__38581) ) ).
fof('$tdef_$_type_44651',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44651___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44651___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11806',axiom,
! [V_24Y] :
( c_24__type__11806___24t(V_24Y)
<=> t(V_24Y,c_24__type__11806) ) ).
fof('$tdef_$_type_11798',axiom,
! [V_24Y] :
( c_24__type__11798___24t(V_24Y)
<=> t(V_24Y,c_24__type__11798) ) ).
fof('$tdef_$_type_1171',axiom,
! [V_24Y] :
( c_24__type__1171___24t(V_24Y)
<=> t(V_24Y,c_24__type__1171) ) ).
fof('$tdef_$_type_45278',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45278___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45278___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_736',axiom,
! [V_24Y] :
( c_24__type__736___24t(V_24Y)
<=> t(V_24Y,c_24__type__736) ) ).
fof('$tdef_$_type_42195',axiom,
! [V_24Y] :
( c_24__type__42195___24t(V_24Y)
<=> t(V_24Y,c_24__type__42195) ) ).
fof('$tdef_$_type_39716',axiom,
! [V_24Y] :
( c_24__type__39716___24t(V_24Y)
<=> t(V_24Y,c_24__type__39716) ) ).
fof('$tdef_$_type_35072',axiom,
! [V_24Y] :
( c_24__type__35072___24t(V_24Y)
<=> t(V_24Y,c_24__type__35072) ) ).
fof('$tdef_$_type_10973',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10973___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10973___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_723',axiom,
! [V_24Y] :
( c_24__type__723___24t(V_24Y)
<=> t(V_24Y,c_24__type__723) ) ).
fof('$tdef_$_type_42604',axiom,
! [V_24Y] :
( c_24__type__42604___24t(V_24Y)
<=> t(V_24Y,c_24__type__42604) ) ).
fof('$tdef_$_type_39737',axiom,
! [V_24Y] :
( c_24__type__39737___24t(V_24Y)
<=> t(V_24Y,c_24__type__39737) ) ).
fof('$tdef_$_type_64985',axiom,
! [V_24X1,V_24Y] :
( c_24__type__64985___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__64985___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37375',axiom,
! [V_24Y] :
( c_24__type__37375___24t(V_24Y)
<=> t(V_24Y,c_24__type__37375) ) ).
fof('$tdef_$_type_45151',axiom,
! [V_24Y] :
( c_24__type__45151___24t(V_24Y)
<=> t(V_24Y,c_24__type__45151) ) ).
fof('$tdef_$_type_39022',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39022___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39022___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45374',axiom,
! [V_24Y] :
( c_24__type__45374___24t(V_24Y)
<=> t(V_24Y,c_24__type__45374) ) ).
fof('$tdef_$_type_42564',axiom,
! [V_24Y] :
( c_24__type__42564___24t(V_24Y)
<=> t(V_24Y,c_24__type__42564) ) ).
fof('$tdef_$_type_45807',axiom,
! [V_24Y] :
( c_24__type__45807___24t(V_24Y)
<=> t(V_24Y,c_24__type__45807) ) ).
fof('$tdef_$_type_39007',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__39007___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__39007___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_ZornsLemma.Families.Family',axiom,
! [V_24X1,V_24Y] :
( cZornsLemma_2eFamilies_2eFamily___24t(V_24X1,V_24Y)
<=> t(V_24Y,cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1)) ) ).
fof('$tdef_$_type_49944',axiom,
! [V_24X1,V_24Y] :
( c_24__type__49944___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__49944___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2667',axiom,
! [V_24Y] :
( c_24__type__2667___24t(V_24Y)
<=> t(V_24Y,c_24__type__2667) ) ).
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_$_type_42669',axiom,
! [V_24Y] :
( c_24__type__42669___24t(V_24Y)
<=> t(V_24Y,c_24__type__42669) ) ).
fof('$tdef_$_type_39684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__39684___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__39684___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_38376',axiom,
! [V_24Y] :
( c_24__type__38376___24t(V_24Y)
<=> t(V_24Y,c_24__type__38376) ) ).
fof('$tdef_$_type_35549',axiom,
! [V_24Y] :
( c_24__type__35549___24t(V_24Y)
<=> t(V_24Y,c_24__type__35549) ) ).
fof('$tdef_Coq.Sets.Partial_Order.Rel',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2ePartial__Order_2eRel___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2ePartial__Order_2eRel___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2429',axiom,
! [V_24Y] :
( c_24__type__2429___24t(V_24Y)
<=> t(V_24Y,c_24__type__2429) ) ).
fof('$tdef_$_type_1767',axiom,
! [V_24Y] :
( c_24__type__1767___24t(V_24Y)
<=> t(V_24Y,c_24__type__1767) ) ).
