%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG365-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:08:58 AM UTC 2026
% Result : Unsatisfiable 126.04s 25.72s
% Output : CNFRefutation 126.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 478
% Syntax : Number of formulae : 4042 (2369 unt; 0 typ; 0 def)
% Number of atoms : 23268 (8477 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 72554 (5861 ~;7666 |; 0 &;59027 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 86 usr; 13 con; 0-5 aty)
% Number of variables : 13368 ( 0 ^;13368 !; 0 ?;13368 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i > $i ).
thf(tp_c_Complex_OIm,type,
c_Complex_OIm: $i ).
thf(tp_c_Complex_ORe,type,
c_Complex_ORe: $i ).
thf(tp_c_Complex_Ocomplex_OComplex,type,
c_Complex_Ocomplex_OComplex: $i > $i > $i ).
thf(tp_c_Deriv_Odifferentiable,type,
c_Deriv_Odifferentiable: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Osetsum,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(tp_c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: $i > $i ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(tp_c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(tp_c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_Lim_OLIM,type,
c_Lim_OLIM: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Lim_OisCont,type,
c_Lim_OisCont: $i > $i > $i > $i > $o ).
thf(tp_c_Lim_OisUCont,type,
c_Lim_OisUCont: $i > $i > $i > $o ).
thf(tp_c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1,type,
c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1: $i > $i > $i > $i ).
thf(tp_c_Limits_OZfun,type,
c_Limits_OZfun: $i > $i > $i > $i > $o ).
thf(tp_c_Limits_Otendsto,type,
c_Limits_Otendsto: $i > $i > $i > $i > $i > $o ).
thf(tp_c_RealVector_Obounded__linear,type,
c_RealVector_Obounded__linear: $i > $i > $i > $o ).
thf(tp_c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: $i > $i ).
thf(tp_c_RealVector_Oof__real,type,
c_RealVector_Oof__real: $i > $i ).
thf(tp_c_RealVector_OscaleR__class_OscaleR,type,
c_RealVector_OscaleR__class_OscaleR: $i > $i ).
thf(tp_c_SEQ_OCauchy,type,
c_SEQ_OCauchy: $i > $i > $o ).
thf(tp_c_SEQ_OLIMSEQ,type,
c_SEQ_OLIMSEQ: $i > $i > $i > $o ).
thf(tp_c_SEQ_OZseq,type,
c_SEQ_OZseq: $i > $i > $o ).
thf(tp_c_SEQ_Oconvergent,type,
c_SEQ_Oconvergent: $i > $i > $o ).
thf(tp_c_SEQ_Olim,type,
c_SEQ_Olim: $i > $i > $i ).
thf(tp_c_SEQ_Omonoseq,type,
c_SEQ_Omonoseq: $i > $o ).
thf(tp_c_SEQ_Osubseq,type,
c_SEQ_Osubseq: $i > $o ).
thf(tp_c_Series_Osuminf,type,
c_Series_Osuminf: $i > $i > $i ).
thf(tp_c_Series_Osummable,type,
c_Series_Osummable: $i > $i > $o ).
thf(tp_c_Series_Osums,type,
c_Series_Osums: $i > $i > $i > $o ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i ).
thf(tp_c_fequal,type,
c_fequal: $i > $i > $i > $o ).
thf(tp_class_HOL_Ozero,type,
class_HOL_Ozero: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(tp_class_RealVector_Ometric__space,type,
class_RealVector_Ometric__space: $i > $o ).
thf(tp_class_RealVector_Oreal__algebra,type,
class_RealVector_Oreal__algebra: $i > $o ).
thf(tp_class_RealVector_Oreal__algebra__1,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(tp_class_RealVector_Oreal__vector,type,
class_RealVector_Oreal__vector: $i > $o ).
thf(tp_class_RealVector_Otopological__space,type,
class_RealVector_Otopological__space: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tp_class_SEQ_Obanach,type,
class_SEQ_Obanach: $i > $o ).
thf(tp_class_SEQ_Ocomplete__space,type,
class_SEQ_Ocomplete__space: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
thf(tp_tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_f____,type,
v_f____: $i ).
thf(tp_v_ga____,type,
v_ga____: $i ).
thf(tp_v_s,type,
v_s: $i ).
thf(tp_v_sko__CHAINED__1,type,
v_sko__CHAINED__1: $i > $i > $i > $i ).
thf(tp_v_thesis____,type,
v_thesis____: $o ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(4,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(5,axiom,
class_HOL_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
thf(6,axiom,
class_SEQ_Obanach @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
thf(7,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(8,axiom,
class_SEQ_Ocomplete__space @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Ocomplete__space) ).
thf(9,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(10,axiom,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(11,axiom,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(12,axiom,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(13,axiom,
class_RealVector_Oreal__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
thf(14,axiom,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(15,axiom,
class_RealVector_Ometric__space @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
thf(16,axiom,
class_RealVector_Oreal__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
thf(17,axiom,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(18,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(19,axiom,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(20,axiom,
class_RealVector_Oreal__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
thf(21,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(22,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(23,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(24,axiom,
class_RealVector_Otopological__space @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Otopological__space) ).
thf(25,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(26,axiom,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(27,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(28,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(29,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(30,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(31,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(32,axiom,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(33,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(34,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(35,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(36,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(37,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(38,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(39,axiom,
class_HOL_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
thf(40,axiom,
class_SEQ_Obanach @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
thf(41,axiom,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
thf(42,axiom,
class_SEQ_Ocomplete__space @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Ocomplete__space) ).
thf(43,axiom,
class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
thf(44,axiom,
class_Ring__and__Field_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
thf(45,axiom,
class_Ring__and__Field_Ofield @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
thf(46,axiom,
class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
thf(47,axiom,
class_RealVector_Oreal__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
thf(48,axiom,
class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
thf(49,axiom,
class_RealVector_Ometric__space @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
thf(50,axiom,
class_RealVector_Oreal__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
thf(51,axiom,
class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
thf(52,axiom,
class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
thf(53,axiom,
class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(54,axiom,
class_RealVector_Oreal__algebra__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
thf(55,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
thf(56,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
thf(57,axiom,
class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(58,axiom,
class_RealVector_Otopological__space @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Otopological__space) ).
thf(59,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
thf(60,axiom,
class_Ring__and__Field_Odivision__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
thf(61,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
thf(62,axiom,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(63,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
thf(64,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(65,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
thf(66,axiom,
class_Ring__and__Field_Odivision__by__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
thf(67,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
thf(68,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(69,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
thf(70,axiom,
class_OrderedGroup_Oordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
thf(71,axiom,
class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
thf(72,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
thf(73,axiom,
class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
thf(74,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(75,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
thf(76,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(77,axiom,
class_HOL_Ozero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
thf(78,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(79,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(80,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(81,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(82,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(83,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(84,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(85,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(86,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(87,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(88,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(89,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(90,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Oboolean__algebra @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(91,axiom,
c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( v_sko__CHAINED__1 @ v_f____ @ v_ga____ @ v_s ) @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(92,axiom,
! [V_X: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osummable_0) ).
thf(93,axiom,
! [V_X: $i] :
( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ V_X @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osuminf_0) ).
thf(94,axiom,
! [T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ c_Complex_OIm @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OLIM_0) ).
thf(95,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__inverse_0) ).
thf(96,axiom,
c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ v_f____ @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f_I2_J_0) ).
thf(97,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(98,axiom,
! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ V_l @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ c_Suc @ tc_nat @ T_a @ tc_nat ) @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Suc__iff_0) ).
thf(99,axiom,
! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ c_Suc @ tc_nat @ T_a @ tc_nat ) @ V_l @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_f @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Suc_0) ).
thf(100,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__imp__Cauchy_0) ).
thf(101,axiom,
! [V_a: $i] : ( c_Lim_OisCont @ c_Complex_OIm @ V_a @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OisCont_0) ).
thf(102,axiom,
! [T_a: $i,V_r: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OLIMSEQ_0) ).
thf(103,axiom,
c_SEQ_Osubseq @ v_f____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f_I1_J_0) ).
thf(104,axiom,
! [T_a: $i,V_f: $i,V_g: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ V_f @ V_g @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_g @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_f @ ( hAPP @ V_g @ V_x ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__compose_0) ).
thf(105,axiom,
! [T_a: $i,V_x: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIMSEQ_0) ).
thf(106,axiom,
c_SEQ_Oconvergent @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conv2_0) ).
thf(107,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( V_a = V_b )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_b @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__unique_0) ).
thf(108,axiom,
! [T_a: $i,T_c: $i,T_b: $i,V_g: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ V_g @ V_f @ T_b @ T_c @ T_a ) @ V_a @ T_a @ T_c )
| ~ ( c_Lim_OisCont @ V_g @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__o2_0) ).
thf(109,axiom,
! [V_g: $i,T_a: $i,V_net: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OZfun_0) ).
thf(110,axiom,
! [V_X: $i,V_a: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osums_0) ).
thf(111,axiom,
! [V_X: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OCauchy_0) ).
thf(112,axiom,
! [V_X: $i,V_a: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OLIMSEQ_0) ).
thf(113,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OLIMSEQ_0) ).
thf(114,axiom,
! [V_g: $i,V_A: $i,T_a: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_a @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_A @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osetsum_0) ).
thf(115,axiom,
! [T_b: $i,T_a: $i,V_X: $i,V_S: $i,V_L: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_X @ V_S @ T_a @ T_b @ tc_nat ) @ V_L @ T_b )
| ~ ( c_SEQ_OLIMSEQ @ V_S @ V_a @ T_a )
| ( ( hAPP @ V_S @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ V_S @ V_a @ T_a ) )
= V_a )
| ~ ( c_Lim_OLIM @ V_X @ V_a @ V_L @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__SEQ__conv1_0) ).
thf(116,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ ( hAPP @ V_f @ V_a ) @ T_b )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OLIMSEQ_0) ).
thf(117,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_x @ T_a @ tc_nat ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__const__iff_1) ).
thf(118,axiom,
! [T_a: $i,V_k: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__const_0) ).
thf(119,axiom,
! [V_X: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OZseq_0) ).
thf(120,axiom,
c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_g_I2_J_0) ).
thf(121,axiom,
! [V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Otendsto_0) ).
thf(122,axiom,
! [T_a: $i,V_X: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( ( c_SEQ_Olim @ V_X @ T_a )
= V_L )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_L @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_limI_0) ).
thf(123,axiom,
! [T_a: $i,V_f: $i,V_a: $i,V_k: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__offset_0) ).
thf(124,axiom,
! [T_a: $i,V_f: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_f @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__ignore__initial__segment_0) ).
thf(125,axiom,
! [V_x: $i,V_y: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ V_x @ V_y ) )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_0) ).
thf(126,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__norm_0) ).
thf(127,axiom,
c_SEQ_Osubseq @ v_ga____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_g_I1_J_0) ).
thf(128,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__norm__zero_1) ).
thf(129,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__norm__zero_0) ).
thf(130,axiom,
! [T_a: $i,T_b: $i,T_c: $i,V_g: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_g @ V_f @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_g @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_Lim_OLIM @ V_g @ V_l @ ( hAPP @ V_g @ V_l ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__compose_0) ).
thf(131,axiom,
! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( V_k = V_l )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__const__iff_0) ).
thf(132,axiom,
c_SEQ_Oconvergent @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ v_f____ @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conv1_0) ).
thf(133,axiom,
! [V_x: $i,V_y: $i] :
( ( ( hAPP @ c_Complex_OIm @ V_x )
!= ( hAPP @ c_Complex_OIm @ V_y ) )
| ( ( hAPP @ c_Complex_ORe @ V_x )
!= ( hAPP @ c_Complex_ORe @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__equality_0) ).
thf(134,axiom,
! [T_a: $i,V_X: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__def_1) ).
thf(135,axiom,
! [T_a: $i,V_X: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_L @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergentI_0) ).
thf(136,axiom,
! [V_y: $i] :
( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ V_y @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
thf(137,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__minus__cancel_0) ).
thf(138,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__minus_0) ).
thf(139,axiom,
! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(140,axiom,
! [V_X: $i,V_a: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OLIMSEQ_0) ).
thf(141,axiom,
c_Lim_OisUCont @ c_Complex_OIm @ tc_Complex_Ocomplex @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OisUCont_0) ).
thf(142,axiom,
! [V_a: $i] : ( c_Lim_OLIM @ c_Complex_OIm @ V_a @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Ocont_0) ).
thf(143,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(144,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(145,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Obounded__linear__right_0) ).
thf(146,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__norm_0) ).
thf(147,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( ( hAPP @ V_f @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b ) )
| ~ ( c_Series_Osummable @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Osuminf_0) ).
thf(148,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osums_0) ).
thf(149,axiom,
! [V_x: $i,V_y: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ V_x @ V_y ) )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_0) ).
thf(150,axiom,
c_Lim_OisUCont @ c_Complex_ORe @ tc_Complex_Ocomplex @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OisUCont_0) ).
thf(151,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(152,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ V_x ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).
thf(153,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__left_0) ).
thf(154,axiom,
! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OCauchy_0) ).
thf(155,axiom,
! [T_b: $i,V_r: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Otendsto_0) ).
thf(156,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
thf(157,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).
thf(158,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__def_0) ).
thf(159,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__def_1) ).
thf(160,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OCauchy @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OCauchy_0) ).
thf(161,axiom,
! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a )
| ( c_Series_Osums @ V_f @ ( c_Series_Osuminf @ V_f @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_2) ).
thf(162,axiom,
! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ V_f @ ( c_Series_Osuminf @ V_f @ T_a ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__sums_0) ).
thf(163,axiom,
! [T_a: $i,V_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OZseq__right_0) ).
thf(164,axiom,
! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OZseq_0) ).
thf(165,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Ocont_0) ).
thf(166,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(167,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(168,axiom,
! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__minus_0) ).
thf(169,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(170,axiom,
! [V_X: $i] :
( ( c_SEQ_Oconvergent @ V_X @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__Cauchy__convergent_0) ).
thf(171,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__Cauchy_0) ).
thf(172,axiom,
! [T_a: $i,V_r: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OisUCont_0) ).
thf(173,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_SEQ_Ocomplete__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cauchy__convergent__iff_0) ).
thf(174,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_SEQ_Ocomplete__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cauchy__convergent__iff_1) ).
thf(175,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(176,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(177,axiom,
! [V_z: $i] :
( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ V_z ) @ ( hAPP @ c_Complex_OIm @ V_z ) )
= V_z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__surj_0) ).
thf(178,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(179,axiom,
! [V_X: $i,V_a: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osums_0) ).
thf(180,axiom,
! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ V_f @ T_a )
= V_x )
| ~ ( c_Series_Osums @ V_f @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_1) ).
thf(181,axiom,
! [T_a: $i,V_s: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( V_s
= ( c_Series_Osuminf @ V_f @ T_a ) )
| ~ ( c_Series_Osums @ V_f @ V_s @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__unique_0) ).
thf(182,axiom,
! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__LIMSEQ__zero_0) ).
thf(183,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Series_Osums @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ ( hAPP @ V_f @ V_a ) @ T_b )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Osums_0) ).
thf(184,axiom,
! [V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Otendsto_0) ).
thf(185,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(186,axiom,
! [T_a: $i,V_z: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(187,axiom,
! [T_b: $i,T_a: $i,V_r: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OLIM_0) ).
thf(188,axiom,
! [T_a: $i,V_f: $i,V_k: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__ignore__initial__segment_0) ).
thf(189,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(190,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(191,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(192,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(193,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(194,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(195,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(196,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(197,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_y )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(198,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(199,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(200,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
thf(201,axiom,
! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_w ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_w ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(202,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_d ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_d ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(203,axiom,
! [T_a: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_g @ tc_RealDef_Oreal @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osetsum_0) ).
thf(204,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(205,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(206,axiom,
! [V_x: $i,V_y: $i] :
( ( ( hAPP @ c_Suc @ V_x )
!= ( hAPP @ c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(207,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( hAPP @ c_Suc @ V_nat )
!= ( hAPP @ c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(208,axiom,
! [T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_x @ V_k @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__const_0) ).
thf(209,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).
thf(210,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(211,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(212,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(213,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(214,axiom,
! [T_b: $i,V_k: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Otopological__space @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_k @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__const_0) ).
thf(215,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OZseq_0) ).
thf(216,axiom,
! [T_a: $i,V_ra: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_ra ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_ra ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OscaleR_0) ).
thf(217,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
thf(218,axiom,
! [T_a: $i,V_a: $i,V_r: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).
thf(219,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
thf(220,axiom,
! [T_a: $i,T_b: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__0_0) ).
thf(221,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ c_Suc @ V_n ) )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(222,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(223,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__norm_0) ).
thf(224,axiom,
! [T_a: $i,V_r: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OisCont_0) ).
thf(225,axiom,
! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_0) ).
thf(226,axiom,
! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__summable_0) ).
thf(227,axiom,
! [T_b: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_b @ T_a ) @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__zero_0) ).
thf(228,axiom,
! [T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__mult_0) ).
thf(229,axiom,
! [T_a: $i,V_x: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osums_0) ).
thf(230,axiom,
! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osummable_0) ).
thf(231,axiom,
! [T_a: $i,V_c: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__mult_0) ).
thf(232,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__isCont__iff_0) ).
thf(233,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__isCont__iff_1) ).
thf(234,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_L @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__offset__zero_0) ).
thf(235,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_L @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__offset__zero__cancel_0) ).
thf(236,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_SEQ_OCauchy @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_Lim_OisUCont @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isUCont__Cauchy_0) ).
thf(237,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( ( hAPP @ V_f @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ ( hAPP @ V_f @ V_x ) ) )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OscaleR_0) ).
thf(238,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_f @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__of__real_0) ).
thf(239,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(240,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).
thf(241,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).
thf(242,axiom,
! [T_a: $i,V_xa: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OscaleR_0) ).
thf(243,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osummable_0) ).
thf(244,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(245,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(246,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(247,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(248,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(249,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(250,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(251,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(252,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(253,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(254,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(255,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(256,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(257,axiom,
! [T_a: $i,V_f: $i,T_b: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_f @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(258,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__zero_0) ).
thf(259,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisUCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OisUCont_0) ).
thf(260,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_g: $i,T_c: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Limits_OZfun @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_net @ T_c @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OZfun_0) ).
thf(261,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= V_y )
| ( V_x
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(262,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_b_H ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b_H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Oadd__right_0) ).
thf(263,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Oadd_0) ).
thf(264,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) @ T_a @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__inverse__fun_0) ).
thf(265,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__minus__iff_1) ).
thf(266,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__minus__iff_0) ).
thf(267,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__norm_0) ).
thf(268,axiom,
! [V_X: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osummable_0) ).
thf(269,axiom,
! [T_a: $i,V_a: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_g @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osetsum_0) ).
thf(270,axiom,
! [T_a: $i,V_g: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_g @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_SEQ_Olim @ V_g @ T_a ) ) )
| ~ ( c_SEQ_Oconvergent @ V_g @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lim__uminus_0) ).
thf(271,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_Series_Osuminf @ V_X @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osuminf_0) ).
thf(272,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OisCont_0) ).
thf(273,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(274,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(275,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(276,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(277,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ ( c_SEQ_Olim @ V_X @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__LIMSEQ__iff_1) ).
thf(278,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ ( c_SEQ_Olim @ V_X @ T_a ) @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__LIMSEQ__iff_0) ).
thf(279,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_e ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_e ) ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_e ) ) @ V_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(280,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_1) ).
thf(281,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
thf(282,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ozero__left_0) ).
thf(283,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
thf(284,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__inverse_0) ).
thf(285,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Series_Osummable @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_Series_Osummable @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Osummable_0) ).
thf(286,axiom,
! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(287,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(288,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(289,axiom,
! [T_a: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_r ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).
thf(290,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(291,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(292,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(293,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(294,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(295,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(296,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(297,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(298,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(299,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(300,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(301,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__norm__zero__iff_0) ).
thf(302,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__norm__zero_0) ).
thf(303,axiom,
! [T_a: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ V_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OisCont_0) ).
thf(304,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(305,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(306,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(307,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_g: $i,T_c: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Limits_Otendsto @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ ( hAPP @ V_f @ V_a ) @ V_net @ T_c @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Otendsto_0) ).
thf(308,axiom,
! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_f @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ( ( hAPP @ V_f @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Deriv_Odifferentiable @ V_f @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__inverse_0) ).
thf(309,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(310,axiom,
! [T_b: $i,V_x: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OZfun_0) ).
thf(311,axiom,
! [T_b: $i,V_a: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_a ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__mult__right_0) ).
thf(312,axiom,
! [T_a: $i,T_b: $i,T_c: $i,V_f: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_f @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OLIM_0) ).
thf(313,axiom,
! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_d ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(314,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(315,axiom,
! [V_g: $i,V_A: $i,T_a: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_a @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_A @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osetsum_0) ).
thf(316,axiom,
! [T_b: $i,T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_RealVector_Oof__real @ T_b ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__of__real_0) ).
thf(317,axiom,
! [T_a: $i,T_b: $i,T_c: $i,V_g: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_g @ V_f @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_g @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_Lim_OisCont @ V_g @ V_l @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__LIM__compose_0) ).
thf(318,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OZseq @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OZseq @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OZseq_0) ).
thf(319,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__zero_0) ).
thf(320,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_L ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__minus_0) ).
thf(321,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_x )
!= ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
thf(322,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
thf(323,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
thf(324,axiom,
! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
thf(325,axiom,
! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osummable_0) ).
thf(326,axiom,
! [V_a: $i] : ( c_Lim_OisCont @ c_Complex_ORe @ V_a @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OisCont_0) ).
thf(327,axiom,
! [T_a: $i,V_r: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osums_0) ).
thf(328,axiom,
! [T_b: $i,T_a: $i,V_r: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OLIM__zero_0) ).
thf(329,axiom,
! [T_b: $i,T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_c ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OLIM__right__zero_0) ).
thf(330,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b )
| ~ ( c_Lim_OisUCont @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isUCont__isCont_0) ).
thf(331,axiom,
! [T_a: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_y ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ocont_0) ).
thf(332,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(333,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_b ) )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(334,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__iff_1) ).
thf(335,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__iff_0) ).
thf(336,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__zero_0) ).
thf(337,axiom,
! [T_b: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Otendsto_0) ).
thf(338,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(339,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__zero_0) ).
thf(340,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(341,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(342,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(343,axiom,
! [T_a: $i,V_a: $i,V_r: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__right_0) ).
thf(344,axiom,
! [T_a: $i,V_r: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OscaleR_0) ).
thf(345,axiom,
! [T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).
thf(346,axiom,
! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_0) ).
thf(347,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_Series_Osuminf @ V_X @ T_a ) ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__minus_0) ).
thf(348,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__minus_0) ).
thf(349,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_L ) @ T_a @ T_b )
| ( V_L
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__inverse_0) ).
thf(350,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ c_Suc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(351,axiom,
! [T_a: $i,V_r: $i,V_f: $i,V_A: $i,T_b: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_f @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(352,axiom,
! [T_a: $i,V_x: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_g @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osetsum_0) ).
thf(353,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(354,axiom,
! [T_b: $i,T_a: $i,V_k: $i,V_L: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( V_k = V_L )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_a @ V_L @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__const__eq_0) ).
thf(355,axiom,
! [T_a: $i,T_b: $i,V_k: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_a @ V_L @ T_b @ T_a )
| ( V_k = V_L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__const__not__eq_0) ).
thf(356,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(357,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(358,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(359,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(360,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(361,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(362,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(363,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(364,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(365,axiom,
! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_f @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_f @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__minus_0) ).
thf(366,axiom,
! [T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ c_Complex_ORe @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OLIM_0) ).
thf(367,axiom,
! [T_b: $i,T_a: $i,V_x: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIM_0) ).
thf(368,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(369,axiom,
! [V_X: $i] :
( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ V_X @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osuminf_0) ).
thf(370,axiom,
! [T_a: $i,V_c: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ ( c_Series_Osuminf @ V_f @ T_a ) ) )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__mult_0) ).
thf(371,axiom,
! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osuminf_0) ).
thf(372,axiom,
! [V_X: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OZseq_0) ).
thf(373,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
thf(374,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__add_0) ).
thf(375,axiom,
! [T_b: $i,V_a: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_a ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OZfun__right_0) ).
thf(376,axiom,
! [T_b: $i,V_r: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OZfun_0) ).
thf(377,axiom,
! [T_b: $i,V_x: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Otendsto_0) ).
thf(378,axiom,
! [T_b: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OZfun_0) ).
thf(379,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(380,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(381,axiom,
! [T_a: $i,V_xa: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(382,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(383,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) ) @ V_y )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(384,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(385,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_RealVector_Obounded__linear @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b @ T_a @ T_a @ T_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Obounded__linear__left_0) ).
thf(386,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(387,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(388,axiom,
! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osuminf_0) ).
thf(389,axiom,
! [T_a: $i,T_b: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_HOL_Ozero @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_b @ T_a )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__not__zero_0) ).
thf(390,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(391,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(392,axiom,
! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a_H ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a_H ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(393,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_ya )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_ya ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_ya ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(394,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_b_H ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b_H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(395,axiom,
! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(396,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(397,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(398,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(399,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ V_ry ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(400,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ V_rx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(401,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ V_ly ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(402,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(403,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__minus_0) ).
thf(404,axiom,
! [V_a: $i] : ( c_Lim_OLIM @ c_Complex_ORe @ V_a @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Ocont_0) ).
thf(405,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
thf(406,axiom,
! [T_b: $i,T_a: $i,T_c: $i,V_f: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OLIM__zero_0) ).
thf(407,axiom,
! [T_b: $i,V_f: $i,V_a: $i,V_net: $i,T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_a ) @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__minus__cancel_0) ).
thf(408,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__minus_0) ).
thf(409,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(410,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(411,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(412,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(413,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
thf(414,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Obounded__linear__right_0) ).
thf(415,axiom,
! [T_b: $i,T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_c ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult__right__zero_0) ).
thf(416,axiom,
! [T_b: $i,T_a: $i,V_x: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIM__zero_0) ).
thf(417,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(418,axiom,
! [T_a: $i,V_r: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Ocont_0) ).
thf(419,axiom,
! [V_n: $i] :
( ( hAPP @ c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(420,axiom,
! [V_n: $i] :
( V_n
!= ( hAPP @ c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(421,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_y ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(422,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_y ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(423,axiom,
! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_c ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_d ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(424,axiom,
! [T_b: $i,T_a: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OLIM__zero_0) ).
thf(425,axiom,
! [V_real1: $i,V_real2: $i,V_real1_H: $i,V_real2_H: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ V_real1 @ V_real2 )
!= ( c_Complex_Ocomplex_OComplex @ V_real1_H @ V_real2_H ) )
| ( V_real1 = V_real1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex_Oinject_0) ).
thf(426,axiom,
! [V_real1: $i,V_real2: $i,V_real1_H: $i,V_real2_H: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ V_real1 @ V_real2 )
!= ( c_Complex_Ocomplex_OComplex @ V_real1_H @ V_real2_H ) )
| ( V_real2 = V_real2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex_Oinject_1) ).
thf(427,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b ) )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(428,axiom,
! [V_X: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OCauchy_0) ).
thf(429,axiom,
! [V_g: $i,T_a: $i,V_net: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OZfun_0) ).
thf(430,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(431,axiom,
! [T_a: $i,V_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__mult__right_0) ).
thf(432,axiom,
! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OZseq_0) ).
thf(433,axiom,
! [T_a: $i,T_b: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisUCont @ V_f @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OisUCont_0) ).
thf(434,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(435,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(436,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__minus_0) ).
thf(437,axiom,
! [T_a: $i,T_b: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_a @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__const_0) ).
thf(438,axiom,
! [T_b: $i,V_f: $i,V_net: $i,T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__norm__iff_0) ).
thf(439,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__norm__iff_1) ).
thf(440,axiom,
! [T_b: $i,T_a: $i,V_L: $i,V_M: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( V_L = V_M )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_M @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__unique_0) ).
thf(441,axiom,
! [T_a: $i,V_k: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_SEQ_OZseq @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__const__iff_0) ).
thf(442,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(443,axiom,
! [T_b: $i,T_a: $i,V_g: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_OLIM__zero_0) ).
thf(444,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_c: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_f @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_c @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OLIM__left__zero_0) ).
thf(445,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OisCont_0) ).
thf(446,axiom,
! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OCauchy_0) ).
thf(447,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__norm__iff_1) ).
thf(448,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ V_X @ T_a )
| ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__norm__iff_0) ).
thf(449,axiom,
! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBK @ V_a @ T_a @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__const_0) ).
thf(450,axiom,
! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ( ( hAPP @ V_f @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__inverse_0) ).
thf(451,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ocont_0) ).
thf(452,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Ozero_0) ).
thf(453,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__0_0) ).
thf(454,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(455,axiom,
! [T_a: $i,V_f: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_f @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__norm__cancel_0) ).
thf(456,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ V_ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(457,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(458,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(459,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__minus_0) ).
thf(460,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OisUCont_0) ).
thf(461,axiom,
! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OCauchy_0) ).
thf(462,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(463,axiom,
! [T_b: $i,V_g: $i,T_a: $i,V_x: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_a ) @ V_x ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_Otendsto_0) ).
thf(464,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_f @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_a @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OZfun__left_0) ).
thf(465,axiom,
! [T_b: $i,V_g: $i,T_a: $i,V_x: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_OZfun_0) ).
thf(466,axiom,
! [T_b: $i,T_a: $i,V_g: $i,V_x: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_l ) @ V_x ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_OLIM_0) ).
thf(467,axiom,
! [T_a: $i,V_g: $i,V_A: $i,T_b: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ tc_RealDef_Oreal ) ) @ V_x )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_x @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_Osetsum_0) ).
thf(468,axiom,
! [T_a: $i,V_f: $i,V_A: $i,T_b: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) ) @ V_r )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_f @ T_a @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_r @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
thf(469,axiom,
! [T_a: $i,V_g: $i,V_A: $i,T_b: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) ) @ V_y )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_g @ T_a @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_y @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Osetsum_0) ).
thf(470,axiom,
! [T_b: $i,T_a: $i,V_g: $i,V_y: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_l ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OLIM_0) ).
thf(471,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_f @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_a @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__mult__left_0) ).
thf(472,axiom,
! [T_b: $i,V_g: $i,T_a: $i,V_y: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OZfun_0) ).
thf(473,axiom,
! [T_b: $i,V_g: $i,T_a: $i,V_y: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_a ) @ V_y ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Otendsto_0) ).
thf(474,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_c: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_f @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_c @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult__left__zero_0) ).
thf(475,axiom,
! [T_b: $i,T_a: $i,V_g: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OLIM__zero_0) ).
thf(476,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(477,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[476]) ).
thf(478,negated_conjecture,
! [V_x: $i] :
( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ V_x @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(479,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(480,plain,
$false = $false,
inference(unfold_def,[status(thm)],[477]) ).
thf(481,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(482,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(483,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(484,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(485,plain,
( ( class_HOL_Ozero @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(486,plain,
( ( class_SEQ_Obanach @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(487,plain,
( ( class_Int_Onumber__ring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(488,plain,
( ( class_SEQ_Ocomplete__space @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(489,plain,
( ( class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(490,plain,
( ( class_Ring__and__Field_Oring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(491,plain,
( ( class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(492,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(493,plain,
( ( class_RealVector_Oreal__vector @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(494,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(495,plain,
( ( class_RealVector_Ometric__space @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(496,plain,
( ( class_RealVector_Oreal__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(497,plain,
( ( class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(498,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(499,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(500,plain,
( ( class_RealVector_Oreal__algebra__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(501,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(502,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(503,plain,
( ( class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(504,plain,
( ( class_RealVector_Otopological__space @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(505,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(506,plain,
( ( class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(507,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(508,plain,
( ( class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(509,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(510,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(511,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(512,plain,
( ( class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(513,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(514,plain,
( ( class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(515,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(516,plain,
( ( class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(517,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(518,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(519,plain,
( ( class_HOL_Ozero @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(520,plain,
( ( class_SEQ_Obanach @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(521,plain,
( ( class_Int_Onumber__ring @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(522,plain,
( ( class_SEQ_Ocomplete__space @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(523,plain,
( ( class_Ring__and__Field_Oidom @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(524,plain,
( ( class_Ring__and__Field_Oring @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(525,plain,
( ( class_Ring__and__Field_Ofield @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(526,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(527,plain,
( ( class_RealVector_Oreal__vector @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(528,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(529,plain,
( ( class_RealVector_Ometric__space @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(530,plain,
( ( class_RealVector_Oreal__algebra @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(531,plain,
( ( class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(532,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(533,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(534,plain,
( ( class_RealVector_Oreal__algebra__1 @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(535,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(536,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(537,plain,
( ( class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(538,plain,
( ( class_RealVector_Otopological__space @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(539,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(540,plain,
( ( class_Ring__and__Field_Odivision__ring @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(541,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(542,plain,
( ( class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(543,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(544,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(545,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(546,plain,
( ( class_Ring__and__Field_Odivision__by__zero @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(547,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(548,plain,
( ( class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(549,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(550,plain,
( ( class_OrderedGroup_Oordered__ab__group__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(551,plain,
( ( class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(552,plain,
( ( class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(553,plain,
( ( class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(554,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(555,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(556,plain,
( ( class_Lattices_Oboolean__algebra @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(557,plain,
( ( class_HOL_Ozero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(558,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(559,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(560,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(561,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(562,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(563,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(564,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(565,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(566,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(567,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(568,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(569,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(570,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Oboolean__algebra @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(571,plain,
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( v_sko__CHAINED__1 @ v_f____ @ v_ga____ @ v_s ) @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(572,plain,
( ( ! [V_X: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(573,plain,
( ( ! [V_X: $i] :
( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ V_X @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(574,plain,
( ( ! [T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ c_Complex_OIm @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(575,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(576,plain,
( ( c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ v_f____ @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(577,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(578,plain,
( ( ! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ V_l @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ c_Suc @ tc_nat @ T_a @ tc_nat ) @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(579,plain,
( ( ! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ c_Suc @ tc_nat @ T_a @ tc_nat ) @ V_l @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_f @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(580,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(581,plain,
( ( ! [V_a: $i] : ( c_Lim_OisCont @ c_Complex_OIm @ V_a @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(582,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(583,plain,
( ( c_SEQ_Osubseq @ v_f____ )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(584,plain,
( ( ! [T_a: $i,V_f: $i,V_g: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ V_f @ V_g @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_g @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_f @ ( hAPP @ V_g @ V_x ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(585,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(586,plain,
( ( c_SEQ_Oconvergent @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(587,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( V_a = V_b )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_b @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(588,plain,
( ( ! [T_a: $i,T_c: $i,T_b: $i,V_g: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ V_g @ V_f @ T_b @ T_c @ T_a ) @ V_a @ T_a @ T_c )
| ~ ( c_Lim_OisCont @ V_g @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(589,plain,
( ( ! [V_g: $i,T_a: $i,V_net: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(590,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(591,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(592,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(593,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(594,plain,
( ( ! [V_g: $i,V_A: $i,T_a: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_a @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_A @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(595,plain,
( ( ! [T_b: $i,T_a: $i,V_X: $i,V_S: $i,V_L: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_X @ V_S @ T_a @ T_b @ tc_nat ) @ V_L @ T_b )
| ~ ( c_SEQ_OLIMSEQ @ V_S @ V_a @ T_a )
| ( ( hAPP @ V_S @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ V_S @ V_a @ T_a ) )
= V_a )
| ~ ( c_Lim_OLIM @ V_X @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(596,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ ( hAPP @ V_f @ V_a ) @ T_b )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(597,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_x @ T_a @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(598,plain,
( ( ! [T_a: $i,V_k: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(599,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(600,plain,
( ( c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(601,plain,
( ( ! [V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(602,plain,
( ( ! [T_a: $i,V_X: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( ( c_SEQ_Olim @ V_X @ T_a )
= V_L )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_L @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(603,plain,
( ( ! [T_a: $i,V_f: $i,V_a: $i,V_k: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(604,plain,
( ( ! [T_a: $i,V_f: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_f @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(605,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ V_x @ V_y ) )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(606,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(607,plain,
( ( c_SEQ_Osubseq @ v_ga____ )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(608,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(609,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(610,plain,
( ( ! [T_a: $i,T_b: $i,T_c: $i,V_g: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_g @ V_f @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_g @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_Lim_OLIM @ V_g @ V_l @ ( hAPP @ V_g @ V_l ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(611,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( V_k = V_l )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(612,plain,
( ( c_SEQ_Oconvergent @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ v_f____ @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(613,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( hAPP @ c_Complex_OIm @ V_x )
!= ( hAPP @ c_Complex_OIm @ V_y ) )
| ( ( hAPP @ c_Complex_ORe @ V_x )
!= ( hAPP @ c_Complex_ORe @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(614,plain,
( ( ! [T_a: $i,V_X: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(615,plain,
( ( ! [T_a: $i,V_X: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_L @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(616,plain,
( ( ! [V_y: $i] :
( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ V_y @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(617,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(618,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(619,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(620,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(621,plain,
( ( c_Lim_OisUCont @ c_Complex_OIm @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(622,plain,
( ( ! [V_a: $i] : ( c_Lim_OLIM @ c_Complex_OIm @ V_a @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(623,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(624,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(625,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(626,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(627,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( ( hAPP @ V_f @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b ) )
| ~ ( c_Series_Osummable @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(628,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(629,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ V_x @ V_y ) )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(630,plain,
( ( c_Lim_OisUCont @ c_Complex_ORe @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(631,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(632,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ V_x ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(633,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(634,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(635,plain,
( ( ! [T_b: $i,V_r: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(636,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(637,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(638,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(639,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(640,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OCauchy @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(641,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a )
| ( c_Series_Osums @ V_f @ ( c_Series_Osuminf @ V_f @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(642,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ V_f @ ( c_Series_Osuminf @ V_f @ T_a ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(643,plain,
( ( ! [T_a: $i,V_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(644,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(645,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(646,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(647,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(648,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(649,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(650,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_Oconvergent @ V_X @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(651,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(652,plain,
( ( ! [T_a: $i,V_r: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(653,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_SEQ_Ocomplete__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(654,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_SEQ_Ocomplete__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(655,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(656,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(657,plain,
( ( ! [V_z: $i] :
( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ V_z ) @ ( hAPP @ c_Complex_OIm @ V_z ) )
= V_z ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(658,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(659,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(660,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ V_f @ T_a )
= V_x )
| ~ ( c_Series_Osums @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(661,plain,
( ( ! [T_a: $i,V_s: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( V_s
= ( c_Series_Osuminf @ V_f @ T_a ) )
| ~ ( c_Series_Osums @ V_f @ V_s @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(662,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(663,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Series_Osums @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ ( hAPP @ V_f @ V_a ) @ T_b )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(664,plain,
( ( ! [V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(665,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(666,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(667,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(668,plain,
( ( ! [T_a: $i,V_f: $i,V_k: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(669,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(670,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(671,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(672,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(673,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(674,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(675,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(676,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(677,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_y )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(678,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(679,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(680,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(681,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_w ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_w ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(682,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_d ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_d ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(683,plain,
( ( ! [T_a: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_g @ tc_RealDef_Oreal @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(684,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(685,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(686,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( hAPP @ c_Suc @ V_x )
!= ( hAPP @ c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(687,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( hAPP @ c_Suc @ V_nat )
!= ( hAPP @ c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(688,plain,
( ( ! [T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_x @ V_k @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(689,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(690,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(691,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(692,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(693,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(694,plain,
( ( ! [T_b: $i,V_k: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Otopological__space @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_k @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(695,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(696,plain,
( ( ! [T_a: $i,V_ra: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_ra ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_ra ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(697,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(698,plain,
( ( ! [T_a: $i,V_a: $i,V_r: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(699,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(700,plain,
( ( ! [T_a: $i,T_b: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(701,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ c_Suc @ V_n ) )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(702,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(703,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(704,plain,
( ( ! [T_a: $i,V_r: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(705,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(706,plain,
( ( ! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(707,plain,
( ( ! [T_b: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_b @ T_a ) @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(708,plain,
( ( ! [T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(709,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(710,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(711,plain,
( ( ! [T_a: $i,V_c: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(712,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(713,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(714,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_L @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(715,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(716,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_SEQ_OCauchy @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_Lim_OisUCont @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(717,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( ( hAPP @ V_f @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ ( hAPP @ V_f @ V_x ) ) )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(718,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_f @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(719,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(720,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(721,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(722,plain,
( ( ! [T_a: $i,V_xa: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(723,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(724,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(725,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(726,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(727,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(728,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(729,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(730,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(731,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(732,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(733,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(734,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(735,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(736,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(737,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_f @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(738,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(739,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisUCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(740,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_g: $i,T_c: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Limits_OZfun @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_net @ T_c @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(741,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= V_y )
| ( V_x
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(742,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_b_H ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b_H ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(743,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(744,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) @ T_a @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(745,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(746,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(747,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(748,plain,
( ( ! [V_X: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(749,plain,
( ( ! [T_a: $i,V_a: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_g @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(750,plain,
( ( ! [T_a: $i,V_g: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_g @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_SEQ_Olim @ V_g @ T_a ) ) )
| ~ ( c_SEQ_Oconvergent @ V_g @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(751,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_Series_Osuminf @ V_X @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(752,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(753,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(754,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(755,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(756,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(757,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ ( c_SEQ_Olim @ V_X @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(758,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ ( c_SEQ_Olim @ V_X @ T_a ) @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(759,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_e ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_e ) ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_e ) ) @ V_c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(760,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(761,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(762,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(763,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(764,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(765,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Series_Osummable @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_Series_Osummable @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(766,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(767,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(768,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(769,plain,
( ( ! [T_a: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_r ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(770,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(771,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(772,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(773,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(774,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(775,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(776,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(777,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(778,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(779,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(780,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(781,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(782,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(783,plain,
( ( ! [T_a: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ V_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(784,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(785,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(786,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(787,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_g: $i,T_c: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Limits_Otendsto @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ ( hAPP @ V_f @ V_a ) @ V_net @ T_c @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(788,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_f @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ( ( hAPP @ V_f @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Deriv_Odifferentiable @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(789,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(790,plain,
( ( ! [T_b: $i,V_x: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(791,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_a ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(792,plain,
( ( ! [T_a: $i,T_b: $i,T_c: $i,V_f: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_f @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(793,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_d ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(794,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(795,plain,
( ( ! [V_g: $i,V_A: $i,T_a: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_a @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_A @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(796,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_RealVector_Oof__real @ T_b ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(797,plain,
( ( ! [T_a: $i,T_b: $i,T_c: $i,V_g: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_g @ V_f @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_g @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_Lim_OisCont @ V_g @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(798,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OZseq @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OZseq @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(799,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(800,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_L ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(801,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_x )
!= ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(802,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(803,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(804,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(805,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(806,plain,
( ( ! [V_a: $i] : ( c_Lim_OisCont @ c_Complex_ORe @ V_a @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(807,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(808,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(809,plain,
( ( ! [T_b: $i,T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_c ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(810,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b )
| ~ ( c_Lim_OisUCont @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(811,plain,
( ( ! [T_a: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_y ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(812,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(813,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_b ) )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(814,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(815,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(816,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(817,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(818,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(819,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(820,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(821,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(822,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(823,plain,
( ( ! [T_a: $i,V_a: $i,V_r: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(824,plain,
( ( ! [T_a: $i,V_r: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(825,plain,
( ( ! [T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(826,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(827,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_Series_Osuminf @ V_X @ T_a ) ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(828,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(829,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_L ) @ T_a @ T_b )
| ( V_L
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(830,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ c_Suc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(831,plain,
( ( ! [T_a: $i,V_r: $i,V_f: $i,V_A: $i,T_b: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_f @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(832,plain,
( ( ! [T_a: $i,V_x: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_g @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(833,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(834,plain,
( ( ! [T_b: $i,T_a: $i,V_k: $i,V_L: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( V_k = V_L )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(835,plain,
( ( ! [T_a: $i,T_b: $i,V_k: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_a @ V_L @ T_b @ T_a )
| ( V_k = V_L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(836,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(837,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(838,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(839,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(840,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(841,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(842,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(843,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(844,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(845,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_f @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(846,plain,
( ( ! [T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ c_Complex_ORe @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(847,plain,
( ( ! [T_b: $i,T_a: $i,V_x: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(848,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(849,plain,
( ( ! [V_X: $i] :
( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ V_X @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(850,plain,
( ( ! [T_a: $i,V_c: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ ( c_Series_Osuminf @ V_f @ T_a ) ) )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(851,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(852,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(853,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(854,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(855,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_a ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(856,plain,
( ( ! [T_b: $i,V_r: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(857,plain,
( ( ! [T_b: $i,V_x: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(858,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(859,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(860,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(861,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(862,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(863,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) ) @ V_y )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(864,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(865,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_RealVector_Obounded__linear @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b @ T_a @ T_a @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(866,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(867,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(868,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(869,plain,
( ( ! [T_a: $i,T_b: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_HOL_Ozero @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_b @ T_a )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(870,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(871,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(872,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a_H ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a_H ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(873,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_ya )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_ya ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_ya ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(874,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_b_H ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b_H ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(875,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(876,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(877,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(878,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(879,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ V_ry ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(880,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ V_rx ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(881,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ V_ly ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(882,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(883,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(884,plain,
( ( ! [V_a: $i] : ( c_Lim_OLIM @ c_Complex_ORe @ V_a @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(885,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(886,plain,
( ( ! [T_b: $i,T_a: $i,T_c: $i,V_f: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(887,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_net: $i,T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_a ) @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(888,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(889,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(890,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(891,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(892,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(893,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(894,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(895,plain,
( ( ! [T_b: $i,T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_c ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(896,plain,
( ( ! [T_b: $i,T_a: $i,V_x: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(897,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(898,plain,
( ( ! [T_a: $i,V_r: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(899,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(900,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(901,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_y ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(902,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_y ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(903,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_c ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_d ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(904,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(905,plain,
( ( ! [V_real1: $i,V_real2: $i,V_real1_H: $i,V_real2_H: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ V_real1 @ V_real2 )
!= ( c_Complex_Ocomplex_OComplex @ V_real1_H @ V_real2_H ) )
| ( V_real1 = V_real1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(906,plain,
( ( ! [V_real1: $i,V_real2: $i,V_real1_H: $i,V_real2_H: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ V_real1 @ V_real2 )
!= ( c_Complex_Ocomplex_OComplex @ V_real1_H @ V_real2_H ) )
| ( V_real2 = V_real2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(907,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b ) )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(908,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(909,plain,
( ( ! [V_g: $i,T_a: $i,V_net: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(910,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(911,plain,
( ( ! [T_a: $i,V_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(912,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(913,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisUCont @ V_f @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(914,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(915,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(916,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(917,plain,
( ( ! [T_a: $i,T_b: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(918,plain,
( ( ! [T_b: $i,V_f: $i,V_net: $i,T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(919,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(920,plain,
( ( ! [T_b: $i,T_a: $i,V_L: $i,V_M: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( V_L = V_M )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_M @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(921,plain,
( ( ! [T_a: $i,V_k: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_SEQ_OZseq @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(922,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(923,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(924,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_c: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_f @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_c @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(925,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(926,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(927,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(928,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ V_X @ T_a )
| ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(929,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBK @ V_a @ T_a @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(930,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ( ( hAPP @ V_f @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(931,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(932,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(933,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(934,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(935,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_f @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(936,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ V_ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(937,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(938,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(939,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(940,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(941,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(942,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(943,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_x: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_a ) @ V_x ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(944,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_f @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_a @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(945,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_x: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(946,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_x: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_l ) @ V_x ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(947,plain,
( ( ! [T_a: $i,V_g: $i,V_A: $i,T_b: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ tc_RealDef_Oreal ) ) @ V_x )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_x @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(948,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) ) @ V_r )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_f @ T_a @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_r @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(949,plain,
( ( ! [T_a: $i,V_g: $i,V_A: $i,T_b: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) ) @ V_y )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_g @ T_a @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_y @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(950,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_y: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_l ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(951,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_f @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_a @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(952,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_y: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(953,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_y: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_a ) @ V_y ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(954,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_c: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_f @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_c @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(955,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(956,plain,
( ( ! [V_x: $i] :
( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ V_x @ tc_RealDef_Oreal ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(957,plain,
( ( ~ v_thesis____ ) = $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(958,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[480]) ).