fof('$tdef_$_type_10998',axiom,
! [V_24Y] :
( c_24__type__10998___24t(V_24Y)
<=> t(V_24Y,c_24__type__10998) ) ).
fof('$tdef_$_type_52112',axiom,
! [V_24Y] :
( c_24__type__52112___24t(V_24Y)
<=> t(V_24Y,c_24__type__52112) ) ).
fof('$tdef_$_type_43912',axiom,
! [V_24Y] :
( c_24__type__43912___24t(V_24Y)
<=> t(V_24Y,c_24__type__43912) ) ).
fof('$tdef_$_type_37638',axiom,
! [V_24Y] :
( c_24__type__37638___24t(V_24Y)
<=> t(V_24Y,c_24__type__37638) ) ).
fof('$tdef_$_type_372',axiom,
! [V_24Y] :
( c_24__type__372___24t(V_24Y)
<=> t(V_24Y,c_24__type__372) ) ).
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_$_type_37592',axiom,
! [V_24Y] :
( c_24__type__37592___24t(V_24Y)
<=> t(V_24Y,c_24__type__37592) ) ).
fof('$tdef_$_type_35554',axiom,
! [V_24Y] :
( c_24__type__35554___24t(V_24Y)
<=> t(V_24Y,c_24__type__35554) ) ).
fof('$tdef_$_type_24662',axiom,
! [V_24Y] :
( c_24__type__24662___24t(V_24Y)
<=> t(V_24Y,c_24__type__24662) ) ).
fof('$tdef_$_type_49583',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__49583___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__49583___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_42344',axiom,
! [V_24Y] :
( c_24__type__42344___24t(V_24Y)
<=> t(V_24Y,c_24__type__42344) ) ).
fof('$tdef_$_type_38461',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38461___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38461___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_35688',axiom,
! [V_24Y] :
( c_24__type__35688___24t(V_24Y)
<=> t(V_24Y,c_24__type__35688) ) ).
fof('$tdef_$_type_45236',axiom,
! [V_24Y] :
( c_24__type__45236___24t(V_24Y)
<=> t(V_24Y,c_24__type__45236) ) ).
fof('$tdef_$_type_3122',axiom,
! [V_24Y] :
( c_24__type__3122___24t(V_24Y)
<=> t(V_24Y,c_24__type__3122) ) ).
fof('$tdef_$_type_4368',axiom,
! [V_24Y] :
( c_24__type__4368___24t(V_24Y)
<=> t(V_24Y,c_24__type__4368) ) ).
fof('$tdef_$_type_3701',axiom,
! [V_24Y] :
( c_24__type__3701___24t(V_24Y)
<=> t(V_24Y,c_24__type__3701) ) ).
fof('$tdef_Topology.Filters.Filter',axiom,
! [V_24X1,V_24Y] :
( cTopology_2eFilters_2eFilter___24t(V_24X1,V_24Y)
<=> t(V_24Y,cTopology_2eFilters_2eFilter___24a1(V_24X1)) ) ).
fof('$tdef_$_type_45785',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__45785___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__45785___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_42499',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__42499___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__42499___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45617',axiom,
! [V_24Y] :
( c_24__type__45617___24t(V_24Y)
<=> t(V_24Y,c_24__type__45617) ) ).
fof('$tdef_$_type_37271',axiom,
! [V_24Y] :
( c_24__type__37271___24t(V_24Y)
<=> t(V_24Y,c_24__type__37271) ) ).
fof('$tdef_$_type_919',axiom,
! [V_24Y] :
( c_24__type__919___24t(V_24Y)
<=> t(V_24Y,c_24__type__919) ) ).
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_$_type_24680',axiom,
! [V_24Y] :
( c_24__type__24680___24t(V_24Y)
<=> t(V_24Y,c_24__type__24680) ) ).
fof('$tdef_$_type_16074',axiom,
! [V_24X1,V_24Y] :
( c_24__type__16074___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__16074___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35099',axiom,
! [V_24Y] :
( c_24__type__35099___24t(V_24Y)
<=> t(V_24Y,c_24__type__35099) ) ).
fof('$tdef_ZornsLemma.IndexedFamilies.IndexedFamily',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18227',axiom,
! [V_24Y] :
( c_24__type__18227___24t(V_24Y)
<=> t(V_24Y,c_24__type__18227) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1770',axiom,
! [V_24Y] :
( c_24__type__1770___24t(V_24Y)
<=> t(V_24Y,c_24__type__1770) ) ).