thf(959,plain,
( ( ~ v_thesis____ ) = $true ),
inference(copy,[status(thm)],[957]) ).
thf(960,plain,
( ( ! [V_x: $i] :
( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ V_x @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(961,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(962,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_c: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_f @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_c @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(963,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_y: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_a ) @ V_y ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(964,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_y: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(965,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_f @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_a @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(966,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_y: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_g @ T_b @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_y @ T_a @ T_b @ T_b ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_l ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(967,plain,
( ( ! [T_a: $i,V_g: $i,V_A: $i,T_b: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) ) @ V_y )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_g @ T_a @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_y @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(968,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) ) @ V_r )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_f @ T_a @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_r @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(969,plain,
( ( ! [T_a: $i,V_g: $i,V_A: $i,T_b: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ tc_RealDef_Oreal ) ) @ V_x )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_a @ T_a ) @ T_b ) @ V_x @ T_b @ T_a @ T_a ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(970,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_x: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_l ) @ V_x ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(971,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_x: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(972,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_f @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_a @ T_a @ T_b @ T_b ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(973,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_x: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_a ) @ V_x ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(974,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(975,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(976,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(977,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(978,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(979,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(980,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ V_ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(981,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_f @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(982,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(983,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(984,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(985,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(986,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ( ( hAPP @ V_f @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(987,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBK @ V_a @ T_a @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(988,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ V_X @ T_a )
| ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(989,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(990,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(991,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(992,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_c: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_f @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_c @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(993,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_x: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_g @ tc_RealDef_Oreal @ ( tc_fun @ T_b @ T_b ) @ T_a ) @ V_x @ T_a @ T_b @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(994,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(995,plain,
( ( ! [T_a: $i,V_k: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_SEQ_OZseq @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(996,plain,
( ( ! [T_b: $i,T_a: $i,V_L: $i,V_M: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( V_L = V_M )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_M @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(997,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(998,plain,
( ( ! [T_b: $i,V_f: $i,V_net: $i,T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(999,plain,
( ( ! [T_a: $i,T_b: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(1000,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1001,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(1003,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisUCont @ V_f @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(1004,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(1005,plain,
( ( ! [T_a: $i,V_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1006,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(1007,plain,
( ( ! [V_g: $i,T_a: $i,V_net: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(1008,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1009,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b ) )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1010,plain,
( ( ! [V_real1: $i,V_real2: $i,V_real1_H: $i,V_real2_H: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ V_real1 @ V_real2 )
!= ( c_Complex_Ocomplex_OComplex @ V_real1_H @ V_real2_H ) )
| ( V_real2 = V_real2_H ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1011,plain,
( ( ! [V_real1: $i,V_real2: $i,V_real1_H: $i,V_real2_H: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ V_real1 @ V_real2 )
!= ( c_Complex_Ocomplex_OComplex @ V_real1_H @ V_real2_H ) )
| ( V_real1 = V_real1_H ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(1012,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1013,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_c ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_d ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(1014,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_y ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1015,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_y ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1016,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(1017,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_r: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1019,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1020,plain,
( ( ! [T_b: $i,T_a: $i,V_x: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(1021,plain,
( ( ! [T_b: $i,T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_c ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1022,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1023,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1024,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(1025,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(1026,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(1027,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1028,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1029,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_net: $i,T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_a ) @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1030,plain,
( ( ! [T_b: $i,T_a: $i,T_c: $i,V_f: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1031,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(1032,plain,
( ( ! [V_a: $i] : ( c_Lim_OLIM @ c_Complex_ORe @ V_a @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(1033,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1034,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(1035,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ V_ly ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1036,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_ly ) @ V_rx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(1037,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ V_ry ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(1038,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_rx ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1039,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1040,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1041,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1042,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_b_H ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b_H ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(1043,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_ya )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_ya ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_ya ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(1044,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a_H ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a_H ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(1045,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(1046,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1047,plain,
( ( ! [T_a: $i,T_b: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_HOL_Ozero @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_b @ T_a )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(1048,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1049,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
!= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1050,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1051,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_RealVector_Obounded__linear @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b @ T_a @ T_a @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(1052,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(1053,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) ) @ V_y )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(1055,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(1056,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(1057,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(1058,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1059,plain,
( ( ! [T_b: $i,V_x: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1060,plain,
( ( ! [T_b: $i,V_r: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1061,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_a ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(1062,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(1063,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1064,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1065,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1066,plain,
( ( ! [T_a: $i,V_c: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ ( c_Series_Osuminf @ V_f @ T_a ) ) )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1067,plain,
( ( ! [V_X: $i] :
( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ V_X @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1068,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1069,plain,
( ( ! [T_b: $i,T_a: $i,V_x: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1070,plain,
( ( ! [T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ c_Complex_ORe @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1071,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_f @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1072,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1073,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1074,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1075,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(1076,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1077,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(1078,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(1079,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1080,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1081,plain,
( ( ! [T_a: $i,T_b: $i,V_k: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_a @ V_L @ T_b @ T_a )
| ( V_k = V_L ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1082,plain,
( ( ! [T_b: $i,T_a: $i,V_k: $i,V_L: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( V_k = V_L )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(1084,plain,
( ( ! [T_a: $i,V_x: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_g @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1085,plain,
( ( ! [T_a: $i,V_r: $i,V_f: $i,V_A: $i,T_b: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_r ) @ V_f @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1086,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ c_Suc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(1087,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_L ) @ T_a @ T_b )
| ( V_L
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(1088,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(1089,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_Series_Osuminf @ V_X @ T_a ) ) )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1090,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1091,plain,
( ( ! [T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1092,plain,
( ( ! [T_a: $i,V_r: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1093,plain,
( ( ! [T_a: $i,V_a: $i,V_r: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(1095,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1096,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1097,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1098,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(1099,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(1100,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1101,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1102,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_b ) )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1104,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1105,plain,
( ( ! [T_a: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_y ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1106,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_x @ T_a @ T_b )
| ~ ( c_Lim_OisUCont @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1107,plain,
( ( ! [T_b: $i,T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_c ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1108,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_g: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1109,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1110,plain,
( ( ! [V_a: $i] : ( c_Lim_OisCont @ c_Complex_ORe @ V_a @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1111,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1112,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(1113,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1114,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_x )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(1115,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_x )
!= ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(1116,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_b ) @ V_L ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1117,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1118,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OZseq @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OZseq @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(1119,plain,
( ( ! [T_a: $i,T_b: $i,T_c: $i,V_g: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_g @ V_f @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_g @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_Lim_OisCont @ V_g @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1120,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_g @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ ( hAPP @ ( c_RealVector_Oof__real @ T_b ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(1121,plain,
( ( ! [V_g: $i,V_A: $i,T_a: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_a @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_A @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1122,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1123,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_d ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1124,plain,
( ( ! [T_a: $i,T_b: $i,T_c: $i,V_f: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_f @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1125,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_a ) @ V_f @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_f @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1126,plain,
( ( ! [T_b: $i,V_x: $i,V_g: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_b )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_b ) @ V_x ) @ V_g @ T_b @ T_b @ T_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1127,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1128,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_f @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ( ( hAPP @ V_f @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Deriv_Odifferentiable @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1129,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_g: $i,T_c: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Limits_Otendsto @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ ( hAPP @ V_f @ V_a ) @ V_net @ T_c @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1131,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1133,plain,
( ( ! [T_a: $i,V_y: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ V_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1134,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(1135,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ V_f @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(1137,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1138,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1139,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1140,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(1141,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(1142,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1143,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1144,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1145,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1146,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1147,plain,
( ( ! [T_a: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_r ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1148,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1149,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1150,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1151,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Series_Osummable @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_Series_Osummable @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(1152,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_f @ T_b @ T_b @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_b ) @ V_a ) @ V_net @ T_a @ T_b )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_b ) )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1155,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1156,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_e ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_e ) ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_e ) ) @ V_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1158,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ ( c_SEQ_Olim @ V_X @ T_a ) @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1159,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ ( c_SEQ_Olim @ V_X @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(1160,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1161,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(1163,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(1164,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1165,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_Series_Osuminf @ V_X @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a ) )
| ~ ( c_Series_Osummable @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1166,plain,
( ( ! [T_a: $i,V_g: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_g @ T_a @ T_a @ tc_nat ) @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_SEQ_Olim @ V_g @ T_a ) ) )
| ~ ( c_SEQ_Oconvergent @ V_g @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(1167,plain,
( ( ! [T_a: $i,V_a: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ T_a ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_g @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(1168,plain,
( ( ! [V_X: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(1169,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(1170,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(1171,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(1172,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) @ T_a @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1173,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1174,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_b_H ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b_H ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1175,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= V_y )
| ( V_x
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1176,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_g: $i,T_c: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Limits_OZfun @ ( c_COMBB @ V_f @ V_g @ T_a @ T_b @ T_c ) @ V_net @ T_c @ T_b )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_c @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1177,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Lim_OisUCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_y @ T_a @ T_a @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1178,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ tc_nat ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1179,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_f @ T_a @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_b @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(1180,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(1181,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1182,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(1183,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1184,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(1185,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(1186,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1187,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1188,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1189,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1190,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1191,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1192,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1193,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1194,plain,
( ( ! [T_a: $i,V_xa: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_xa ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1195,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(1196,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(1197,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(1198,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_b ) @ V_f @ tc_RealDef_Oreal @ T_b @ T_a ) @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1199,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( ( hAPP @ V_f @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ ( hAPP @ V_f @ V_x ) ) )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1200,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_SEQ_OCauchy @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_Lim_OisUCont @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1201,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1202,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_a: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_L @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1203,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(1204,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ ( c_COMBB @ V_f @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ T_a @ T_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1205,plain,
( ( ! [T_a: $i,V_c: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(1206,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(1207,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(1208,plain,
( ( ! [T_a: $i,V_c: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_f @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_c ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(1209,plain,
( ( ! [T_b: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_b ) @ T_b @ T_a ) @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1210,plain,
( ( ! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(1211,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ V_f @ T_a )
| ~ ( c_Series_Osums @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(1212,plain,
( ( ! [T_a: $i,V_r: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(1213,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_f @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(1214,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(1215,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ c_Suc @ V_n ) )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(1216,plain,
( ( ! [T_a: $i,T_b: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(1217,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_x ) )
= ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(1218,plain,
( ( ! [T_a: $i,V_a: $i,V_r: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(1219,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(1220,plain,
( ( ! [T_a: $i,V_ra: $i,V_r: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_ra ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_x ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_ra ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(1221,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(1222,plain,
( ( ! [T_b: $i,V_k: $i,T_a: $i,V_net: $i] :
( ~ ( class_RealVector_Otopological__space @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_k @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(1223,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(1224,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(1225,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(1226,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(1227,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1228,plain,
( ( ! [T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBK @ V_k @ T_b @ T_a ) @ V_x @ V_k @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(1229,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( hAPP @ c_Suc @ V_nat )
!= ( hAPP @ c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1230,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( hAPP @ c_Suc @ V_x )
!= ( hAPP @ c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(1231,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1232,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(1233,plain,
( ( ! [T_a: $i,V_g: $i,V_A: $i,T_b: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_b @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_g @ tc_RealDef_Oreal @ T_a @ T_b ) @ V_A @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(1234,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_d ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_d ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_c ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(1235,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_w ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_w ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_y ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1236,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1237,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(1238,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1239,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_y )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1240,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1241,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1242,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1243,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1244,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1245,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(1246,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_b )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(1247,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(1248,plain,
( ( ! [T_a: $i,V_f: $i,V_k: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osummable @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(1249,plain,
( ( ! [T_b: $i,T_a: $i,V_r: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ V_a @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_l ) @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(1250,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= V_y ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(1251,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(1252,plain,
( ( ! [V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1253,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Series_Osums @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ ( hAPP @ V_f @ V_a ) @ T_b )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(1254,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(1255,plain,
( ( ! [T_a: $i,V_s: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( V_s
= ( c_Series_Osuminf @ V_f @ T_a ) )
| ~ ( c_Series_Osums @ V_f @ V_s @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(1256,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_Series_Osuminf @ V_f @ T_a )
= V_x )
| ~ ( c_Series_Osums @ V_f @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(1257,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(1258,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1259,plain,
( ( ! [V_z: $i] :
( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ V_z ) @ ( hAPP @ c_Complex_OIm @ V_z ) )
= V_z ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1260,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1261,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(1262,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_SEQ_Ocomplete__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(1263,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_SEQ_Ocomplete__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[653]) ).
thf(1264,plain,
( ( ! [T_a: $i,V_r: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(1265,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_Oconvergent @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(1266,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_Oconvergent @ V_X @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(1267,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(1268,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(1269,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(1270,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(1271,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(1272,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(1273,plain,
( ( ! [T_a: $i,V_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OZseq @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(1274,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_Series_Osums @ V_f @ ( c_Series_Osuminf @ V_f @ T_a ) @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(1275,plain,
( ( ! [T_a: $i,V_f: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( c_Series_Osummable @ V_f @ T_a )
| ( c_Series_Osums @ V_f @ ( c_Series_Osuminf @ V_f @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(1276,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OCauchy @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(1277,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(1278,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OLIM @ V_f @ V_a @ ( hAPP @ V_f @ V_a ) @ T_a @ T_b )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1279,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(1280,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(1281,plain,
( ( ! [T_b: $i,V_r: $i,V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_g @ T_b @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_b ) @ V_r ) @ V_a ) @ V_net @ T_a @ T_b )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(1282,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ T_a )
| ~ ( c_SEQ_OCauchy @ V_X @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1283,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_y ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(1284,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__vector @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ V_x )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_b ) @ V_x ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(1285,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(1286,plain,
( ( c_Lim_OisUCont @ c_Complex_ORe @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(1287,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ V_x @ V_y ) )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(1288,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_a ) @ T_a )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(1289,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( ( hAPP @ V_f @ ( c_Series_Osuminf @ V_X @ T_a ) )
= ( c_Series_Osuminf @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ T_b ) )
| ~ ( c_Series_Osummable @ V_X @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(1290,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_b ) @ V_f @ T_b @ tc_RealDef_Oreal @ T_a ) @ V_a @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(1291,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(1292,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(1293,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(1294,plain,
( ( ! [V_a: $i] : ( c_Lim_OLIM @ c_Complex_OIm @ V_a @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(1295,plain,
( ( c_Lim_OisUCont @ c_Complex_OIm @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(1296,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(1297,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(1298,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(1299,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ T_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(1300,plain,
( ( ! [V_y: $i] :
( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ V_y @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(1301,plain,
( ( ! [T_a: $i,V_X: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_L @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(1302,plain,
( ( ! [T_a: $i,V_X: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_Oconvergent @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(1303,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( hAPP @ c_Complex_OIm @ V_x )
!= ( hAPP @ c_Complex_OIm @ V_y ) )
| ( ( hAPP @ c_Complex_ORe @ V_x )
!= ( hAPP @ c_Complex_ORe @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(1304,plain,
( ( c_SEQ_Oconvergent @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ v_f____ @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(1305,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( V_k = V_l )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(1306,plain,
( ( ! [T_a: $i,T_b: $i,T_c: $i,V_g: $i,V_f: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ( c_Lim_OLIM @ ( c_COMBB @ V_g @ V_f @ T_a @ T_b @ T_c ) @ V_a @ ( hAPP @ V_g @ V_l ) @ T_c @ T_b )
| ~ ( c_Lim_OLIM @ V_f @ V_a @ V_l @ T_c @ T_a )
| ~ ( c_Lim_OLIM @ V_g @ V_l @ ( hAPP @ V_g @ V_l ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(1307,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ V_X @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(1308,plain,
( ( ! [T_a: $i,V_X: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(1309,plain,
( ( c_SEQ_Osubseq @ v_ga____ )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(1310,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_X @ T_a @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ T_a ) @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(1311,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ V_x @ V_y ) )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(1312,plain,
( ( ! [T_a: $i,V_f: $i,V_k: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_f @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(1313,plain,
( ( ! [T_a: $i,V_f: $i,V_a: $i,V_k: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ V_a @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ T_a @ tc_nat ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(1314,plain,
( ( ! [T_a: $i,V_X: $i,V_L: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( ( c_SEQ_Olim @ V_X @ T_a )
= V_L )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_L @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(1315,plain,
( ( ! [V_g: $i,T_a: $i,V_a: $i,V_net: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ V_g @ V_a @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(1316,plain,
( ( c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(1317,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(1318,plain,
( ( ! [T_a: $i,V_k: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_k @ T_a @ tc_nat ) @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(1319,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ V_x @ T_a @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(1320,plain,
( ( ! [T_a: $i,T_b: $i,V_f: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__normed__vector @ T_b )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ V_X @ T_a @ T_b @ tc_nat ) @ ( hAPP @ V_f @ V_a ) @ T_b )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a )
| ~ ( c_RealVector_Obounded__linear @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(1321,plain,
( ( ! [T_b: $i,T_a: $i,V_X: $i,V_S: $i,V_L: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_b )
| ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_X @ V_S @ T_a @ T_b @ tc_nat ) @ V_L @ T_b )
| ~ ( c_SEQ_OLIMSEQ @ V_S @ V_a @ T_a )
| ( ( hAPP @ V_S @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ V_S @ V_a @ T_a ) )
= V_a )
| ~ ( c_Lim_OLIM @ V_X @ V_a @ V_L @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(1322,plain,
( ( ! [V_g: $i,V_A: $i,T_a: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ V_g @ V_A @ T_a @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_A @ T_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(1323,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ~ ( class_RealVector_Oreal__algebra__1 @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ T_a ) @ V_X @ tc_RealDef_Oreal @ T_a @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ T_a ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_RealDef_Oreal ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(1324,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(1325,plain,
( ( ! [V_X: $i] :
( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(1326,plain,
( ( ! [V_X: $i,V_a: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ V_a ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ V_X @ V_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(1327,plain,
( ( ! [V_g: $i,T_a: $i,V_net: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_net @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ V_g @ V_net @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(1328,plain,
( ( ! [T_a: $i,T_c: $i,T_b: $i,V_g: $i,V_f: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ~ ( class_RealVector_Ometric__space @ T_c )
| ~ ( class_RealVector_Ometric__space @ T_b )
| ( c_Lim_OisCont @ ( c_COMBB @ V_g @ V_f @ T_b @ T_c @ T_a ) @ V_a @ T_a @ T_c )
| ~ ( c_Lim_OisCont @ V_g @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ~ ( c_Lim_OisCont @ V_f @ V_a @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(1329,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_X: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( V_a = V_b )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_b @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(1330,plain,
( ( c_SEQ_Oconvergent @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(1331,plain,
( ( ! [T_a: $i,V_x: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ T_a ) @ V_x ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(1332,plain,
( ( ! [T_a: $i,V_f: $i,V_g: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ V_f @ V_g @ T_a @ T_a @ T_a ) @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_g @ V_x @ T_a )
| ~ ( c_Deriv_Odifferentiable @ V_f @ ( hAPP @ V_g @ V_x ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(1333,plain,
( ( c_SEQ_Osubseq @ v_f____ )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(1334,plain,
( ( ! [T_a: $i,V_r: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ T_a ) @ V_r ) @ V_a ) @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(1335,plain,
( ( ! [V_a: $i] : ( c_Lim_OisCont @ c_Complex_OIm @ V_a @ tc_Complex_Ocomplex @ tc_RealDef_Oreal ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(1336,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OCauchy @ V_X @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(1337,plain,
( ( ! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ c_Suc @ tc_nat @ T_a @ tc_nat ) @ V_l @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ V_f @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1338,plain,
( ( ! [T_a: $i,V_f: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_SEQ_OLIMSEQ @ V_f @ V_l @ T_a )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ V_f @ c_Suc @ tc_nat @ T_a @ tc_nat ) @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(1339,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(1340,plain,
( ( c_SEQ_Omonoseq @ ( c_COMBB @ c_Complex_ORe @ ( c_COMBB @ v_s @ v_f____ @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(1341,plain,
( ( ! [T_a: $i,V_X: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_X @ T_a @ T_a @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ T_a ) @ V_a ) @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_SEQ_OLIMSEQ @ V_X @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(1342,plain,
( ( ! [T_a: $i,V_g: $i,V_a: $i,V_l: $i] :
( ~ ( class_RealVector_Ometric__space @ T_a )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ V_g @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ T_a ) @ V_a @ ( hAPP @ c_Complex_OIm @ V_l ) @ T_a @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ V_g @ V_a @ V_l @ T_a @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(1343,plain,
( ( ! [V_X: $i] :
( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ V_X @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1344,plain,
( ( ! [V_X: $i] :
( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ V_X @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ V_X @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1345,plain,
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( v_sko__CHAINED__1 @ v_f____ @ v_ga____ @ v_s ) @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(1346,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Oboolean__algebra @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(1347,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(1348,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(1349,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(1350,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(1351,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(1352,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(1353,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(1354,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(1355,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(1356,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1357,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1358,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(1359,plain,
( ( class_HOL_Ozero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1360,plain,
( ( class_Lattices_Oboolean__algebra @ tc_bool )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1361,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1362,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1363,plain,
( ( class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1364,plain,
( ( class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(1365,plain,
( ( class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(1366,plain,
( ( class_OrderedGroup_Oordered__ab__group__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(1367,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(1368,plain,
( ( class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(1369,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(1370,plain,
( ( class_Ring__and__Field_Odivision__by__zero @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(1371,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(1372,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(1373,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(1374,plain,
( ( class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(1375,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(1376,plain,
( ( class_Ring__and__Field_Odivision__ring @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(1377,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(1378,plain,
( ( class_RealVector_Otopological__space @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1379,plain,
( ( class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(1380,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1381,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(1382,plain,
( ( class_RealVector_Oreal__algebra__1 @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1383,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1384,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1385,plain,
( ( class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1386,plain,
( ( class_RealVector_Oreal__algebra @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1387,plain,
( ( class_RealVector_Ometric__space @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(1388,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1389,plain,
( ( class_RealVector_Oreal__vector @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1390,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(1391,plain,
( ( class_Ring__and__Field_Ofield @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(1392,plain,
( ( class_Ring__and__Field_Oring @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(1393,plain,
( ( class_Ring__and__Field_Oidom @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(1394,plain,
( ( class_SEQ_Ocomplete__space @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(1395,plain,
( ( class_Int_Onumber__ring @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(1396,plain,
( ( class_SEQ_Obanach @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(1397,plain,
( ( class_HOL_Ozero @ tc_RealDef_Oreal )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(1398,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(1399,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(1400,plain,
( ( class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(1401,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(1402,plain,
( ( class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(1403,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(1404,plain,
( ( class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(1405,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(1406,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(1407,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1408,plain,
( ( class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(1409,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(1410,plain,
( ( class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(1411,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(1412,plain,
( ( class_RealVector_Otopological__space @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(1413,plain,
( ( class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(1414,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(1415,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(1416,plain,
( ( class_RealVector_Oreal__algebra__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(1417,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(1418,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(1419,plain,
( ( class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(1420,plain,
( ( class_RealVector_Oreal__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(1421,plain,
( ( class_RealVector_Ometric__space @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(1422,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(1423,plain,
( ( class_RealVector_Oreal__vector @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(1424,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(1425,plain,
( ( class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(1426,plain,
( ( class_Ring__and__Field_Oring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(1427,plain,
( ( class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(1428,plain,
( ( class_SEQ_Ocomplete__space @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1429,plain,
( ( class_Int_Onumber__ring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(1430,plain,
( ( class_SEQ_Obanach @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(1431,plain,
( ( class_HOL_Ozero @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(1432,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(1433,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(1434,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1435,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1436,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[958]) ).
thf(1437,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX2 ) @ SX2 ) )
| ( SX1
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1103]) ).
thf(1438,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX3 ) @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1078]) ).
thf(1439,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1017]) ).
thf(1440,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1096]) ).
thf(1441,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1073]) ).
thf(1442,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ SX0 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1023]) ).
thf(1443,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX2 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX3 ) @ SX4 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX4 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX3 ) @ SX2 ) ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1234]) ).
thf(1444,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1098]) ).
thf(1445,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SX0 ) @ SX1 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1025]) ).
thf(1446,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1232]) ).
thf(1447,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX1 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX2 ) @ SX2 ) )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1014]) ).
thf(1448,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1094]) ).
thf(1449,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SX0 @ SX1 )
!= ( c_Complex_Ocomplex_OComplex @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1010]) ).
thf(1450,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX2 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX3 ) @ SX4 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX4 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX3 ) @ SX2 ) ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1235]) ).
thf(1451,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1261]) ).
thf(1452,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_RealVector_Oreal__vector @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1283]) ).
thf(1453,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1074]) ).
thf(1454,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Suc @ SX0 )
!= ( hAPP @ c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1229]) ).
thf(1455,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_RealVector_Oreal__vector @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1090]) ).
thf(1456,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1077]) ).
thf(1457,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX2 ) @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1072]) ).
thf(1458,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX1 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1231]) ).
thf(1459,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( SX1
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1104]) ).
thf(1460,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1095]) ).
thf(1461,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1260]) ).
thf(1462,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX1 ) @ SX1 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX2 ) @ SX2 ) )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1015]) ).
thf(1463,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SX0 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX1 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[994]) ).
thf(1464,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_RealVector_Oreal__vector @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SX0 ) @ SX3 ) @ SX2 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1284]) ).
thf(1465,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SX0 )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1114]) ).
thf(1466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SX0 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX1 )
!= SX1 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1049]) ).
thf(1467,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[982]) ).
thf(1468,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SX0 @ SX1 )
!= ( c_Complex_Ocomplex_OComplex @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1011]) ).
thf(1469,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Complex_OIm @ SX0 )
!= ( hAPP @ c_Complex_OIm @ SX1 ) )
| ( ( hAPP @ c_Complex_ORe @ SX0 )
!= ( hAPP @ c_Complex_ORe @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1303]) ).
thf(1470,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX1 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1148]) ).
thf(1471,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SX0 ) @ SX1 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1024]) ).
thf(1472,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX1 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[974]) ).
thf(1473,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1075]) ).
thf(1474,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ SX0 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SX0 ) @ SX1 )
!= ( hAPP @ ( c_RealVector_Oof__real @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1115]) ).
thf(1475,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX2 ) @ SX3 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SX0 ) @ SX2 ) @ SX4 ) ) )
| ( SX3 = SX4 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1013]) ).
thf(1476,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1016]) ).
thf(1477,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1076]) ).
thf(1478,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Suc @ SX0 )
!= ( hAPP @ c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1230]) ).
thf(1479,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX2 ) @ SX3 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX2 ) @ SX4 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1197]) ).
thf(1480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX2 ) @ SX3 ) )
!= SX2 )
| ( SX1
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SX0 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1175]) ).
thf(1481,plain,
v_thesis____ = $false,
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1482,plain,
! [SV1: $i] :
( ( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ SV1 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1483,plain,
! [SV2: $i] :
( ( ! [SY1241: $i,SY1242: $i,SY1243: $i,SY1244: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV2 )
| ~ ( class_RealVector_Ometric__space @ SY1241 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SY1242 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SY1241 ) @ SY1243 @ SY1241 @ SV2 @ SV2 ) @ SY1244 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SY1241 @ SV2 )
| ~ ( c_Lim_OLIM @ SY1242 @ SY1244 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SY1241 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1484,plain,
! [SV3: $i] :
( ( ! [SY1245: $i,SY1246: $i,SY1247: $i,SY1248: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV3 )
| ~ ( class_RealVector_Ometric__space @ SY1245 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SY1246 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SY1245 ) @ SY1247 @ SY1245 @ SV3 @ SV3 ) @ SY1248 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SY1245 @ SV3 )
| ~ ( c_Lim_OLIM @ SY1246 @ SY1248 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SY1245 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1485,plain,
! [SV4: $i] :
( ( ! [SY1249: $i,SY1250: $i,SY1251: $i,SY1252: $i,SY1253: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV4 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SY1249 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SY1250 ) @ SY1251 @ SY1250 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SY1252 ) @ SY1251 ) @ SY1253 @ SY1250 @ SV4 )
| ~ ( c_Limits_Otendsto @ SY1249 @ SY1252 @ SY1253 @ SY1250 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1486,plain,
! [SV5: $i] :
( ( ! [SY1254: $i,SY1255: $i,SY1256: $i,SY1257: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV5 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SY1254 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SY1255 ) @ SY1256 @ SY1255 @ SV5 @ SV5 ) @ SY1257 @ SY1255 @ SV5 )
| ~ ( c_Limits_OZfun @ SY1254 @ SY1257 @ SY1255 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1487,plain,
! [SV6: $i] :
( ( ! [SY1258: $i,SY1259: $i,SY1260: $i,SY1261: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV6 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SY1258 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SY1259 ) @ SY1260 @ SY1259 @ SV6 @ SV6 ) @ SY1261 @ SY1259 @ SV6 )
| ~ ( c_Limits_OZfun @ SY1258 @ SY1261 @ SY1259 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1488,plain,
! [SV7: $i] :
( ( ! [SY1262: $i,SY1263: $i,SY1264: $i,SY1265: $i,SY1266: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV7 )
| ~ ( class_RealVector_Ometric__space @ SY1262 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SY1263 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SY1262 ) @ SY1264 @ SY1262 @ SV7 @ SV7 ) @ SY1265 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SY1266 ) @ SY1264 ) @ SY1262 @ SV7 )
| ~ ( c_Lim_OLIM @ SY1263 @ SY1265 @ SY1266 @ SY1262 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1489,plain,
! [SV8: $i] :
( ( ! [SY1267: $i,SY1268: $i,SY1269: $i,SY1270: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV8 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ ( c_Finite__Set_Osetsum @ SY1267 @ SY1268 @ SY1269 @ SV8 ) ) @ SY1270 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ SY1267 @ SV8 @ ( tc_fun @ SV8 @ SV8 ) @ SY1269 ) @ SY1270 @ SY1269 @ SV8 @ SV8 ) @ SY1268 @ SY1269 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1490,plain,
! [SV9: $i] :
( ( ! [SY1271: $i,SY1272: $i,SY1273: $i,SY1274: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ ( c_Finite__Set_Osetsum @ SY1271 @ SY1272 @ SY1273 @ SV9 ) ) @ SY1274 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ SY1271 @ SV9 @ ( tc_fun @ SV9 @ SV9 ) @ SY1273 ) @ SY1274 @ SY1273 @ SV9 @ SV9 ) @ SY1272 @ SY1273 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1491,plain,
! [SV10: $i] :
( ( ! [SY1275: $i,SY1276: $i,SY1277: $i,SY1278: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ ( c_Finite__Set_Osetsum @ SY1275 @ SY1276 @ SY1277 @ tc_RealDef_Oreal ) ) @ SY1278 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ SY1275 @ tc_RealDef_Oreal @ ( tc_fun @ SV10 @ SV10 ) @ SY1277 ) @ SY1278 @ SY1277 @ SV10 @ SV10 ) @ SY1276 @ SY1277 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1492,plain,
! [SV11: $i] :
( ( ! [SY1279: $i,SY1280: $i,SY1281: $i,SY1282: $i,SY1283: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV11 )
| ~ ( class_RealVector_Ometric__space @ SY1279 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SY1280 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SY1279 ) @ SY1281 @ SY1279 @ SV11 @ SV11 ) @ SY1282 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SY1283 ) @ SY1281 ) @ SY1279 @ SV11 )
| ~ ( c_Lim_OLIM @ SY1280 @ SY1282 @ SY1283 @ SY1279 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1493,plain,
! [SV12: $i] :
( ( ! [SY1284: $i,SY1285: $i,SY1286: $i,SY1287: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV12 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SY1284 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SY1285 ) @ SY1286 @ SY1285 @ SV12 @ SV12 ) @ SY1287 @ SY1285 @ SV12 )
| ~ ( c_Limits_OZfun @ SY1284 @ SY1287 @ SY1285 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1494,plain,
! [SV13: $i] :
( ( ! [SY1288: $i,SY1289: $i,SY1290: $i,SY1291: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV13 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SY1288 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SY1289 ) @ SY1290 @ SY1289 @ SV13 @ SV13 ) @ SY1291 @ SY1289 @ SV13 )
| ~ ( c_Limits_OZfun @ SY1288 @ SY1291 @ SY1289 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1495,plain,
! [SV14: $i] :
( ( ! [SY1292: $i,SY1293: $i,SY1294: $i,SY1295: $i,SY1296: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV14 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SY1292 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SY1293 ) @ SY1294 @ SY1293 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SY1295 ) @ SY1294 ) @ SY1296 @ SY1293 @ SV14 )
| ~ ( c_Limits_Otendsto @ SY1292 @ SY1295 @ SY1296 @ SY1293 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1496,plain,
! [SV15: $i] :
( ( ! [SY1297: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV15 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV15 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SY1297 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
| ~ ( c_SEQ_OCauchy @ SY1297 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1497,plain,
! [SV16: $i] :
( ( ! [SY1298: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV16 )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV16 ) @ SY1298 ) @ SV16 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1498,plain,
! [SV17: $i] :
( ( ! [SY1299: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV17 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV17 ) @ SY1299 @ SV17 @ SV17 @ tc_nat ) @ SV17 )
| ~ ( c_SEQ_OZseq @ SY1299 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1499,plain,
! [SV18: $i] :
( ( ! [SY1300: $i,SY1301: $i,SY1302: $i,SY1303: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY1300 ) @ SY1301 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY1302 ) @ SY1303 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY1302 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY1300 ) @ SY1301 ) ) @ SY1303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1500,plain,
! [SV19: $i] :
( ( ! [SY1304: $i,SY1305: $i,SY1306: $i,SY1307: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY1304 ) @ SY1305 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY1306 ) @ SY1307 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY1304 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY1305 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY1306 ) @ SY1307 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1501,plain,
! [SV20: $i] :
( ( ! [SY1308: $i,SY1309: $i,SY1310: $i,SY1311: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SY1308 ) @ SY1309 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SY1310 ) @ SY1311 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SY1308 ) @ SY1310 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SY1309 ) @ SY1311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1502,plain,
! [SV21: $i] :
( ( ! [SY1312: $i] :
( ~ ( class_SEQ_Obanach @ SV21 )
| ( c_Series_Osummable @ SY1312 @ SV21 )
| ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV21 ) @ SY1312 @ SV21 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1503,plain,
! [SV22: $i] :
( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV22 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV22 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1504,plain,
! [SV23: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV23 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV23 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV23 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1505,plain,
! [SV24: $i] :
( ( ! [SY1313: $i,SY1314: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV24 )
| ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SY1313 ) @ SY1314 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SY1313 ) @ SY1314 ) @ SV24 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1506,plain,
! [SV25: $i] :
( ( ! [SY1315: $i,SY1316: $i,SY1317: $i] :
( ~ ( class_RealVector_Ometric__space @ SV25 )
| ~ ( class_RealVector_Oreal__normed__div__algebra @ SY1315 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SY1315 ) @ SY1316 @ SY1315 @ SY1315 @ SV25 ) @ SY1317 @ SV25 @ SY1315 )
| ( ( hAPP @ SY1316 @ SY1317 )
= ( c_HOL_Ozero__class_Ozero @ SY1315 ) )
| ~ ( c_Lim_OisCont @ SY1316 @ SY1317 @ SV25 @ SY1315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1507,plain,
! [SV26: $i] :
( ( ! [SY1318: $i,SY1319: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV26 )
| ( c_Deriv_Odifferentiable @ ( c_COMBK @ SY1318 @ SV26 @ SV26 ) @ SY1319 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1508,plain,
! [SV27: $i] :
( ( ! [SY1320: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV27 )
| ( c_SEQ_OZseq @ SY1320 @ SV27 )
| ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV27 ) @ SY1320 @ SV27 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1509,plain,
! [SV28: $i] :
( ( ! [SY1321: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV28 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV28 ) @ SY1321 @ SV28 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ SY1321 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1510,plain,
! [SV29: $i] :
( ( ! [SY1322: $i,SY1323: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV29 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV29 ) @ SY1322 ) @ SY1323 @ SV29 @ SV29 @ tc_nat ) @ SV29 )
| ~ ( c_SEQ_OCauchy @ SY1323 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1511,plain,
! [SV30: $i] :
( ( ! [SY1324: $i,SY1325: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV30 )
| ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV30 ) @ SY1324 ) @ SY1325 @ SV30 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1512,plain,
! [SV31: $i] :
( ( ! [SY1326: $i,SY1327: $i,SY1328: $i,SY1329: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV31 )
| ~ ( class_RealVector_Ometric__space @ SY1326 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SY1327 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SY1326 ) @ SY1328 @ SY1326 @ SV31 @ SV31 ) @ SY1329 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SY1326 @ SV31 )
| ~ ( c_Lim_OLIM @ SY1327 @ SY1329 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SY1326 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1513,plain,
! [SV32: $i] :
( ( ! [SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV32 )
| ~ ( class_RealVector_Ometric__space @ SY1330 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SY1331 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SY1330 ) @ SY1332 @ SY1330 @ SV32 @ SV32 ) @ SY1333 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SY1330 @ SV32 )
| ~ ( c_Lim_OLIM @ SY1331 @ SY1333 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SY1330 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1514,plain,
! [SV33: $i] :
( ( ! [SY1334: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV33 )
| ( SY1334
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ~ ( c_SEQ_OZseq @ ( c_COMBK @ SY1334 @ SV33 @ tc_nat ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1515,plain,
! [SV34: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i,SY1338: $i,SY1339: $i] :
( ~ ( class_RealVector_Ometric__space @ SV34 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SY1335 )
| ( SY1336 = SY1337 )
| ~ ( c_Lim_OLIM @ SY1338 @ SY1339 @ SY1337 @ SY1335 @ SV34 )
| ~ ( c_Lim_OLIM @ SY1338 @ SY1339 @ SY1336 @ SY1335 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1516,plain,
! [SV35: $i] :
( ( ! [SY1340: $i,SY1341: $i,SY1342: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV35 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SY1340 @ SV35 @ tc_RealDef_Oreal @ SY1341 ) @ SY1342 @ SY1341 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SY1340 @ SY1342 @ SY1341 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1517,plain,
! [SV36: $i] :
( ( ! [SY1343: $i,SY1344: $i,SY1345: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV36 )
| ( c_Limits_OZfun @ SY1343 @ SY1344 @ SY1345 @ SV36 )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SY1343 @ SV36 @ tc_RealDef_Oreal @ SY1345 ) @ SY1344 @ SY1345 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1518,plain,
! [SV37: $i] :
( ( ! [SY1346: $i,SY1347: $i,SY1348: $i] :
( ~ ( class_RealVector_Ometric__space @ SV37 )
| ~ ( class_RealVector_Ometric__space @ SY1346 )
| ( c_Lim_OisCont @ ( c_COMBK @ SY1347 @ SY1346 @ SV37 ) @ SY1348 @ SV37 @ SY1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1519,plain,
! [SV38: $i] :
( ( ! [SY1349: $i,SY1350: $i,SY1351: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV38 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SY1349 @ SV38 @ SV38 @ SY1350 ) @ SY1351 @ SY1350 @ SV38 )
| ~ ( c_Limits_OZfun @ SY1349 @ SY1351 @ SY1350 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1520,plain,
! [SV39: $i] :
( ( ! [SY1352: $i,SY1353: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV39 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ SY1352 ) @ SY1353 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ SY1352 ) ) @ SY1353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1521,plain,
! [SV40: $i] :
( ( ! [SY1354: $i,SY1355: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV40 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SY1354 ) @ SY1355 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SY1354 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ SY1355 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1522,plain,
! [SV41: $i] :
( ( ! [SY1356: $i,SY1357: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV41 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1356 )
| ( c_Lim_OisUCont @ SY1357 @ SV41 @ SY1356 )
| ~ ( c_RealVector_Obounded__linear @ SY1357 @ SV41 @ SY1356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1523,plain,
! [SV42: $i] :
( ( ! [SY1358: $i,SY1359: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV42 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV42 ) @ SY1358 ) @ SY1359 @ SV42 @ SV42 @ tc_nat ) @ SV42 )
| ~ ( c_SEQ_OZseq @ SY1359 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1524,plain,
! [SV43: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV43 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV43 ) @ SY1360 ) @ SY1361 @ SV43 @ SV43 @ tc_nat ) @ SV43 )
| ~ ( c_SEQ_OZseq @ SY1361 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1525,plain,
! [SV44: $i] :
( ( ! [SY1362: $i,SY1363: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV44 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SY1362 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SY1362 ) @ SY1363 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SY1362 ) @ SY1363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1526,plain,
! [SV45: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ SV45 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY1364 ) @ SY1365 @ SY1364 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV45 @ SY1365 @ SY1364 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1527,plain,
! [SV46: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ SV46 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ SV46 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1528,plain,
! [SV47: $i] :
( ( ! [SY1366: $i,SY1367: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV47 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SY1366 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV47 ) @ SY1366 ) ) @ SY1367 ) )
= SY1367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1529,plain,
! [SV48: $i] :
( ( ! [SY1368: $i,SY1369: $i,SY1370: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV48 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV48 )
| ~ ( class_RealVector_Ometric__space @ SY1368 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SY1369 @ tc_RealDef_Oreal @ SV48 @ SY1368 ) @ SY1370 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SY1368 @ SV48 )
| ~ ( c_Lim_OLIM @ SY1369 @ SY1370 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SY1368 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1530,plain,
! [SV49: $i] :
( ( ! [SY1371: $i,SY1372: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV49 )
| ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SY1371 ) @ SY1372 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SY1371 ) @ SY1372 ) @ SV49 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1531,plain,
! [SV50: $i] :
( ( ! [SY1373: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV50 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV50 ) @ SY1373 ) @ SY1373 )
= SY1373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1532,plain,
! [SV51: $i] :
( ( ! [SY1374: $i,SY1375: $i,SY1376: $i,SY1377: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV51 )
| ~ ( class_RealVector_Ometric__space @ SY1374 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SY1375 ) @ SY1376 @ SV51 @ SV51 @ SY1374 ) @ SY1377 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SY1374 @ SV51 )
| ~ ( c_Lim_OLIM @ SY1376 @ SY1377 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SY1374 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1533,plain,
! [SV52: $i] :
( ( ! [SY1378: $i,SY1379: $i,SY1380: $i,SY1381: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV52 )
| ~ ( class_RealVector_Ometric__space @ SY1378 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SY1379 ) @ SY1380 @ SV52 @ SV52 @ SY1378 ) @ SY1381 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SY1378 @ SV52 )
| ~ ( c_Lim_OLIM @ SY1380 @ SY1381 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SY1378 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1534,plain,
! [SV53: $i] :
( ( ! [SY1382: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV53 )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV53 ) @ SY1382 ) @ SV53 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1535,plain,
! [SV54: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV54 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV54 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV54 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1536,plain,
! [SV55: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV55 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) )
= ( c_HOL_Ozero__class_Ozero @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1537,plain,
! [SV56: $i] :
( ( ! [SY1383: $i,SY1384: $i,SY1385: $i,SY1386: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV56 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SY1383 @ SV56 @ SV56 @ SY1384 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SY1385 ) @ SY1386 @ SY1384 @ SV56 )
| ~ ( c_Limits_Otendsto @ SY1383 @ SY1385 @ SY1386 @ SY1384 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1538,plain,
! [SV57: $i] :
( ( ! [SY1387: $i,SY1388: $i,SY1389: $i,SY1390: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV57 )
| ( c_Limits_Otendsto @ SY1387 @ SY1388 @ SY1389 @ SY1390 @ SV57 )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SY1387 @ SV57 @ SV57 @ SY1390 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SY1388 ) @ SY1389 @ SY1390 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1539,plain,
! [SV58: $i] :
( ( ! [SY1391: $i,SY1392: $i,SY1393: $i,SY1394: $i,SY1395: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV58 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1391 )
| ~ ( class_RealVector_Ometric__space @ SY1392 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY1393 @ SY1394 @ SY1391 @ SV58 @ SY1392 ) @ SY1395 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SY1392 @ SV58 )
| ~ ( c_Lim_OLIM @ SY1394 @ SY1395 @ ( c_HOL_Ozero__class_Ozero @ SY1391 ) @ SY1392 @ SY1391 )
| ~ ( c_RealVector_Obounded__linear @ SY1393 @ SY1391 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1540,plain,
! [SV59: $i] :
( ( ! [SY1396: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV59 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ SY1396 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ SY1396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1541,plain,
! [SV60: $i] :
( ( c_Lim_OLIM @ c_Complex_ORe @ SV60 @ ( hAPP @ c_Complex_ORe @ SV60 ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1542,plain,
! [SV61: $i] :
( ( ! [SY1397: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV61 )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV61 ) @ SY1397 @ SV61 @ SV61 @ tc_nat ) @ SV61 )
| ~ ( c_Series_Osummable @ SY1397 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1543,plain,
! [SV62: $i] :
( ( ! [SY1398: $i,SY1399: $i,SY1400: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV62 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SY1398 ) @ SY1399 ) ) @ SY1400 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SY1398 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SY1399 ) @ SY1400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1544,plain,
! [SV63: $i] :
( ( ! [SY1401: $i,SY1402: $i,SY1403: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SY1401 ) @ SY1402 ) ) @ SY1403 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SY1401 ) @ SY1403 ) ) @ SY1402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1545,plain,
! [SV64: $i] :