fof('$tdef_$_type_1216',axiom,
! [V_24Y] :
( c_24__type__1216___24t(V_24Y)
<=> t(V_24Y,c_24__type__1216) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_ZornsLemma.ZornsLemma.chains',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cZornsLemma_2eZornsLemma_2echains___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cZornsLemma_2eZornsLemma_2echains___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_49970',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__49970___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__49970___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_42722',axiom,
! [V_24Y] :
( c_24__type__42722___24t(V_24Y)
<=> t(V_24Y,c_24__type__42722) ) ).
fof('$tdef_$_type_38607',axiom,
! [V_24Y] :
( c_24__type__38607___24t(V_24Y)
<=> t(V_24Y,c_24__type__38607) ) ).
fof('$tdef_$_type_38762',axiom,
! [V_24Y] :
( c_24__type__38762___24t(V_24Y)
<=> t(V_24Y,c_24__type__38762) ) ).
fof('$tdef_$_type_39564',axiom,
! [V_24Y] :
( c_24__type__39564___24t(V_24Y)
<=> t(V_24Y,c_24__type__39564) ) ).
fof('$tdef_$_type_42738',axiom,
! [V_24Y] :
( c_24__type__42738___24t(V_24Y)
<=> t(V_24Y,c_24__type__42738) ) ).
fof('$tdef_$_type_10955',axiom,
! [V_24Y] :
( c_24__type__10955___24t(V_24Y)
<=> t(V_24Y,c_24__type__10955) ) ).
fof('$tdef_$_type_45411',axiom,
! [V_24Y] :
( c_24__type__45411___24t(V_24Y)
<=> t(V_24Y,c_24__type__45411) ) ).
fof('$tdef_$_type_37437',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37437___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37437___24a1(V_24X1)) ) ).
fof('$tdef_Topology.DirectedSets.DirectedSet',axiom,
! [V_24Y] :
( cTopology_2eDirectedSets_2eDirectedSet___24t(V_24Y)
<=> t(V_24Y,cTopology_2eDirectedSets_2eDirectedSet) ) ).
fof('$tdef_Coq.Reals.RiemannInt_SF.IsStepFun',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRiemannInt__SF_2eIsStepFun___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Vectors.VectorDef.t',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35122',axiom,
! [V_24Y] :
( c_24__type__35122___24t(V_24Y)
<=> t(V_24Y,c_24__type__35122) ) ).
fof('$tdef_$_type_45316',axiom,
! [V_24Y] :
( c_24__type__45316___24t(V_24Y)
<=> t(V_24Y,c_24__type__45316) ) ).
fof('$tdef_Coq.Sets.Relations_1.Relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2890',axiom,
! [V_24Y] :
( c_24__type__2890___24t(V_24Y)
<=> t(V_24Y,c_24__type__2890) ) ).
fof('$tdef_$_type_1034',axiom,
! [V_24Y] :
( c_24__type__1034___24t(V_24Y)
<=> t(V_24Y,c_24__type__1034) ) ).
fof('$tdef_$_type_3130',axiom,
! [V_24Y] :
( c_24__type__3130___24t(V_24Y)
<=> t(V_24Y,c_24__type__3130) ) ).
fof('$tdef_$_type_50483',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__50483___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__50483___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32518',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32518___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32518___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_44548',axiom,
! [V_24X1,V_24Y] :
( c_24__type__44548___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__44548___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1211',axiom,
! [V_24Y] :
( c_24__type__1211___24t(V_24Y)
<=> t(V_24Y,c_24__type__1211) ) ).
fof('$tdef_$_type_44684',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44684___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44684___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_38488',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38488___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38488___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8712',axiom,
! [V_24Y] :
( c_24__type__8712___24t(V_24Y)
<=> t(V_24Y,c_24__type__8712) ) ).
fof('$tdef_$_type_11',axiom,
! [V_24Y] :
( c_24__type__11___24t(V_24Y)
<=> t(V_24Y,c_24__type__11) ) ).
fof('$tdef_$_type_38472',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38472___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38472___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Topology.FiltersAndNets.filter_to_net_DS_set',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cTopology_2eFiltersAndNets_2efilter__to__net__DS__set___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11775',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__11775___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__11775___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_38820',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38820___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38820___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_37324',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__37324___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__37324___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_682',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__682___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__682___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_39547',axiom,
! [V_24Y] :
( c_24__type__39547___24t(V_24Y)
<=> t(V_24Y,c_24__type__39547) ) ).
fof('$tdef_$_type_38494',axiom,
! [V_24Y] :
( c_24__type__38494___24t(V_24Y)
<=> t(V_24Y,c_24__type__38494) ) ).