( ( ! [SY1404: $i,SY1405: $i,SY1406: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV64 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SY1404 ) @ SY1405 ) ) @ SY1406 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SY1404 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SY1405 ) @ SY1406 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1546,plain,
! [SV65: $i] :
( ( ! [SY1407: $i,SY1408: $i,SY1409: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SY1407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SY1408 ) @ SY1409 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SY1407 ) @ SY1408 ) ) @ SY1409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1547,plain,
! [SV66: $i] :
( ( ! [SY1410: $i,SY1411: $i,SY1412: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SY1410 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SY1411 ) @ SY1412 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SY1411 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SY1410 ) @ SY1412 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1548,plain,
! [SV67: $i] :
( ( ! [SY1413: $i,SY1414: $i,SY1415: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SY1413 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SY1414 ) @ SY1415 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SY1413 ) @ SY1414 ) ) @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1549,plain,
! [SV68: $i] :
( ( ! [SY1416: $i,SY1417: $i,SY1418: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY1416 ) @ SY1417 ) ) @ SY1418 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SY1416 ) @ SY1418 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SY1417 ) @ SY1418 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1550,plain,
! [SV69: $i] :
( ( ! [SY1419: $i,SY1420: $i,SY1421: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SY1419 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY1420 ) @ SY1421 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SY1419 ) @ SY1420 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SY1419 ) @ SY1421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1551,plain,
! [SV70: $i] :
( ( ! [SY1422: $i,SY1423: $i,SY1424: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV70 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SY1422 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SY1423 ) @ SY1424 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SY1422 ) @ SY1423 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SY1422 ) @ SY1424 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1552,plain,
! [SV71: $i] :
( ( ! [SY1425: $i,SY1426: $i,SY1427: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV71 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SY1425 ) @ SY1426 ) ) @ SY1427 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SY1425 ) @ SY1427 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SY1426 ) @ SY1427 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1553,plain,
! [SV72: $i] :
( ( ! [SY1428: $i,SY1429: $i,SY1430: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV72 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY1428 ) @ SY1429 ) ) @ SY1430 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SY1428 ) @ SY1430 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SY1429 ) @ SY1430 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1554,plain,
! [SV73: $i] :
( ( ! [SY1431: $i,SY1432: $i,SY1433: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV73 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SY1431 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY1432 ) @ SY1433 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SY1431 ) @ SY1432 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SY1431 ) @ SY1433 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1555,plain,
! [SV74: $i] :
( ( ! [SY1434: $i,SY1435: $i,SY1436: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV74 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SY1434 ) @ SY1435 ) ) @ SY1436 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SY1434 ) @ SY1436 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SY1435 ) @ SY1436 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1556,plain,
! [SV75: $i] :
( ( ! [SY1437: $i,SY1438: $i,SY1439: $i] :
( ~ ( class_RealVector_Ometric__space @ SV75 )
| ~ ( class_HOL_Ozero @ SV75 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SY1437 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SY1438 @ SV75 @ SY1437 ) @ SY1439 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SY1437 @ SV75 )
| ( SY1438
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1557,plain,
! [SV76: $i] :
( ( ! [SY1440: $i,SY1441: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV76 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SY1440 ) @ ( c_Series_Osuminf @ SY1441 @ SV76 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SY1440 ) @ SY1441 @ SV76 @ SV76 @ tc_nat ) @ SV76 ) )
| ~ ( c_Series_Osummable @ SY1441 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1558,plain,
! [SV77: $i] :
( ( ! [SY1442: $i,SY1443: $i,SY1444: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV77 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SY1442 ) @ SY1443 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SY1444 ) @ SY1443 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SY1442 ) @ SY1444 ) ) @ SY1443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1559,plain,
! [SV78: $i] :
( ( ! [SY1445: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV78 )
| ( c_RealVector_Obounded__linear @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV78 ) @ SY1445 @ SV78 @ SV78 @ SV78 ) @ SV78 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1560,plain,
! [SV79: $i] :
( ( ! [SY1446: $i,SY1447: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV79 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ SY1446 ) ) @ SY1447 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ SY1446 ) @ SY1447 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1561,plain,
! [SV80: $i] :
( ( ! [SY1448: $i,SY1449: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV80 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ SY1448 ) ) @ SY1449 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ SY1448 ) @ SY1449 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1562,plain,
! [SV81: $i] :
( ( ! [SY1450: $i,SY1451: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SY1450 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ SY1451 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SY1450 ) @ SY1451 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1563,plain,
! [SV82: $i] :
( ( ! [SY1452: $i,SY1453: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SY1452 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ SY1453 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SY1452 ) @ SY1453 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1564,plain,
! [SV83: $i] :
( ( ! [SY1454: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV83 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SY1454 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SY1454 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ SY1454 ) @ SY1454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1565,plain,
! [SV84: $i] :
( ( ! [SY1455: $i,SY1456: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV84 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SY1455 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SY1456 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ SY1455 ) @ SY1456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1566,plain,
! [SV85: $i] :
( ( ! [SY1457: $i,SY1458: $i,SY1459: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV85 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV85 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SY1457 @ tc_RealDef_Oreal @ SV85 @ SY1458 ) @ SY1459 @ SY1458 @ SV85 )
| ~ ( c_Limits_OZfun @ SY1457 @ SY1459 @ SY1458 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1567,plain,
! [SV86: $i] :
( ( ! [SY1460: $i,SY1461: $i,SY1462: $i,SY1463: $i,SY1464: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV86 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SY1460 ) @ SY1461 @ SV86 @ SV86 @ SY1462 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SY1460 ) @ SY1463 ) @ SY1464 @ SY1462 @ SV86 )
| ~ ( c_Limits_Otendsto @ SY1461 @ SY1463 @ SY1464 @ SY1462 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1568,plain,
! [SV87: $i] :
( ( ! [SY1465: $i,SY1466: $i,SY1467: $i,SY1468: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV87 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SY1465 ) @ SY1466 @ SV87 @ SV87 @ SY1467 ) @ SY1468 @ SY1467 @ SV87 )
| ~ ( c_Limits_OZfun @ SY1466 @ SY1468 @ SY1467 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1569,plain,
! [SV88: $i] :
( ( ! [SY1469: $i,SY1470: $i,SY1471: $i,SY1472: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV88 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SY1469 ) @ SY1470 @ SV88 @ SV88 @ SY1471 ) @ SY1472 @ SY1471 @ SV88 )
| ~ ( c_Limits_OZfun @ SY1470 @ SY1472 @ SY1471 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1570,plain,
! [SV89: $i] :
( ( ! [SY1473: $i,SY1474: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV89 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SY1473 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SY1474 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY1473 ) @ SY1474 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SY1473 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SY1474 ) ) )
| ( SY1474
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
| ( SY1473
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1571,plain,
! [SV90: $i] :
( ( ! [SY1475: $i,SY1476: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SY1475 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SY1476 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SY1475 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SY1475 ) @ SY1476 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SY1476 ) ) )
| ( SY1476
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SY1475
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1572,plain,
! [SV91: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ SV91 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ SV91 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1573,plain,
! [SV92: $i] :
( ( ! [SY1477: $i,SY1478: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SY1477 ) @ ( c_Series_Osuminf @ SY1478 @ SV92 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SY1477 ) @ SY1478 @ SV92 @ SV92 @ tc_nat ) @ SV92 ) )
| ~ ( c_Series_Osummable @ SY1478 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1574,plain,
! [SV93: $i] :
( ( ! [SY1479: $i,SY1480: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV93 )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SY1479 ) @ SY1480 @ SV93 @ SV93 @ tc_nat ) @ SV93 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SY1479 ) @ ( c_Series_Osuminf @ SY1480 @ SV93 ) ) )
| ~ ( c_Series_Osummable @ SY1480 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1575,plain,
! [SV94: $i] :
( ( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ SV94 @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ SV94 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ SV94 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1576,plain,
! [SV95: $i] :
( ( ! [SY1481: $i,SY1482: $i,SY1483: $i,SY1484: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV95 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1481 ) @ SY1482 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1483 ) @ SY1484 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1481 ) @ SY1483 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1482 ) @ SY1484 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1577,plain,
! [SV96: $i] :
( ( ! [SY1485: $i,SY1486: $i,SY1487: $i,SY1488: $i,SY1489: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV96 )
| ~ ( class_RealVector_Ometric__space @ SY1485 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SY1486 ) @ SY1487 @ SV96 @ SV96 @ SY1485 ) @ SY1488 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SY1486 ) @ SY1489 ) @ SY1485 @ SV96 )
| ~ ( c_Lim_OLIM @ SY1487 @ SY1488 @ SY1489 @ SY1485 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1578,plain,
! [SV97: $i] :
( ( ! [SY1490: $i,SY1491: $i,SY1492: $i] :
( ~ ( class_RealVector_Ometric__space @ SV97 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SY1490 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SY1491 @ ( hAPP @ c_Complex_ORe @ SY1492 ) @ SV97 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SY1490 @ SY1491 @ SY1492 @ SV97 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1579,plain,
! [SV98: $i] :
( ( ! [SY1493: $i,SY1494: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV98 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV98 ) @ SY1493 @ SV98 @ SV98 @ SV98 ) @ SY1494 @ SV98 )
| ~ ( c_Deriv_Odifferentiable @ SY1493 @ SY1494 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1580,plain,
! [SV99: $i] :
( ( ! [SY1495: $i,SY1496: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV99 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV99 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ SY1495 ) @ SY1496 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SY1495 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SY1496 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1581,plain,
! [SV100: $i] :
( ( ! [SY1497: $i,SY1498: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV100 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ SY1497 ) @ SY1498 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SY1498 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SY1497 ) ) )
| ( SY1498
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
| ( SY1497
= ( c_HOL_Ozero__class_Ozero @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1582,plain,
! [SV101: $i] :
( ( ! [SY1499: $i,SY1500: $i,SY1501: $i,SY1502: $i] :
( ~ ( class_RealVector_Ometric__space @ SV101 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SY1499 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SY1500 @ SV101 @ SY1499 ) @ SY1501 @ SY1502 @ SY1499 @ SV101 )
| ( SY1500 = SY1502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1583,plain,
! [SV102: $i] :
( ( ! [SY1503: $i,SY1504: $i,SY1505: $i,SY1506: $i] :
( ~ ( class_RealVector_Ometric__space @ SV102 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SY1503 )
| ( SY1504 = SY1505 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SY1504 @ SV102 @ SY1503 ) @ SY1506 @ SY1505 @ SY1503 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1584,plain,
! [SV103: $i] :
( ( ! [SY1507: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV103 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ SY1507 ) )
= SY1507 )
| ( SY1507
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1585,plain,
! [SV104: $i] :
( ( ! [SY1508: $i,SY1509: $i,SY1510: $i,SY1511: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV104 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SY1508 ) @ ( c_Finite__Set_Osetsum @ SY1509 @ SY1510 @ SY1511 @ SV104 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SY1508 ) @ SY1509 @ SV104 @ SV104 @ SY1511 ) @ SY1510 @ SY1511 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1586,plain,
! [SV105: $i] :
( ( ! [SY1512: $i,SY1513: $i,SY1514: $i,SY1515: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SY1512 ) @ ( c_Finite__Set_Osetsum @ SY1513 @ SY1514 @ SY1515 @ SV105 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SY1512 ) @ SY1513 @ SV105 @ SV105 @ SY1515 ) @ SY1514 @ SY1515 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1587,plain,
! [SV106: $i] :
( ( ! [SY1516: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ SV106 ) ) @ SY1516 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV106 ) @ ( hAPP @ c_Suc @ SY1516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1588,plain,
! [SV107: $i] :
( ( ! [SY1517: $i,SY1518: $i,SY1519: $i,SY1520: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
| ~ ( class_RealVector_Ometric__space @ SY1517 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SY1518 @ SV107 @ SV107 @ SY1517 ) @ SY1519 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SY1520 ) @ SY1517 @ SV107 )
| ( SY1520
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SY1518 @ SY1519 @ SY1520 @ SY1517 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1589,plain,
! [SV108: $i] :
( ( ! [SY1521: $i,SY1522: $i,SY1523: $i] :
( ~ ( class_RealVector_Ometric__space @ SV108 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1521 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SY1521 ) @ SY1522 @ SY1521 @ SY1521 @ SV108 ) @ SY1523 @ SV108 @ SY1521 )
| ~ ( c_Lim_OisCont @ SY1522 @ SY1523 @ SV108 @ SY1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1590,plain,
! [SV109: $i] :
( ( ! [SY1524: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV109 )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ SY1524 @ SV109 @ SV109 @ tc_nat ) @ SV109 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ ( c_Series_Osuminf @ SY1524 @ SV109 ) ) )
| ~ ( c_Series_Osummable @ SY1524 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1591,plain,
! [SV110: $i] :
( ( ! [SY1525: $i,SY1526: $i,SY1527: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SY1525 ) @ SY1526 ) ) @ SY1527 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SY1525 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ SY1526 ) @ SY1527 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1592,plain,
! [SV111: $i] :
( ( ! [SY1528: $i,SY1529: $i,SY1530: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SY1528 ) @ SY1529 ) ) @ SY1530 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SY1528 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ SY1529 ) @ SY1530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1593,plain,
! [SV112: $i] :
( ( ! [SY1531: $i,SY1532: $i,SY1533: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SY1531 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SY1532 ) @ SY1533 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SY1532 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SY1531 ) @ SY1533 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1594,plain,
! [SV113: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV113 )
| ( c_Series_Osummable @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 @ tc_nat ) @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1595,plain,
! [SV114: $i] :
( ( ! [SY1534: $i,SY1535: $i,SY1536: $i,SY1537: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV114 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV114 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SY1534 @ tc_RealDef_Oreal @ SV114 @ SY1535 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SY1536 ) @ SY1537 @ SY1535 @ SV114 )
| ~ ( c_Limits_Otendsto @ SY1534 @ SY1536 @ SY1537 @ SY1535 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1596,plain,
! [SV115: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV115 )
| ( c_Series_Osums @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1597,plain,
! [SV116: $i] :
( ( ! [SY1538: $i,SY1539: $i,SY1540: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV116 )
| ~ ( class_RealVector_Ometric__space @ SY1538 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY1539 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY1540 ) @ SV116 @ SY1538 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SY1539 @ SY1540 ) @ SV116 @ SY1538 )
| ~ ( c_Lim_OisCont @ SY1539 @ SY1540 @ SV116 @ SY1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1598,plain,
! [SV117: $i] :
( ( ! [SY1541: $i,SY1542: $i,SY1543: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV117 )
| ~ ( class_RealVector_Ometric__space @ SY1541 )
| ( c_Lim_OisCont @ SY1542 @ SY1543 @ SV117 @ SY1541 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SY1542 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY1543 ) @ SV117 @ SY1541 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SY1542 @ SY1543 ) @ SV117 @ SY1541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1599,plain,
! [SV118: $i] :
( ( ! [SY1544: $i,SY1545: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV118 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SY1544 @ SV118 @ SV118 @ SV118 ) @ SY1545 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SY1545 ) @ SY1544 ) @ SV118 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1600,plain,
! [SV119: $i] :
( ( ! [SY1546: $i,SY1547: $i,SY1548: $i] :
( ~ ( class_RealVector_Ometric__space @ SV119 )
| ~ ( class_RealVector_Ometric__space @ SY1546 )
| ( c_Lim_OisCont @ SY1547 @ SY1548 @ SV119 @ SY1546 )
| ~ ( c_Lim_OisUCont @ SY1547 @ SV119 @ SY1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1601,plain,
! [SV120: $i] :
( ( ! [SY1549: $i,SY1550: $i,SY1551: $i,SY1552: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV120 )
| ~ ( class_RealVector_Ometric__space @ SY1549 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SY1550 ) @ SY1551 @ SV120 @ SV120 @ SY1549 ) @ SY1552 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SY1549 @ SV120 )
| ~ ( c_Lim_OLIM @ SY1551 @ SY1552 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SY1549 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1602,plain,
! [SV121: $i] :
( ( ! [SY1553: $i,SY1554: $i,SY1555: $i,SY1556: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV121 )
| ~ ( class_RealVector_Ometric__space @ SY1553 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SY1554 ) @ SY1555 @ SV121 @ SV121 @ SY1553 ) @ SY1556 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY1553 @ SV121 )
| ~ ( c_Lim_OLIM @ SY1555 @ SY1556 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY1553 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1603,plain,
! [SV122: $i] :
( ( ! [SY1557: $i,SY1558: $i,SY1559: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV122 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SY1557 ) @ SY1558 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SY1557 ) @ SY1559 ) @ SV122 )
| ~ ( c_Series_Osums @ SY1558 @ SY1559 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1604,plain,
! [SV123: $i] :
( ( c_Lim_OisCont @ c_Complex_ORe @ SV123 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1605,plain,
! [SV124: $i] :
( ( ! [SY1560: $i,SY1561: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV124 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV124 ) @ SY1560 ) @ SY1561 @ SV124 @ SV124 @ tc_nat ) @ SV124 )
| ~ ( c_Series_Osummable @ SY1561 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1606,plain,
! [SV125: $i] :
( ( ! [SY1562: $i,SY1563: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV125 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SY1562 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ SY1563 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SY1562 ) @ SY1563 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1607,plain,
! [SV126: $i] :
( ( ! [SY1564: $i,SY1565: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV126 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SY1564 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ SY1565 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SY1564 ) @ SY1565 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1608,plain,
! [SV127: $i] :
( ( ! [SY1566: $i,SY1567: $i,SY1568: $i,SY1569: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV127 )
| ~ ( class_RealVector_Ometric__space @ SY1566 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SY1567 @ SV127 @ SV127 @ SY1566 ) @ SY1568 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SY1569 ) @ SY1566 @ SV127 )
| ~ ( c_Lim_OLIM @ SY1567 @ SY1568 @ SY1569 @ SY1566 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1609,plain,
! [SV128: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV128 )
| ( ( c_Series_Osuminf @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ tc_nat ) @ SV128 )
= ( c_HOL_Ozero__class_Ozero @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1610,plain,
! [SV129: $i] :
( ( ! [SY1570: $i,SY1571: $i,SY1572: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV129 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1570 )
| ( c_SEQ_OZseq @ ( c_COMBB @ SY1571 @ SY1572 @ SV129 @ SY1570 @ tc_nat ) @ SY1570 )
| ~ ( c_SEQ_OZseq @ SY1572 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SY1571 @ SV129 @ SY1570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1611,plain,
! [SV130: $i] :
( ( ! [SY1573: $i,SY1574: $i,SY1575: $i,SY1576: $i,SY1577: $i,SY1578: $i] :
( ~ ( class_RealVector_Ometric__space @ SV130 )
| ~ ( class_RealVector_Ometric__space @ SY1573 )
| ~ ( class_RealVector_Ometric__space @ SY1574 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY1575 @ SY1576 @ SV130 @ SY1573 @ SY1574 ) @ SY1577 @ ( hAPP @ SY1575 @ SY1578 ) @ SY1574 @ SY1573 )
| ~ ( c_Lim_OLIM @ SY1576 @ SY1577 @ SY1578 @ SY1574 @ SV130 )
| ~ ( c_Lim_OisCont @ SY1575 @ SY1578 @ SV130 @ SY1573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1612,plain,
! [SV131: $i] :
( ( ! [SY1579: $i,SY1580: $i,SY1581: $i,SY1582: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV131 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV131 )
| ~ ( class_RealVector_Ometric__space @ SY1579 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SY1580 @ tc_RealDef_Oreal @ SV131 @ SY1579 ) @ SY1581 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SY1582 ) @ SY1579 @ SV131 )
| ~ ( c_Lim_OLIM @ SY1580 @ SY1581 @ SY1582 @ SY1579 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1613,plain,
! [SV132: $i] :
( ( ! [SY1583: $i,SY1584: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ SV132 @ SY1583 @ SY1584 @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ SV132 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY1584 ) @ SY1583 @ SY1584 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1614,plain,
! [SV133: $i] :
( ( ! [SY1585: $i,SY1586: $i,SY1587: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV133 )
| ~ ( class_Int_Onumber__ring @ SV133 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SY1585 ) @ SY1586 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SY1585 ) @ SY1587 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SY1585 ) @ SY1587 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SY1585 ) @ SY1586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1615,plain,
! [SV134: $i] :
( ( ! [SY1588: $i,SY1589: $i,SY1590: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV134 )
| ~ ( class_Int_Onumber__ring @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SY1588 ) @ SY1589 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SY1588 ) @ SY1590 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SY1588 ) @ SY1590 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SY1588 ) @ SY1589 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1616,plain,
! [SV135: $i] :
( ( ! [SY1591: $i,SY1592: $i,SY1593: $i,SY1594: $i,SY1595: $i,SY1596: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV135 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1591 )
| ~ ( class_RealVector_Ometric__space @ SY1592 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY1593 @ SY1594 @ SV135 @ SY1591 @ SY1592 ) @ SY1595 @ ( hAPP @ SY1593 @ SY1596 ) @ SY1592 @ SY1591 )
| ~ ( c_Lim_OLIM @ SY1594 @ SY1595 @ SY1596 @ SY1592 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SY1593 @ SV135 @ SY1591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1617,plain,
! [SV136: $i] :
( ( ! [SY1597: $i,SY1598: $i,SY1599: $i,SY1600: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV136 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SY1597 ) @ SY1598 @ SV136 @ SV136 @ SY1599 ) @ SY1600 @ SY1599 @ SV136 )
| ~ ( c_Limits_OZfun @ SY1598 @ SY1600 @ SY1599 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1618,plain,
! [SV137: $i] :
( ( ! [SY1601: $i,SY1602: $i,SY1603: $i,SY1604: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV137 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SY1601 ) @ SY1602 @ SV137 @ SV137 @ SY1603 ) @ SY1604 @ SY1603 @ SV137 )
| ~ ( c_Limits_OZfun @ SY1602 @ SY1604 @ SY1603 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1619,plain,
! [SV138: $i] :
( ( ! [SY1605: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV138 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV138 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ SY1605 ) )
= SY1605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1620,plain,
! [SV139: $i] :
( ( ! [SY1606: $i,SY1607: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV139 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SY1606 @ SV139 @ SV139 @ SV139 ) @ SY1607 @ SV139 )
| ( ( hAPP @ SY1606 @ SY1607 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
| ~ ( c_Deriv_Odifferentiable @ SY1606 @ SY1607 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1621,plain,
! [SV140: $i] :
( ( ! [SY1608: $i,SY1609: $i,SY1610: $i,SY1611: $i,SY1612: $i,SY1613: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV140 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1608 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SY1609 @ SY1610 @ SY1608 @ SV140 @ SY1611 ) @ ( hAPP @ SY1609 @ SY1612 ) @ SY1613 @ SY1611 @ SV140 )
| ~ ( c_Limits_Otendsto @ SY1610 @ SY1612 @ SY1613 @ SY1611 @ SY1608 )
| ~ ( c_RealVector_Obounded__linear @ SY1609 @ SY1608 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1622,plain,
! [SV141: $i] :
( ( ! [SY1614: $i,SY1615: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV141 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SY1614 ) @ SY1615 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SY1615 ) @ SY1614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1623,plain,
! [SV142: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV142 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Ozero__class_Ozero @ SV142 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV142 ) )
= ( c_HOL_Ozero__class_Ozero @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1624,plain,
! [SV143: $i] :
( ( ! [SY1616: $i,SY1617: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SY1616 ) @ SY1617 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SY1617 ) @ SY1616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1625,plain,
! [SV144: $i] :
( ( ! [SY1618: $i,SY1619: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV144 )
| ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV144 ) @ SY1618 @ SV144 @ SV144 @ SV144 ) @ SY1619 @ SV144 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1626,plain,
! [SV145: $i] :
( ( ! [SY1620: $i,SY1621: $i,SY1622: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV145 )
| ~ ( class_RealVector_Ometric__space @ SY1620 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SY1621 @ SV145 @ tc_RealDef_Oreal @ SY1620 ) @ SY1622 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SY1620 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SY1621 @ SY1622 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SY1620 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1627,plain,
! [SV146: $i] :
( ( ! [SY1623: $i,SY1624: $i,SY1625: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV146 )
| ~ ( class_RealVector_Ometric__space @ SY1623 )
| ( c_Lim_OLIM @ SY1624 @ SY1625 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SY1623 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SY1624 @ SV146 @ tc_RealDef_Oreal @ SY1623 ) @ SY1625 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SY1623 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1628,plain,
! [SV147: $i] :
( ( ! [SY1626: $i,SY1627: $i,SY1628: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1626 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1627 ) @ SY1628 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1627 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1626 ) @ SY1628 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1629,plain,
! [SV148: $i] :
( ( ! [SY1629: $i,SY1630: $i,SY1631: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY1629 ) @ SY1630 ) ) @ SY1631 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY1629 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY1630 ) @ SY1631 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1630,plain,
! [SV149: $i] :
( ( ! [SY1632: $i,SY1633: $i,SY1634: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV149 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY1632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY1633 ) @ SY1634 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY1632 ) @ SY1633 ) ) @ SY1634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1631,plain,
! [SV150: $i] :
( ( ! [SY1635: $i,SY1636: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ SY1635 ) ) @ SY1636 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1635 ) @ SY1636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1632,plain,
! [SV151: $i] :
( ( ! [SY1637: $i,SY1638: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV151 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1637 ) @ SY1638 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1637 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV151 ) @ SY1638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1633,plain,
! [SV152: $i] :
( ( ! [SY1639: $i,SY1640: $i,SY1641: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1639 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1640 ) @ SY1641 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1640 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1639 ) @ SY1641 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1634,plain,
! [SV153: $i] :
( ( ! [SY1642: $i,SY1643: $i,SY1644: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1642 ) @ SY1643 ) ) @ SY1644 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1642 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1643 ) @ SY1644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1635,plain,
! [SV154: $i] :
( ( ! [SY1645: $i,SY1646: $i,SY1647: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV154 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY1645 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY1646 ) @ SY1647 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY1645 ) @ SY1646 ) ) @ SY1647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1636,plain,
! [SV155: $i] :
( ( ! [SY1648: $i,SY1649: $i,SY1650: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV155 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SY1648 ) @ SY1649 ) ) @ SY1650 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SY1648 ) @ SY1650 ) ) @ SY1649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1637,plain,
! [SV156: $i] :
( ( ! [SY1651: $i,SY1652: $i,SY1653: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1651 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1652 ) @ SY1653 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1652 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1651 ) @ SY1653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1638,plain,
! [SV157: $i] :
( ( ! [SY1654: $i,SY1655: $i,SY1656: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1654 ) @ SY1655 ) ) @ SY1656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1654 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1655 ) @ SY1656 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1639,plain,
! [SV158: $i] :
( ( ! [SY1657: $i,SY1658: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV158 ) @ SY1657 ) @ SY1658 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV158 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV158 ) @ SY1657 ) ) @ SY1658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1640,plain,
! [SV159: $i] :
( ( ! [SY1659: $i,SY1660: $i,SY1661: $i,SY1662: $i,SY1663: $i] :
( ( hAPP @ ( c_COMBC @ SV159 @ SY1659 @ SY1660 @ SY1661 @ SY1662 ) @ SY1663 )
= ( hAPP @ ( hAPP @ SV159 @ SY1663 ) @ SY1659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1641,plain,
! [SV160: $i] :
( ( ! [SY1664: $i,SY1665: $i,SY1666: $i] :
( ( hAPP @ ( c_COMBK @ SV160 @ SY1664 @ SY1665 ) @ SY1666 )
= SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1642,plain,
! [SV161: $i] :
( ( ! [SY1667: $i,SY1668: $i,SY1669: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV161 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1667 )
| ( c_Series_Osummable @ ( c_COMBB @ SY1668 @ SY1669 @ SV161 @ SY1667 @ tc_nat ) @ SY1667 )
| ~ ( c_Series_Osummable @ SY1669 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SY1668 @ SV161 @ SY1667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1643,plain,
! [SV162: $i] :
( ( ! [SY1670: $i,SY1671: $i,SY1672: $i,SY1673: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SY1670 @ SV162 @ SV162 @ SY1671 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SY1672 ) @ SY1673 @ SY1671 @ SV162 )
| ( SY1672
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SY1670 @ SY1672 @ SY1673 @ SY1671 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1644,plain,
! [SV163: $i] :
( ( ! [SY1674: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV163 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV163 ) @ SY1674 ) @ ( c_HOL_Ozero__class_Ozero @ SV163 ) )
= ( c_HOL_Ozero__class_Ozero @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1645,plain,
! [SV164: $i] :
( ( ! [SY1675: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV164 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SY1675 )
= ( c_HOL_Ozero__class_Ozero @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1646,plain,
! [SV165: $i] :
( ( ! [SY1676: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV165 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV165 ) @ SY1676 ) @ ( c_HOL_Ozero__class_Ozero @ SV165 ) )
= ( c_HOL_Ozero__class_Ozero @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1647,plain,
! [SV166: $i] :
( ( ! [SY1677: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV166 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV166 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SY1677 )
= ( c_HOL_Ozero__class_Ozero @ SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1648,plain,
! [SV167: $i] :
( ( ! [SY1678: $i,SY1679: $i,SY1680: $i,SY1681: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV167 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SY1678 ) @ SY1679 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SY1680 ) @ SY1679 ) ) @ SY1681 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ SY1678 ) @ SY1680 ) ) @ SY1679 ) ) @ SY1681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1649,plain,
! [SV168: $i] :
( ( ! [SY1682: $i] :
( ~ ( class_RealVector_Ometric__space @ SV168 )
| ( c_SEQ_OLIMSEQ @ SY1682 @ ( c_SEQ_Olim @ SY1682 @ SV168 ) @ SV168 )
| ~ ( c_SEQ_Oconvergent @ SY1682 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1650,plain,
! [SV169: $i] :
( ( ! [SY1683: $i] :
( ~ ( class_RealVector_Ometric__space @ SV169 )
| ( c_SEQ_Oconvergent @ SY1683 @ SV169 )
| ~ ( c_SEQ_OLIMSEQ @ SY1683 @ ( c_SEQ_Olim @ SY1683 @ SV169 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1651,plain,
! [SV170: $i] :
( ( ! [SY1684: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV170 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV170 ) @ SY1684 ) ) @ SY1684 )
= ( c_HOL_Ozero__class_Ozero @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1652,plain,
! [SV171: $i] :
( ( ! [SY1685: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV171 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV171 ) @ SY1685 ) ) @ SY1685 )
= ( c_HOL_Ozero__class_Ozero @ SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1653,plain,
! [SV172: $i] :
( ( ! [SY1686: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV172 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV172 ) @ SY1686 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV172 ) @ SY1686 ) )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1654,plain,
! [SV173: $i] :
( ( ! [SY1687: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV173 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV173 ) @ SY1687 ) ) @ SY1687 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1655,plain,
! [SV174: $i] :
( ( ! [SY1688: $i,SY1689: $i,SY1690: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV174 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1688 )
| ( c_Lim_OisCont @ SY1689 @ SY1690 @ SV174 @ SY1688 )
| ~ ( c_RealVector_Obounded__linear @ SY1689 @ SV174 @ SY1688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1656,plain,
! [SV175: $i] :
( ( ! [SY1691: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV175 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV175 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SY1691 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SY1691 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
| ~ ( c_Series_Osummable @ SY1691 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1657,plain,
! [SV176: $i] :
( ( ! [SY1692: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV176 )
| ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ SY1692 @ SV176 @ SV176 @ tc_nat ) @ SV176 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ ( c_SEQ_Olim @ SY1692 @ SV176 ) ) )
| ~ ( c_SEQ_Oconvergent @ SY1692 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1658,plain,
! [SV177: $i] :
( ( ! [SY1693: $i,SY1694: $i,SY1695: $i,SY1696: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV177 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SY1693 ) @ ( c_Finite__Set_Osetsum @ SY1694 @ SY1695 @ SY1696 @ SV177 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SY1693 ) @ SY1694 @ SV177 @ SV177 @ SY1696 ) @ SY1695 @ SY1696 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1659,plain,
! [SV178: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ SV178 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ SV178 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1660,plain,
! [SV179: $i] :
( ( ! [SY1697: $i,SY1698: $i,SY1699: $i,SY1700: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV179 )
| ~ ( class_RealVector_Ometric__space @ SY1697 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SY1698 @ SV179 @ tc_RealDef_Oreal @ SY1697 ) @ SY1699 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SY1700 ) @ SY1697 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SY1698 @ SY1699 @ SY1700 @ SY1697 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1661,plain,
! [SV180: $i] :
( ( ! [SY1701: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV180 )
| ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV180 ) @ SY1701 @ SV180 @ SV180 @ tc_nat ) @ SV180 )
| ~ ( c_SEQ_Oconvergent @ SY1701 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1662,plain,
! [SV181: $i] :
( ( ! [SY1702: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV181 )
| ( c_SEQ_Oconvergent @ SY1702 @ SV181 )
| ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV181 ) @ SY1702 @ SV181 @ SV181 @ tc_nat ) @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1663,plain,
! [SV182: $i] :
( ( ! [SY1703: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV182 )
| ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SY1703 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SY1703 ) @ SV182 @ SV182 )
| ( SY1703
= ( c_HOL_Ozero__class_Ozero @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1664,plain,
! [SV183: $i] :
( ( ! [SY1704: $i,SY1705: $i,SY1706: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SY1704 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SY1705 ) @ SY1706 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SY1704 ) @ SY1705 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SY1704 ) @ SY1706 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1665,plain,
! [SV184: $i] :
( ( ! [SY1707: $i,SY1708: $i,SY1709: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SY1707 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ SY1708 ) @ SY1709 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SY1707 ) @ SY1708 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SY1707 ) @ SY1709 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1666,plain,
! [SV185: $i] :
( ( ! [SY1710: $i,SY1711: $i,SY1712: $i,SY1713: $i,SY1714: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV185 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1710 )
| ( c_Limits_OZfun @ ( c_COMBB @ SY1711 @ SY1712 @ SY1710 @ SV185 @ SY1713 ) @ SY1714 @ SY1713 @ SV185 )
| ~ ( c_Limits_OZfun @ SY1712 @ SY1714 @ SY1713 @ SY1710 )
| ~ ( c_RealVector_Obounded__linear @ SY1711 @ SY1710 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1667,plain,
! [SV186: $i] :
( ( ! [SY1715: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 )
| ( c_Lim_OisUCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV186 ) @ SY1715 @ SV186 @ SV186 @ SV186 ) @ SV186 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1668,plain,
! [SV187: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV187 )
| ( c_SEQ_OZseq @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV187 @ tc_nat ) @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1669,plain,
! [SV188: $i] :
( ( ! [SY1716: $i,SY1717: $i,SY1718: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV188 )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ SY1716 @ SV188 @ SV188 @ SY1717 ) @ SY1718 @ SY1717 @ SV188 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ ( c_Finite__Set_Osetsum @ SY1716 @ SY1718 @ SY1717 @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1670,plain,
! [SV189: $i] :
( ( ! [SY1719: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV189 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SY1719 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SY1719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1671,plain,
! [SV190: $i] :
( ( ! [SY1720: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV190 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SY1720 )
= SY1720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1672,plain,
! [SV191: $i] :
( ( ! [SY1721: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV191 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SY1721 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SY1721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1673,plain,
! [SV192: $i] :
( ( ! [SY1722: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV192 )
| ~ ( class_Int_Onumber__ring @ SV192 )
| ( SY1722
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SY1722 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1674,plain,
! [SV193: $i] :
( ( ! [SY1723: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SY1723 )
= SY1723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1675,plain,
! [SV194: $i] :
( ( ! [SY1724: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV194 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ ( c_HOL_Ozero__class_Ozero @ SV194 ) ) @ SY1724 )
= SY1724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1676,plain,
! [SV195: $i] :
( ( ! [SY1725: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV195 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV195 ) @ SY1725 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) )
= SY1725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1677,plain,
! [SV196: $i] :
( ( ! [SY1726: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV196 ) @ ( c_HOL_Ozero__class_Ozero @ SV196 ) ) @ SY1726 )
= SY1726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1678,plain,
! [SV197: $i] :
( ( ! [SY1727: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV197 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ SY1727 ) )
= SY1727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1679,plain,
! [SV198: $i] :
( ( ! [SY1728: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV198 )
| ( SY1728
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ SY1728 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1680,plain,
! [SV199: $i] :
( ( ! [SY1729: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV199 )
| ( SY1729
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ SY1729 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1681,plain,
! [SV200: $i] :
( ( ! [SY1730: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV200 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ SY1730 ) )
= SY1730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1682,plain,
! [SV201: $i] :
( ( ! [SY1731: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV201 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ SY1731 ) )
= SY1731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1683,plain,
! [SV202: $i] :
( ( ! [SY1732: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV202 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV202 )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SY1732 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
| ~ ( c_Series_Osummable @ SY1732 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1684,plain,
! [SV203: $i] :
( ( ! [SY1733: $i,SY1734: $i,SY1735: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV203 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SY1733 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SY1734 ) @ SY1735 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SY1734 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SY1733 ) @ SY1735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1685,plain,
! [SV204: $i] :
( ( ! [SY1736: $i,SY1737: $i,SY1738: $i] :
( ~ ( class_RealVector_Oreal__algebra @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SY1736 ) @ SY1737 ) ) @ SY1738 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SY1736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ SY1737 ) @ SY1738 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1686,plain,
! [SV205: $i] :
( ( ! [SY1739: $i,SY1740: $i,SY1741: $i] :
( ~ ( class_RealVector_Oreal__algebra @ SV205 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SY1739 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SY1740 ) @ SY1741 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SY1740 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SY1739 ) @ SY1741 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1687,plain,
! [SV206: $i] :
( ( ! [SY1742: $i,SY1743: $i,SY1744: $i] :
( ~ ( class_RealVector_Ometric__space @ SV206 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SY1742 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SY1742 ) @ SY1743 @ tc_RealDef_Oreal @ SY1742 @ SV206 ) @ SY1744 @ SV206 @ SY1742 )
| ~ ( c_Lim_OisCont @ SY1743 @ SY1744 @ SV206 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1688,plain,
! [SV207: $i] :
( ( ! [SY1745: $i,SY1746: $i,SY1747: $i,SY1748: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV207 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1745 )
| ( ( hAPP @ SY1746 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SY1747 ) @ SY1748 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SY1745 ) @ SY1747 ) @ ( hAPP @ SY1746 @ SY1748 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SY1746 @ SV207 @ SY1745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1689,plain,
! [SV208: $i] :
( ( ! [SY1749: $i,SY1750: $i,SY1751: $i] :
( ~ ( class_RealVector_Ometric__space @ SV208 )
| ~ ( class_RealVector_Ometric__space @ SY1749 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SY1750 @ SY1751 @ SV208 @ SY1749 @ tc_nat ) @ SY1749 )
| ~ ( c_SEQ_OCauchy @ SY1751 @ SV208 )
| ~ ( c_Lim_OisUCont @ SY1750 @ SV208 @ SY1749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1690,plain,
! [SV209: $i] :
( ( ! [SY1752: $i,SY1753: $i,SY1754: $i,SY1755: $i] :
( ~ ( class_RealVector_Ometric__space @ SV209 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1752 )
| ( c_Lim_OLIM @ SY1753 @ SY1754 @ SY1755 @ SY1752 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SY1753 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SY1752 ) @ SY1754 ) @ SY1752 @ SV209 @ SY1752 ) @ ( c_HOL_Ozero__class_Ozero @ SY1752 ) @ SY1755 @ SY1752 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1691,plain,
! [SV210: $i] :
( ( ! [SY1756: $i,SY1757: $i,SY1758: $i,SY1759: $i] :
( ~ ( class_RealVector_Ometric__space @ SV210 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1756 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY1757 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SY1756 ) @ SY1758 ) @ SY1756 @ SV210 @ SY1756 ) @ ( c_HOL_Ozero__class_Ozero @ SY1756 ) @ SY1759 @ SY1756 @ SV210 )
| ~ ( c_Lim_OLIM @ SY1757 @ SY1758 @ SY1759 @ SY1756 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1692,plain,
! [SV211: $i] :
( ( ! [SY1760: $i,SY1761: $i,SY1762: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV211 )
| ~ ( class_RealVector_Ometric__space @ SY1760 )
| ( c_Lim_OLIM @ SY1761 @ SY1762 @ ( hAPP @ SY1761 @ SY1762 ) @ SV211 @ SY1760 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SY1761 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SY1762 ) @ SV211 @ SY1760 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SY1761 @ SY1762 ) @ SV211 @ SY1760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1693,plain,
! [SV212: $i] :
( ( ! [SY1763: $i,SY1764: $i,SY1765: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV212 )
| ~ ( class_RealVector_Ometric__space @ SY1763 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY1764 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SY1765 ) @ SV212 @ SY1763 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SY1764 @ SY1765 ) @ SV212 @ SY1763 )
| ~ ( c_Lim_OLIM @ SY1764 @ SY1765 @ ( hAPP @ SY1764 @ SY1765 ) @ SV212 @ SY1763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1694,plain,
! [SV213: $i] :
( ( ! [SY1766: $i,SY1767: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV213 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV213 ) @ SY1766 ) @ SY1767 @ SV213 @ SV213 @ tc_nat ) @ SV213 )
| ~ ( c_Series_Osummable @ SY1767 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1695,plain,
! [SV214: $i] :
( ( ! [SY1768: $i,SY1769: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV214 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV214 ) @ SY1768 ) @ SY1769 @ SV214 @ SV214 @ tc_nat ) @ SV214 )
| ~ ( c_Series_Osummable @ SY1769 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1696,plain,
! [SV215: $i] :
( ( ! [SY1770: $i,SY1771: $i,SY1772: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV215 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SY1770 ) @ SY1771 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SY1770 ) @ SY1772 ) @ SV215 )
| ~ ( c_Series_Osums @ SY1771 @ SY1772 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1697,plain,
! [SV216: $i] :
( ( ! [SY1773: $i,SY1774: $i,SY1775: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SY1773 ) @ SY1774 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SY1773 ) @ SY1775 ) @ SV216 )
| ~ ( c_Series_Osums @ SY1774 @ SY1775 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1698,plain,
! [SV217: $i] :
( ( ! [SY1776: $i,SY1777: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV217 )
| ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 @ SY1776 ) @ SY1777 @ SY1776 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1699,plain,
! [SV218: $i] :
( ( ! [SY1778: $i,SY1779: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV218 )
| ( c_Series_Osummable @ SY1778 @ SV218 )
| ~ ( c_Series_Osums @ SY1778 @ SY1779 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1700,plain,
! [SV219: $i] :
( ( ! [SY1780: $i,SY1781: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV219 )
| ( c_Series_Osummable @ SY1780 @ SV219 )
| ~ ( c_Series_Osums @ SY1780 @ SY1781 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1701,plain,
! [SV220: $i] :
( ( ! [SY1782: $i,SY1783: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV220 )
| ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV220 ) @ SY1782 ) @ SY1783 @ SV220 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1702,plain,
! [SV221: $i] :
( ( ! [SY1784: $i,SY1785: $i,SY1786: $i,SY1787: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV221 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SY1784 @ SV221 @ tc_RealDef_Oreal @ SY1785 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SY1786 ) @ SY1787 @ SY1785 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SY1784 @ SY1786 @ SY1787 @ SY1785 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1703,plain,
! [SV222: $i] :
( ( ! [SY1788: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ SV222 ) ) @ SY1788 )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV222 ) @ SY1788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1704,plain,
! [SV223: $i] :
( ( ! [SY1789: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV223 ) @ ( hAPP @ c_Suc @ SY1789 ) )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV223 ) @ SY1789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1705,plain,
! [SV224: $i] :
( ( ! [SY1790: $i,SY1791: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV224 )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 @ SY1790 ) @ SY1791 @ SY1790 @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1706,plain,
! [SV225: $i] :
( ( ! [SY1792: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV225 )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV225 ) @ SY1792 ) )
= ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ SY1792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1707,plain,
! [SV226: $i] :
( ( ! [SY1793: $i,SY1794: $i,SY1795: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV226 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SY1793 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SY1794 ) @ SY1795 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SY1794 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SY1793 ) @ SY1795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1708,plain,
! [SV227: $i] :
( ( ! [SY1796: $i,SY1797: $i,SY1798: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV227 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SY1796 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SY1797 ) @ SY1798 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SY1797 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SY1796 ) @ SY1798 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1709,plain,