fof('$tdef_$_type_11793',axiom,
! [V_24Y] :
( c_24__type__11793___24t(V_24Y)
<=> t(V_24Y,c_24__type__11793) ) ).
fof('$tdef_$_type_45622',axiom,
! [V_24Y] :
( c_24__type__45622___24t(V_24Y)
<=> t(V_24Y,c_24__type__45622) ) ).
fof('$tdef_$_type_16677',axiom,
! [V_24Y] :
( c_24__type__16677___24t(V_24Y)
<=> t(V_24Y,c_24__type__16677) ) ).
fof('$tdef_$_type_11381',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11381___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11381___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_49948',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__49948___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__49948___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_51405',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__51405___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__51405___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45485',axiom,
! [V_24Y] :
( c_24__type__45485___24t(V_24Y)
<=> t(V_24Y,c_24__type__45485) ) ).
fof('$tdef_$_type_2611',axiom,
! [V_24Y] :
( c_24__type__2611___24t(V_24Y)
<=> t(V_24Y,c_24__type__2611) ) ).
fof('$tdef_$_type_44608',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__44608___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__44608___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_50009',axiom,
! [V_24Y] :
( c_24__type__50009___24t(V_24Y)
<=> t(V_24Y,c_24__type__50009) ) ).
fof('$tdef_$_type_28214',axiom,
! [V_24Y] :
( c_24__type__28214___24t(V_24Y)
<=> t(V_24Y,c_24__type__28214) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_674',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__674___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__674___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_50033',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__50033___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__50033___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_49982',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__49982___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__49982___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35532',axiom,
! [V_24Y] :
( c_24__type__35532___24t(V_24Y)
<=> t(V_24Y,c_24__type__35532) ) ).
fof('$tdef_$_type_4479',axiom,
! [V_24Y] :
( c_24__type__4479___24t(V_24Y)
<=> t(V_24Y,c_24__type__4479) ) ).
fof('$tdef_$_type_16032',axiom,
! [V_24Y] :
( c_24__type__16032___24t(V_24Y)
<=> t(V_24Y,c_24__type__16032) ) ).
fof('$tdef_$_type_1114',axiom,
! [V_24Y] :
( c_24__type__1114___24t(V_24Y)
<=> t(V_24Y,c_24__type__1114) ) ).
fof('$tdef_$_type_2434',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2434___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2434___24a1(V_24X1)) ) ).
fof('$tdef_$_type_41582',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41582___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41582___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_32601',axiom,
! [V_24Y] :
( c_24__type__32601___24t(V_24Y)
<=> t(V_24Y,c_24__type__32601) ) ).
fof('$tdef_$_type_2632',axiom,
! [V_24Y] :
( c_24__type__2632___24t(V_24Y)
<=> t(V_24Y,c_24__type__2632) ) ).
fof('$tdef_$_type_18348',axiom,
! [V_24Y] :
( c_24__type__18348___24t(V_24Y)
<=> t(V_24Y,c_24__type__18348) ) ).
fof('$tdef_$_type_39840',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39840___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39840___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29998',axiom,
! [V_24Y] :
( c_24__type__29998___24t(V_24Y)
<=> t(V_24Y,c_24__type__29998) ) ).
fof('$tdef_$_type_8708',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8708___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8708___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38828',axiom,
! [V_24Y] :
( c_24__type__38828___24t(V_24Y)
<=> t(V_24Y,c_24__type__38828) ) ).
fof('$tdef_$_type_43866',axiom,
! [V_24Y] :
( c_24__type__43866___24t(V_24Y)
<=> t(V_24Y,c_24__type__43866) ) ).
fof('$tdef_$_type_24018',axiom,
! [V_24Y] :
( c_24__type__24018___24t(V_24Y)
<=> t(V_24Y,c_24__type__24018) ) ).
fof('$tdef_$_type_1774',axiom,
! [V_24Y] :
( c_24__type__1774___24t(V_24Y)
<=> t(V_24Y,c_24__type__1774) ) ).
fof('$tdef_$_type_43805',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__43805___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__43805___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2769',axiom,
! [V_24Y] :
( c_24__type__2769___24t(V_24Y)
<=> t(V_24Y,c_24__type__2769) ) ).
fof('$tdef_$_type_38228',axiom,
! [V_24Y] :
( c_24__type__38228___24t(V_24Y)
<=> t(V_24Y,c_24__type__38228) ) ).
fof('$tdef_$_type_32553',axiom,
! [V_24Y] :
( c_24__type__32553___24t(V_24Y)
<=> t(V_24Y,c_24__type__32553) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cTopology_2eInteriorsClosures_2eclosure___24a2(cX,cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(V0__n)),cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
%------------------------------------------------------------------------------