! [SV228: $i] :
( ( ! [SY1799: $i,SY1800: $i,SY1801: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SY1799 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SY1800 ) @ SY1801 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SY1800 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SY1799 ) @ SY1801 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1710,plain,
! [SV229: $i] :
( ( ! [SY1802: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV229 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV229 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SY1802 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
| ~ ( c_SEQ_OZseq @ SY1802 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1711,plain,
! [SV230: $i] :
( ( ! [SY1803: $i,SY1804: $i,SY1805: $i] :
( ~ ( class_RealVector_Otopological__space @ SV230 )
| ( c_Limits_Otendsto @ ( c_COMBK @ SY1803 @ SV230 @ SY1804 ) @ SY1803 @ SY1805 @ SY1804 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1712,plain,
! [SV231: $i] :
( ( ! [SY1806: $i,SY1807: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV231 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SY1806 ) @ SY1807 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SY1807 ) @ SY1806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1713,plain,
! [SV232: $i] :
( ( ! [SY1808: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV232 ) @ SY1808 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1808 ) @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1714,plain,
! [SV233: $i] :
( ( ! [SY1809: $i,SY1810: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SY1809 ) @ SY1810 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SY1810 ) @ SY1809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1715,plain,
! [SV234: $i] :
( ( ! [SY1811: $i,SY1812: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV234 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SY1811 ) @ SY1812 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SY1812 ) @ SY1811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1716,plain,
! [SV235: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV235 )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV235 ) @ ( c_HOL_Ozero__class_Ozero @ SV235 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1717,plain,
! [SV236: $i] :
( ( ! [SY1813: $i,SY1814: $i,SY1815: $i] :
( ~ ( class_RealVector_Ometric__space @ SV236 )
| ~ ( class_RealVector_Ometric__space @ SY1813 )
| ( c_Lim_OLIM @ ( c_COMBK @ SY1814 @ SV236 @ SY1813 ) @ SY1815 @ SY1814 @ SY1813 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1718,plain,
! [SV237: $i] :
( ( ! [SY1816: $i,SY1817: $i,SY1818: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV237 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV237 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SY1816 @ SY1817 @ SY1818 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SY1816 @ tc_RealDef_Oreal @ SV237 @ SY1818 ) @ SY1817 @ SY1818 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1719,plain,
! [SV238: $i] :
( ( ! [SY1819: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV238 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ SY1819 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ SY1819 ) ) )
| ( SY1819
= ( c_HOL_Ozero__class_Ozero @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1720,plain,
! [SV239: $i] :
( ( ! [SY1820: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) ) @ SY1820 )
= ( c_HOL_Ozero__class_Ozero @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1721,plain,
! [SV240: $i] :
( ( ! [SY1821: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV240 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV240 ) @ SY1821 ) @ ( c_HOL_Ozero__class_Ozero @ SV240 ) )
= ( c_HOL_Ozero__class_Ozero @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1722,plain,
! [SV241: $i] :
( ( ! [SY1822: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV241 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV241 ) @ ( c_HOL_Ozero__class_Ozero @ SV241 ) ) @ SY1822 )
= ( c_HOL_Ozero__class_Ozero @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1723,plain,
! [SV242: $i] :
( ( ! [SY1823: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV242 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV242 ) @ ( c_HOL_Ozero__class_Ozero @ SV242 ) ) @ SY1823 )
= ( c_HOL_Ozero__class_Ozero @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1724,plain,
! [SV243: $i] :
( ( ! [SY1824: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV243 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV243 ) @ SY1824 ) @ ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1725,plain,
! [SV244: $i] :
( ( ! [SY1825: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV244 ) @ SY1825 ) @ ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= ( c_HOL_Ozero__class_Ozero @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1726,plain,
! [SV245: $i] :
( ( ! [SY1826: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV245 ) @ ( c_HOL_Ozero__class_Ozero @ SV245 ) ) @ SY1826 )
= ( c_HOL_Ozero__class_Ozero @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1727,plain,
! [SV246: $i] :
( ( ! [SY1827: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV246 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) ) @ SY1827 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1728,plain,
! [SV247: $i] :
( ( ! [SY1828: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV247 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV247 ) @ SY1828 ) @ ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1729,plain,
! [SV248: $i] :
( ( ! [SY1829: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV248 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV248 ) @ ( c_HOL_Ozero__class_Ozero @ SV248 ) ) @ SY1829 )
= ( c_HOL_Ozero__class_Ozero @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1730,plain,
! [SV249: $i] :
( ( ! [SY1830: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV249 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV249 ) @ SY1830 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= ( c_HOL_Ozero__class_Ozero @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1731,plain,
! [SV250: $i] :
( ( ! [SY1831: $i,SY1832: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV250 )
| ( c_Series_Osummable @ ( c_COMBB @ SY1831 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1832 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV250 @ tc_nat ) @ SV250 )
| ~ ( c_Series_Osummable @ SY1831 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1732,plain,
! [SV251: $i] :
( ( ! [SY1833: $i,SY1834: $i,SY1835: $i,SY1836: $i,SY1837: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV251 )
| ~ ( class_RealVector_Ometric__space @ SY1833 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SY1834 ) @ SY1835 @ SV251 @ SV251 @ SY1833 ) @ SY1836 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SY1834 ) @ SY1837 ) @ SY1833 @ SV251 )
| ~ ( c_Lim_OLIM @ SY1835 @ SY1836 @ SY1837 @ SY1833 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1733,plain,
! [SV252: $i] :
( ( ! [SY1838: $i,SY1839: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV252 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV252 ) @ SY1838 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ SY1839 ) @ SY1838 ) )
= SY1839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1734,plain,
! [SV253: $i] :
( ( ! [SY1840: $i,SY1841: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV253 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV253 ) @ SY1840 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ SY1840 ) @ SY1841 ) )
= SY1841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1735,plain,
! [SV254: $i] :
( ( ! [SY1842: $i,SY1843: $i,SY1844: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ SV254 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY1842 ) @ ( hAPP @ c_Complex_ORe @ SY1843 ) @ SY1844 @ SY1842 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV254 @ SY1843 @ SY1844 @ SY1842 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1736,plain,
! [SV255: $i] :
( ( ! [SY1845: $i,SY1846: $i,SY1847: $i,SY1848: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV255 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1845 )
| ( c_Series_Osums @ ( c_COMBB @ SY1846 @ SY1847 @ SV255 @ SY1845 @ tc_nat ) @ ( hAPP @ SY1846 @ SY1848 ) @ SY1845 )
| ~ ( c_Series_Osums @ SY1847 @ SY1848 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SY1846 @ SV255 @ SY1845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1737,plain,
! [SV256: $i] :
( ( ! [SY1849: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV256 )
| ( c_SEQ_OLIMSEQ @ SY1849 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
| ~ ( c_Series_Osummable @ SY1849 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1738,plain,
! [SV257: $i] :
( ( ! [SY1850: $i,SY1851: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV257 )
| ( SY1850
= ( c_Series_Osuminf @ SY1851 @ SV257 ) )
| ~ ( c_Series_Osums @ SY1851 @ SY1850 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1739,plain,
! [SV258: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV258 )
| ( ( c_Series_Osuminf @ SY1852 @ SV258 )
= SY1853 )
| ~ ( c_Series_Osums @ SY1852 @ SY1853 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1740,plain,
! [SV259: $i] :
( ( ! [SY1854: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ SV259 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SY1854 ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ SV259 @ SY1854 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1741,plain,
! [SV260: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV260 )
| ( ( c_HOL_Ozero__class_Ozero @ SV260 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV260 ) @ ( c_HOL_Ozero__class_Ozero @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1742,plain,
! [SV261: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ SV261 ) @ ( hAPP @ c_Complex_OIm @ SV261 ) )
= SV261 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1743,plain,
! [SV262: $i] :
( ( ! [SY1855: $i] :
( ~ ( class_SEQ_Ocomplete__space @ SV262 )
| ( c_SEQ_OCauchy @ SY1855 @ SV262 )
| ~ ( c_SEQ_Oconvergent @ SY1855 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1744,plain,
! [SV263: $i] :
( ( ! [SY1856: $i] :
( ~ ( class_SEQ_Ocomplete__space @ SV263 )
| ( c_SEQ_Oconvergent @ SY1856 @ SV263 )
| ~ ( c_SEQ_OCauchy @ SY1856 @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1745,plain,
! [SV264: $i] :
( ( ! [SY1857: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV264 )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV264 ) @ SY1857 ) @ SV264 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1746,plain,
! [SV265: $i] :
( ( ! [SY1858: $i] :
( ~ ( class_RealVector_Ometric__space @ SV265 )
| ( c_SEQ_OCauchy @ SY1858 @ SV265 )
| ~ ( c_SEQ_Oconvergent @ SY1858 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1747,plain,
! [SV266: $i] :
( ( ( c_SEQ_Oconvergent @ SV266 @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ SV266 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1748,plain,
! [SV267: $i] :
( ( ! [SY1859: $i,SY1860: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV267 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SY1859 ) ) @ SY1860 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ SY1859 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SY1860 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1749,plain,
! [SV268: $i] :
( ( ! [SY1861: $i,SY1862: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV268 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SY1861 @ SV268 @ SV268 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SY1862 ) @ SV268 )
| ~ ( c_Series_Osums @ SY1861 @ SY1862 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1750,plain,
! [SV269: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV269 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV269 ) @ ( c_HOL_Ozero__class_Ozero @ SV269 ) )
= ( c_HOL_Ozero__class_Ozero @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1751,plain,
! [SV270: $i] :
( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV270 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV270 ) @ ( c_HOL_Ozero__class_Ozero @ SV270 ) )
= ( c_HOL_Ozero__class_Ozero @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1752,plain,
! [SV271: $i] :
( ( ! [SY1863: $i,SY1864: $i,SY1865: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV271 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1863 )
| ( c_Lim_OLIM @ SY1864 @ SY1865 @ ( hAPP @ SY1864 @ SY1865 ) @ SV271 @ SY1863 )
| ~ ( c_RealVector_Obounded__linear @ SY1864 @ SV271 @ SY1863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1753,plain,
! [SV272: $i] :
( ( ! [SY1866: $i,SY1867: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV272 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV272 ) @ SY1866 ) @ SY1867 @ SV272 @ SV272 @ tc_nat ) @ SV272 )
| ~ ( c_SEQ_OZseq @ SY1867 @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1754,plain,
! [SV273: $i] :
( ( ! [SY1868: $i,SY1869: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV273 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV273 ) @ SY1868 ) @ SY1869 @ SV273 @ SV273 @ tc_nat ) @ SV273 )
| ~ ( c_SEQ_OZseq @ SY1869 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1755,plain,
! [SV274: $i] :
( ( ! [SY1870: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV274 )
| ( c_Series_Osums @ SY1870 @ ( c_Series_Osuminf @ SY1870 @ SV274 ) @ SV274 )
| ~ ( c_Series_Osummable @ SY1870 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1756,plain,
! [SV275: $i] :
( ( ! [SY1871: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV275 )
| ~ ( c_Series_Osummable @ SY1871 @ SV275 )
| ( c_Series_Osums @ SY1871 @ ( c_Series_Osuminf @ SY1871 @ SV275 ) @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1757,plain,
! [SV276: $i] :
( ( ! [SY1872: $i,SY1873: $i,SY1874: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV276 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1872 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SY1873 @ SY1874 @ SV276 @ SY1872 @ tc_nat ) @ SY1872 )
| ~ ( c_SEQ_OCauchy @ SY1874 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SY1873 @ SV276 @ SY1872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1758,plain,
! [SV277: $i] :
( ( ! [SY1875: $i,SY1876: $i,SY1877: $i] :
( ~ ( class_RealVector_Ometric__space @ SV277 )
| ~ ( class_RealVector_Ometric__space @ SY1875 )
| ( c_Lim_OisCont @ SY1876 @ SY1877 @ SV277 @ SY1875 )
| ~ ( c_Lim_OLIM @ SY1876 @ SY1877 @ ( hAPP @ SY1876 @ SY1877 ) @ SV277 @ SY1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1759,plain,
! [SV278: $i] :
( ( ! [SY1878: $i,SY1879: $i,SY1880: $i] :
( ~ ( class_RealVector_Ometric__space @ SV278 )
| ~ ( class_RealVector_Ometric__space @ SY1878 )
| ( c_Lim_OLIM @ SY1879 @ SY1880 @ ( hAPP @ SY1879 @ SY1880 ) @ SV278 @ SY1878 )
| ~ ( c_Lim_OisCont @ SY1879 @ SY1880 @ SV278 @ SY1878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1760,plain,
! [SV279: $i] :
( ( ! [SY1881: $i,SY1882: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV279 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SY1881 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SY1882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1761,plain,
! [SV280: $i] :
( ( ! [SY1883: $i,SY1884: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV280 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SY1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SY1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1762,plain,
! [SV281: $i] :
( ( ! [SY1885: $i,SY1886: $i,SY1887: $i,SY1888: $i,SY1889: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV281 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SY1885 ) @ SY1886 @ SV281 @ SV281 @ SY1887 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SY1885 ) @ SY1888 ) @ SY1889 @ SY1887 @ SV281 )
| ~ ( c_Limits_Otendsto @ SY1886 @ SY1888 @ SY1889 @ SY1887 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1763,plain,
! [SV282: $i] :
( ( ! [SY1890: $i,SY1891: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV282 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV282 ) @ SY1890 ) @ SY1891 @ SV282 @ SV282 @ tc_nat ) @ SV282 )
| ~ ( c_SEQ_OCauchy @ SY1891 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1764,plain,
! [SV283: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV283 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV283 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV283 ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV283 ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) )
= ( c_HOL_Ozero__class_Ozero @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1765,plain,
! [SV284: $i] :
( ( ! [SY1892: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ SV284 @ SY1892 ) )
= SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1766,plain,
! [SV285: $i] :
( ( ! [SY1893: $i,SY1894: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV285 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV285 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SY1893 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SY1894 ) @ SV285 )
| ~ ( c_Series_Osums @ SY1893 @ SY1894 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1767,plain,
! [SV286: $i] :
( ( ! [SY1895: $i,SY1896: $i,SY1897: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV286 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1895 )
| ( ( hAPP @ SY1896 @ ( c_Series_Osuminf @ SY1897 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SY1896 @ SY1897 @ SV286 @ SY1895 @ tc_nat ) @ SY1895 ) )
| ~ ( c_Series_Osummable @ SY1897 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SY1896 @ SV286 @ SY1895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1768,plain,
! [SV287: $i] :
( ( ! [SY1898: $i,SY1899: $i,SY1900: $i] :
( ~ ( class_RealVector_Ometric__space @ SV287 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1898 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SY1898 ) @ SY1899 @ SY1898 @ tc_RealDef_Oreal @ SV287 ) @ SY1900 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SY1899 @ SY1900 @ SV287 @ SY1898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1769,plain,
! [SV288: $i] :
( ( ! [SY1901: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV288 )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV288 ) @ SY1901 ) @ SV288 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1770,plain,
! [SV289: $i] :
( ( ! [SY1902: $i,SY1903: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV289 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ SY1902 ) @ SY1903 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SY1903 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SY1902 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1771,plain,
! [SV290: $i] :
( ( ! [SY1904: $i,SY1905: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV290 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ SY1904 ) @ SY1905 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SY1904 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SY1905 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1772,plain,
! [SV291: $i] :
( ( c_Lim_OLIM @ c_Complex_OIm @ SV291 @ ( hAPP @ c_Complex_OIm @ SV291 ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1773,plain,
! [SV292: $i] :
( ( ! [SY1906: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ SV292 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SY1906 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV292 @ SY1906 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1774,plain,
! [SV293: $i] :
( ( ! [SY1907: $i,SY1908: $i,SY1909: $i,SY1910: $i,SY1911: $i] :
( ( c_Set_Oimage @ SV293 @ ( c_Set_Oimage @ SY1907 @ SY1908 @ SY1909 @ SY1910 ) @ SY1910 @ SY1911 )
= ( c_Set_Oimage @ ( c_COMBB @ SV293 @ SY1907 @ SY1910 @ SY1911 @ SY1909 ) @ SY1908 @ SY1909 @ SY1911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1775,plain,
! [SV294: $i] :
( ( ! [SY1912: $i,SY1913: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV294 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SY1912 @ SV294 @ SV294 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SY1913 ) @ SV294 )
| ~ ( c_SEQ_OLIMSEQ @ SY1912 @ SY1913 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1776,plain,
! [SV295: $i] :
( ( ! [SY1914: $i,SY1915: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV295 )
| ( c_SEQ_OLIMSEQ @ SY1914 @ SY1915 @ SV295 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SY1914 @ SV295 @ SV295 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SY1915 ) @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1777,plain,
! [SV296: $i] :
( ( v_thesis____
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ SV296 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1778,plain,
! [SV297: $i] :
( ( ! [SY1916: $i,SY1917: $i] :
( ~ ( class_RealVector_Ometric__space @ SV297 )
| ( c_SEQ_Oconvergent @ SY1916 @ SV297 )
| ~ ( c_SEQ_OLIMSEQ @ SY1916 @ SY1917 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1779,plain,
! [SV298: $i] :
( ( ! [SY1918: $i,SY1919: $i] :
( ~ ( class_RealVector_Ometric__space @ SV298 )
| ( c_SEQ_Oconvergent @ SY1918 @ SV298 )
| ~ ( c_SEQ_OLIMSEQ @ SY1918 @ SY1919 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1780,plain,
! [SV299: $i] :
( ( ! [SY1920: $i,SY1921: $i] :
( ~ ( class_RealVector_Ometric__space @ SV299 )
| ( SY1920 = SY1921 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SY1920 @ SV299 @ tc_nat ) @ SY1921 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1781,plain,
! [SV300: $i] :
( ( ! [SY1922: $i,SY1923: $i,SY1924: $i,SY1925: $i,SY1926: $i,SY1927: $i] :
( ~ ( class_RealVector_Ometric__space @ SV300 )
| ~ ( class_RealVector_Ometric__space @ SY1922 )
| ~ ( class_RealVector_Ometric__space @ SY1923 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY1924 @ SY1925 @ SV300 @ SY1922 @ SY1923 ) @ SY1926 @ ( hAPP @ SY1924 @ SY1927 ) @ SY1923 @ SY1922 )
| ~ ( c_Lim_OLIM @ SY1925 @ SY1926 @ SY1927 @ SY1923 @ SV300 )
| ~ ( c_Lim_OLIM @ SY1924 @ SY1927 @ ( hAPP @ SY1924 @ SY1927 ) @ SV300 @ SY1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1782,plain,
! [SV301: $i] :
( ( ! [SY1928: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV301 )
| ( c_SEQ_OLIMSEQ @ SY1928 @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV301 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV301 ) @ SY1928 @ SV301 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1783,plain,
! [SV302: $i] :
( ( ! [SY1929: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV302 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV302 ) @ SY1929 @ SV302 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SY1929 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1784,plain,
! [SV303: $i] :
( ( ! [SY1930: $i,SY1931: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV303 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SY1930 @ SV303 @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SY1931 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SY1930 @ SY1931 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1785,plain,
! [SV304: $i] :
( ( ! [SY1932: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ SV304 @ SY1932 ) )
= SY1932 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1786,plain,
! [SV305: $i] :
( ( ! [SY1933: $i,SY1934: $i,SY1935: $i] :
( ~ ( class_RealVector_Ometric__space @ SV305 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY1933 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1934 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SY1935 @ SV305 )
| ~ ( c_SEQ_OLIMSEQ @ SY1933 @ SY1935 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1787,plain,
! [SV306: $i] :
( ( ! [SY1936: $i,SY1937: $i,SY1938: $i] :
( ~ ( class_RealVector_Ometric__space @ SV306 )
| ( c_SEQ_OLIMSEQ @ SY1936 @ SY1937 @ SV306 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY1936 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1938 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SY1937 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1788,plain,
! [SV307: $i] :
( ( ! [SY1939: $i,SY1940: $i] :
( ~ ( class_RealVector_Ometric__space @ SV307 )
| ( ( c_SEQ_Olim @ SY1939 @ SV307 )
= SY1940 )
| ~ ( c_SEQ_OLIMSEQ @ SY1939 @ SY1940 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1789,plain,
! [SV308: $i] :
( ( ! [SY1941: $i,SY1942: $i,SY1943: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ SV308 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY1941 ) @ ( hAPP @ c_Complex_OIm @ SY1942 ) @ SY1943 @ SY1941 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV308 @ SY1942 @ SY1943 @ SY1941 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1790,plain,
! [SV309: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ SV309 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ SV309 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1791,plain,
! [SV310: $i] :
( ( ! [SY1944: $i] :
( ~ ( class_RealVector_Ometric__space @ SV310 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SY1944 @ SV310 @ tc_nat ) @ SY1944 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1792,plain,
! [SV311: $i] :
( ( ! [SY1945: $i] :
( ~ ( class_RealVector_Ometric__space @ SV311 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SY1945 @ SV311 @ tc_nat ) @ SY1945 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1793,plain,
! [SV312: $i] :
( ( ! [SY1946: $i,SY1947: $i,SY1948: $i,SY1949: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV312 )
| ~ ( class_RealVector_Oreal__normed__vector @ SY1946 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY1947 @ SY1948 @ SV312 @ SY1946 @ tc_nat ) @ ( hAPP @ SY1947 @ SY1949 ) @ SY1946 )
| ~ ( c_SEQ_OLIMSEQ @ SY1948 @ SY1949 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SY1947 @ SV312 @ SY1946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1794,plain,
! [SV313: $i] :
( ( ! [SY1950: $i,SY1951: $i,SY1952: $i,SY1953: $i,SY1954: $i] :
( ~ ( class_RealVector_Ometric__space @ SV313 )
| ~ ( class_RealVector_Ometric__space @ SY1950 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY1951 @ SY1952 @ SY1950 @ SV313 @ tc_nat ) @ SY1953 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SY1952 @ SY1954 @ SY1950 )
| ( ( hAPP @ SY1952 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SY1952 @ SY1954 @ SY1950 ) )
= SY1954 )
| ~ ( c_Lim_OLIM @ SY1951 @ SY1954 @ SY1953 @ SY1950 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1795,plain,
! [SV314: $i] :
( ( ! [SY1955: $i,SY1956: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ SV314 @ SY1955 @ SY1956 @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ SV314 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY1956 ) @ SY1955 @ SY1956 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1796,plain,
! [SV315: $i] :
( ( ! [SY1957: $i,SY1958: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV315 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV315 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SY1957 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SY1958 ) @ SV315 )
| ~ ( c_SEQ_OLIMSEQ @ SY1957 @ SY1958 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1797,plain,
! [SV316: $i] :
( ( ! [SY1959: $i] :
( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ SV316 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SY1959 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV316 @ SY1959 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1798,plain,
! [SV317: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ SV317 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OCauchy @ SV317 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1799,plain,
! [SV318: $i] :
( ( ! [SY1960: $i] :
( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ SV318 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SY1960 ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ SV318 @ SY1960 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1800,plain,
! [SV319: $i] :
( ( ! [SY1961: $i,SY1962: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ SV319 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY1961 ) @ SY1962 @ SY1961 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV319 @ SY1962 @ SY1961 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1801,plain,
! [SV320: $i] :
( ( ! [SY1963: $i,SY1964: $i,SY1965: $i,SY1966: $i,SY1967: $i] :
( ~ ( class_RealVector_Ometric__space @ SV320 )
| ~ ( class_RealVector_Ometric__space @ SY1963 )
| ~ ( class_RealVector_Ometric__space @ SY1964 )
| ( c_Lim_OisCont @ ( c_COMBB @ SY1965 @ SY1966 @ SY1964 @ SY1963 @ SV320 ) @ SY1967 @ SV320 @ SY1963 )
| ~ ( c_Lim_OisCont @ SY1965 @ ( hAPP @ SY1966 @ SY1967 ) @ SY1964 @ SY1963 )
| ~ ( c_Lim_OisCont @ SY1966 @ SY1967 @ SV320 @ SY1964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1802,plain,
! [SV321: $i] :
( ( ! [SY1968: $i,SY1969: $i,SY1970: $i] :
( ~ ( class_RealVector_Ometric__space @ SV321 )
| ( SY1968 = SY1969 )
| ~ ( c_SEQ_OLIMSEQ @ SY1970 @ SY1969 @ SV321 )
| ~ ( c_SEQ_OLIMSEQ @ SY1970 @ SY1968 @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1803,plain,
! [SV322: $i] :
( ( ! [SY1971: $i,SY1972: $i,SY1973: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV322 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SY1971 ) @ SY1972 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SY1971 ) @ SY1973 ) @ SV322 )
| ~ ( c_SEQ_OLIMSEQ @ SY1972 @ SY1973 @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1804,plain,
! [SV323: $i] :
( ( ! [SY1974: $i,SY1975: $i,SY1976: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV323 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ SY1974 @ SY1975 @ SV323 @ SV323 @ SV323 ) @ SY1976 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SY1975 @ SY1976 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SY1974 @ ( hAPP @ SY1975 @ SY1976 ) @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1805,plain,
! [SV324: $i] :
( ( ! [SY1977: $i,SY1978: $i,SY1979: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV324 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SY1977 ) @ SY1978 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SY1977 ) @ SY1979 ) @ SV324 )
| ~ ( c_SEQ_OLIMSEQ @ SY1978 @ SY1979 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1806,plain,
! [SV325: $i] :
( ( c_Lim_OisCont @ c_Complex_OIm @ SV325 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1807,plain,
! [SV326: $i] :
( ( ! [SY1980: $i,SY1981: $i] :
( ~ ( class_RealVector_Ometric__space @ SV326 )
| ( c_SEQ_OCauchy @ SY1980 @ SV326 )
| ~ ( c_SEQ_OLIMSEQ @ SY1980 @ SY1981 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1808,plain,
! [SV327: $i] :
( ( ! [SY1982: $i,SY1983: $i] :
( ~ ( class_RealVector_Ometric__space @ SV327 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY1982 @ c_Suc @ tc_nat @ SV327 @ tc_nat ) @ SY1983 @ SV327 )
| ~ ( c_SEQ_OLIMSEQ @ SY1982 @ SY1983 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1809,plain,
! [SV328: $i] :
( ( ! [SY1984: $i,SY1985: $i] :
( ~ ( class_RealVector_Ometric__space @ SV328 )
| ( c_SEQ_OLIMSEQ @ SY1984 @ SY1985 @ SV328 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY1984 @ c_Suc @ tc_nat @ SV328 @ tc_nat ) @ SY1985 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1810,plain,
! [SV329: $i] :
( ( ! [SY1986: $i,SY1987: $i,SY1988: $i,SY1989: $i,SY1990: $i] :
( ( hAPP @ ( c_COMBB @ SV329 @ SY1986 @ SY1987 @ SY1988 @ SY1989 ) @ SY1990 )
= ( hAPP @ SV329 @ ( hAPP @ SY1986 @ SY1990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1811,plain,
! [SV330: $i] :
( ( ! [SY1991: $i,SY1992: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV330 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SY1991 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SY1992 ) @ SV330 )
| ( SY1992
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ~ ( c_SEQ_OLIMSEQ @ SY1991 @ SY1992 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1812,plain,
! [SV331: $i] :
( ( ! [SY1993: $i,SY1994: $i,SY1995: $i] :
( ~ ( class_RealVector_Ometric__space @ SV331 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SY1993 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SY1994 @ ( hAPP @ c_Complex_OIm @ SY1995 ) @ SV331 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SY1993 @ SY1994 @ SY1995 @ SV331 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1813,plain,
! [SV332: $i] :
( ( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ SV332 @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ SV332 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
| ~ ( c_Series_Osummable @ SV332 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1814,plain,
! [SV333: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ SV333 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osummable @ SV333 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1815,plain,
! [SV334: $i] :
( ( ! [SY1996: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV334 @ SY1996 ) )
| ~ ( class_Lattices_Oboolean__algebra @ SY1996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1816,plain,
! [SV335: $i] :
( ( ! [SY1997: $i,SY1998: $i,SY1999: $i,SY2000: $i,SY2001: $i] :
( ( hAPP @ ( c_COMBC @ SV335 @ SY1997 @ SY1998 @ SY1999 @ SY2000 ) @ SY2001 )
= ( hAPP @ ( hAPP @ SV335 @ SY2001 ) @ SY1997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1817,plain,
! [SV336: $i] :
( ( ! [SY2002: $i,SY2003: $i,SY2004: $i,SY2005: $i,SY2006: $i] :
( ( hAPP @ ( c_COMBB @ SV336 @ SY2002 @ SY2003 @ SY2004 @ SY2005 ) @ SY2006 )
= ( hAPP @ SV336 @ ( hAPP @ SY2002 @ SY2006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1818,plain,
! [SV337: $i] :
( ( ! [SY2007: $i] : ( c_fequal @ SV337 @ SV337 @ SY2007 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1819,plain,
! [SV338: $i] :
( ( ! [SY2008: $i,SY2009: $i] :
( ( SV338 = SY2008 )
| ~ ( c_fequal @ SV338 @ SY2008 @ SY2009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1820,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1821,plain,
! [SV339: $i] :
( ( ! [SY2010: $i,SY2011: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV339 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SY2010 ) @ SY2010 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SY2011 ) @ SY2011 ) )
| ( SY2010
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SY2011 ) )
| ( SY2010 = SY2011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1822,plain,
! [SV340: $i] :
( ( ! [SY2012: $i,SY2013: $i,SY2014: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY2012 ) @ SY2013 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY2014 ) @ SY2013 ) )
| ( SY2012 = SY2014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1823,plain,
! [SV341: $i] :
( ( ( hAPP @ c_Suc @ SV341 )
!= SV341 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1824,plain,
! [SV342: $i] :
( ( ! [SY2015: $i,SY2016: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV342 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SY2015 ) @ SY2016 )
!= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SY2015
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SY2016
= ( c_HOL_Ozero__class_Ozero @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1825,plain,
! [SV343: $i] :
( ( ! [SY2017: $i,SY2018: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SY2017 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SY2018 ) )
| ( SY2017 = SY2018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1826,plain,
! [SV344: $i] :
( ( ! [SY2019: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ SV344 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV344 ) @ SY2019 )
!= ( c_HOL_Ozero__class_Ozero @ SV344 ) )
| ( SY2019
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1827,plain,
! [SV345: $i] :
( ( ! [SY2020: $i,SY2021: $i,SY2022: $i,SY2023: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV345 )
| ~ ( class_Int_Onumber__ring @ SV345 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2020 ) @ SY2021 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2022 ) @ SY2023 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2020 ) @ SY2023 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2022 ) @ SY2021 ) ) )
| ( SY2021 = SY2023 )
| ( SY2020 = SY2022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1828,plain,
! [SV346: $i] :
( ( ! [SY2024: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV346 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV346 ) @ SY2024 ) @ SY2024 )
!= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
| ( SY2024
= ( c_HOL_Ozero__class_Ozero @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1829,plain,
! [SV347: $i] :
( ( ! [SY2025: $i,SY2026: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV347 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SY2025 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SY2026 ) )
| ( SY2025 = SY2026 )
| ( SY2026
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SY2025
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1830,plain,
! [SV348: $i] :
( ( ! [SY2027: $i,SY2028: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV348 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ SY2027 ) @ SY2028 )
!= ( c_HOL_Ozero__class_Ozero @ SV348 ) )
| ( SY2027
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV348 ) @ SY2028 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1831,plain,
! [SV349: $i] :
( ( ! [SY2029: $i,SY2030: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV349 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SY2029 ) @ SY2029 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SY2030 ) @ SY2030 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
| ( SY2029
= ( c_HOL_Ozero__class_Ozero @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1832,plain,
! [SV350: $i] :
( ( ! [SY2031: $i,SY2032: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SY2031 ) @ SY2032 )
!= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SY2032
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SY2031
= ( c_HOL_Ozero__class_Ozero @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1833,plain,
! [SV351: $i] :
( ( ! [SY2033: $i,SY2034: $i,SY2035: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SV351 @ SY2033 )
!= ( c_Complex_Ocomplex_OComplex @ SY2034 @ SY2035 ) )
| ( SY2033 = SY2035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1834,plain,
! [SV352: $i] :
( ( ! [SY2036: $i,SY2037: $i,SY2038: $i,SY2039: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV352 )
| ~ ( class_Int_Onumber__ring @ SV352 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2036 ) @ SY2037 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2038 ) @ SY2039 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2036 ) @ SY2039 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2038 ) @ SY2037 ) ) )
| ( SY2037 = SY2039 )
| ( SY2036 = SY2038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1835,plain,
! [SV353: $i] :
( ( ! [SY2040: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV353 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV353 ) @ SY2040 )
!= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
| ( SY2040
= ( c_HOL_Ozero__class_Ozero @ SV353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1836,plain,
! [SV354: $i] :
( ( ! [SY2041: $i,SY2042: $i,SY2043: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV354 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SY2041 ) @ SY2042 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SY2041 ) @ SY2043 ) )
| ( SY2041
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SY2042 = SY2043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1837,plain,
! [SV355: $i] :
( ( ! [SY2044: $i,SY2045: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SY2044 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SY2045 ) )
| ( SY2044 = SY2045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1838,plain,
! [SV356: $i] :
( ( ! [SY2046: $i] :
( ( ( hAPP @ c_Suc @ SV356 )
!= ( hAPP @ c_Suc @ SY2046 ) )
| ( SV356 = SY2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1839,plain,
! [SV357: $i] :
( ( ! [SY2047: $i,SY2048: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV357 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SY2047 ) @ SY2048 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SY2048
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SY2047
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1840,plain,
! [SV358: $i] :
( ( ! [SY2049: $i,SY2050: $i,SY2051: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2049 ) @ SY2050 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SY2049 ) @ SY2051 ) )
| ( SY2050 = SY2051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1841,plain,
! [SV359: $i] :
( ( ! [SY2052: $i,SY2053: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV359 ) @ SY2052 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2053 ) @ SY2052 ) )
| ( SV359 = SY2053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1842,plain,
! [SV360: $i] :
( ( ! [SY2054: $i,SY2055: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV360 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SY2054 ) @ SY2055 )
!= ( c_HOL_Ozero__class_Ozero @ SV360 ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV360 ) @ SY2054 )
= SY2055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1843,plain,
! [SV361: $i] :
( ( ! [SY2056: $i,SY2057: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV361 )
| ~ ( class_Int_Onumber__ring @ SV361 )
| ( SY2056
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SY2056 ) @ SY2057 ) )
| ( SY2057
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1844,plain,
! [SV362: $i] :
( ( ! [SY2058: $i,SY2059: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV362 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SY2058 ) @ SY2059 )
!= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SY2059
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SY2058
= ( c_HOL_Ozero__class_Ozero @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1845,plain,
! [SV363: $i] :
( ( ! [SY2060: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV363 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV363 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SY2060 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( SY2060
= ( c_HOL_Ozero__class_Ozero @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1846,plain,
! [SV364: $i] :
( ( ! [SY2061: $i,SY2062: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV364 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SY2061 ) @ SY2061 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SY2062 ) @ SY2062 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
| ( SY2062
= ( c_HOL_Ozero__class_Ozero @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1847,plain,
! [SV365: $i] :
( ( ! [SY2063: $i,SY2064: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV365 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SY2063 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SY2064 ) )
| ( SY2063 = SY2064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1848,plain,
! [SV366: $i] :
( ( ! [SY2065: $i,SY2066: $i,SY2067: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV366 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SY2065 ) @ SY2066 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SY2067 ) @ SY2066 ) )
| ( SY2066
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SY2065 = SY2067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1849,plain,
! [SV367: $i] :
( ( ! [SY2068: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV367 )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV367 ) @ SY2068 )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SY2068
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1850,plain,
! [SV368: $i] :
( ( ! [SY2069: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV368 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV368 ) @ SY2069 )
!= SY2069 )
| ( SY2069
= ( c_HOL_Ozero__class_Ozero @ SV368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1851,plain,
! [SV369: $i] :
( ( ! [SY2070: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV369 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV369 ) @ SY2070 )
!= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
| ( SY2070
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1852,plain,
! [SV370: $i] :
( ( ! [SY2071: $i,SY2072: $i,SY2073: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SV370 @ SY2071 )
!= ( c_Complex_Ocomplex_OComplex @ SY2072 @ SY2073 ) )
| ( SV370 = SY2072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1853,plain,
! [SV371: $i] :
( ( ! [SY2074: $i] :
( ( ( hAPP @ c_Complex_OIm @ SV371 )
!= ( hAPP @ c_Complex_OIm @ SY2074 ) )
| ( ( hAPP @ c_Complex_ORe @ SV371 )
!= ( hAPP @ c_Complex_ORe @ SY2074 ) )
| ( SV371 = SY2074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1854,plain,
! [SV372: $i] :
( ( ! [SY2075: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV372 )
| ( ( c_HOL_Ozero__class_Ozero @ SV372 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV372 ) @ SY2075 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV372 )
= SY2075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1855,plain,
! [SV373: $i] :
( ( ! [SY2076: $i,SY2077: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV373 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SY2076 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SY2077 ) )
| ( SY2076 = SY2077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1856,plain,
! [SV374: $i] :
( ( ! [SY2078: $i,SY2079: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV374 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SY2078 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SY2079 ) )
| ( SY2078 = SY2079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1857,plain,
! [SV375: $i] :
( ( ! [SY2080: $i,SY2081: $i,SY2082: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV375 )
| ~ ( class_Int_Onumber__ring @ SV375 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SY2080 ) @ SY2081 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SY2080 ) @ SY2082 ) )
| ( SY2081 = SY2082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1858,plain,
! [SV376: $i] :
( ( ! [SY2083: $i,SY2084: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ SV376 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SY2083 )
!= ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SY2084 ) )
| ( SY2083 = SY2084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1859,plain,
! [SV377: $i] :
( ( ! [SY2085: $i,SY2086: $i,SY2087: $i,SY2088: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SY2085 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SY2086 ) @ SY2087 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SY2085 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SY2086 ) @ SY2088 ) ) )
| ( SY2087 = SY2088 )
| ( SY2086
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1860,plain,
! [SV378: $i] :
( ( SV378
!= ( hAPP @ c_Suc @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1861,plain,
! [SV379: $i] :
( ( ! [SY2089: $i,SY2090: $i,SY2091: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SY2089 ) @ SY2090 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SY2089 ) @ SY2091 ) )
| ( SY2090 = SY2091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1862,plain,
! [SV380: $i] :
( ( ! [SY2092: $i] :
( ( ( hAPP @ c_Suc @ SV380 )
!= ( hAPP @ c_Suc @ SY2092 ) )
| ( SV380 = SY2092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1863,plain,
! [SV381: $i] :
( ( ! [SY2093: $i,SY2094: $i,SY2095: $i,SY2096: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV381 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2094 ) @ SY2095 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2094 ) @ SY2096 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2093 ) @ SY2095 )
= SY2096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1864,plain,
! [SV382: $i] :
( ( ! [SY2097: $i,SY2098: $i,SY2099: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV382 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SY2097 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SY2098 ) @ SY2099 ) )
!= SY2098 )
| ( SY2097
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SY2099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1865,plain,
! [SV1: $i] :
( ( v_thesis____ = $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ SV1 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1866,plain,
! [SV383: $i,SV2: $i] :
( ( ! [SY2100: $i,SY2101: $i,SY2102: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV2 )
| ~ ( class_RealVector_Ometric__space @ SV383 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SY2100 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SY2101 @ SV383 @ SV2 @ SV2 ) @ SY2102 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SY2100 @ SY2102 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1867,plain,
! [SV384: $i,SV3: $i] :
( ( ! [SY2103: $i,SY2104: $i,SY2105: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV3 )
| ~ ( class_RealVector_Ometric__space @ SV384 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SY2103 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SY2104 @ SV384 @ SV3 @ SV3 ) @ SY2105 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SY2103 @ SY2105 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1868,plain,
! [SV385: $i,SV4: $i] :
( ( ! [SY2106: $i,SY2107: $i,SY2108: $i,SY2109: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV4 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SY2106 ) @ SY2107 @ SY2106 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SY2108 ) @ SY2107 ) @ SY2109 @ SY2106 @ SV4 )
| ~ ( c_Limits_Otendsto @ SV385 @ SY2108 @ SY2109 @ SY2106 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1869,plain,
! [SV386: $i,SV5: $i] :
( ( ! [SY2110: $i,SY2111: $i,SY2112: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV5 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SY2110 ) @ SY2111 @ SY2110 @ SV5 @ SV5 ) @ SY2112 @ SY2110 @ SV5 )
| ~ ( c_Limits_OZfun @ SV386 @ SY2112 @ SY2110 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1870,plain,
! [SV387: $i,SV6: $i] :
( ( ! [SY2113: $i,SY2114: $i,SY2115: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV6 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SY2113 ) @ SY2114 @ SY2113 @ SV6 @ SV6 ) @ SY2115 @ SY2113 @ SV6 )
| ~ ( c_Limits_OZfun @ SV387 @ SY2115 @ SY2113 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1871,plain,
! [SV388: $i,SV7: $i] :
( ( ! [SY2116: $i,SY2117: $i,SY2118: $i,SY2119: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV7 )
| ~ ( class_RealVector_Ometric__space @ SV388 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SY2116 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SY2117 @ SV388 @ SV7 @ SV7 ) @ SY2118 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SY2119 ) @ SY2117 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SY2116 @ SY2118 @ SY2119 @ SV388 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1872,plain,
! [SV389: $i,SV8: $i] :
( ( ! [SY2120: $i,SY2121: $i,SY2122: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV8 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ ( c_Finite__Set_Osetsum @ SV389 @ SY2120 @ SY2121 @ SV8 ) ) @ SY2122 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ SV389 @ SV8 @ ( tc_fun @ SV8 @ SV8 ) @ SY2121 ) @ SY2122 @ SY2121 @ SV8 @ SV8 ) @ SY2120 @ SY2121 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1873,plain,
! [SV390: $i,SV9: $i] :
( ( ! [SY2123: $i,SY2124: $i,SY2125: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ ( c_Finite__Set_Osetsum @ SV390 @ SY2123 @ SY2124 @ SV9 ) ) @ SY2125 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ SV390 @ SV9 @ ( tc_fun @ SV9 @ SV9 ) @ SY2124 ) @ SY2125 @ SY2124 @ SV9 @ SV9 ) @ SY2123 @ SY2124 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1874,plain,
! [SV391: $i,SV10: $i] :
( ( ! [SY2126: $i,SY2127: $i,SY2128: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ ( c_Finite__Set_Osetsum @ SV391 @ SY2126 @ SY2127 @ tc_RealDef_Oreal ) ) @ SY2128 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ SV391 @ tc_RealDef_Oreal @ ( tc_fun @ SV10 @ SV10 ) @ SY2127 ) @ SY2128 @ SY2127 @ SV10 @ SV10 ) @ SY2126 @ SY2127 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1875,plain,
! [SV392: $i,SV11: $i] :
( ( ! [SY2129: $i,SY2130: $i,SY2131: $i,SY2132: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV11 )
| ~ ( class_RealVector_Ometric__space @ SV392 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SY2129 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SY2130 @ SV392 @ SV11 @ SV11 ) @ SY2131 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SY2132 ) @ SY2130 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SY2129 @ SY2131 @ SY2132 @ SV392 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1876,plain,
! [SV393: $i,SV12: $i] :
( ( ! [SY2133: $i,SY2134: $i,SY2135: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV12 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SY2133 ) @ SY2134 @ SY2133 @ SV12 @ SV12 ) @ SY2135 @ SY2133 @ SV12 )
| ~ ( c_Limits_OZfun @ SV393 @ SY2135 @ SY2133 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1877,plain,
! [SV394: $i,SV13: $i] :
( ( ! [SY2136: $i,SY2137: $i,SY2138: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV13 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SY2136 ) @ SY2137 @ SY2136 @ SV13 @ SV13 ) @ SY2138 @ SY2136 @ SV13 )
| ~ ( c_Limits_OZfun @ SV394 @ SY2138 @ SY2136 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1878,plain,
! [SV395: $i,SV14: $i] :
( ( ! [SY2139: $i,SY2140: $i,SY2141: $i,SY2142: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV14 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SY2139 ) @ SY2140 @ SY2139 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SY2141 ) @ SY2140 ) @ SY2142 @ SY2139 @ SV14 )
| ~ ( c_Limits_Otendsto @ SV395 @ SY2141 @ SY2142 @ SY2139 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1879,plain,
! [SV396: $i,SV15: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV15 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV15 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SV396 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
| ~ ( c_SEQ_OCauchy @ SV396 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1880,plain,
! [SV397: $i,SV16: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV16 )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV16 ) @ SV397 ) @ SV16 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1881,plain,
! [SV398: $i,SV17: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV17 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV17 ) @ SV398 @ SV17 @ SV17 @ tc_nat ) @ SV17 )
| ~ ( c_SEQ_OZseq @ SV398 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1882,plain,
! [SV399: $i,SV18: $i] :
( ( ! [SY2143: $i,SY2144: $i,SY2145: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SY2143 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY2144 ) @ SY2145 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY2144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SY2143 ) ) @ SY2145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1883,plain,
! [SV400: $i,SV19: $i] :
( ( ! [SY2146: $i,SY2147: $i,SY2148: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ SY2146 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY2147 ) @ SY2148 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY2146 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY2147 ) @ SY2148 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1884,plain,
! [SV401: $i,SV20: $i] :
( ( ! [SY2149: $i,SY2150: $i,SY2151: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SY2149 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SY2150 ) @ SY2151 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SY2150 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SY2149 ) @ SY2151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1885,plain,
! [SV402: $i,SV21: $i] :
( ( ~ ( class_SEQ_Obanach @ SV21 )
| ( c_Series_Osummable @ SV402 @ SV21 )
| ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV21 ) @ SV402 @ SV21 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1886,plain,
! [SV22: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV22 ) )
= $true )
| ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV22 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1887,plain,
! [SV23: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV23 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV23 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV23 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1888,plain,
! [SV403: $i,SV24: $i] :
( ( ! [SY2152: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV24 )
| ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SY2152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SY2152 ) @ SV24 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1889,plain,
! [SV404: $i,SV25: $i] :
( ( ! [SY2153: $i,SY2154: $i] :
( ~ ( class_RealVector_Ometric__space @ SV25 )
| ~ ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SY2153 @ SV404 @ SV404 @ SV25 ) @ SY2154 @ SV25 @ SV404 )
| ( ( hAPP @ SY2153 @ SY2154 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SY2153 @ SY2154 @ SV25 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1890,plain,
! [SV405: $i,SV26: $i] :
( ( ! [SY2155: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV26 )
| ( c_Deriv_Odifferentiable @ ( c_COMBK @ SV405 @ SV26 @ SV26 ) @ SY2155 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1891,plain,
! [SV406: $i,SV27: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV27 )
| ( c_SEQ_OZseq @ SV406 @ SV27 )
| ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV27 ) @ SV406 @ SV27 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1892,plain,
! [SV407: $i,SV28: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV28 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV28 ) @ SV407 @ SV28 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ SV407 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1893,plain,
! [SV408: $i,SV29: $i] :
( ( ! [SY2156: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV29 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV29 ) @ SV408 ) @ SY2156 @ SV29 @ SV29 @ tc_nat ) @ SV29 )
| ~ ( c_SEQ_OCauchy @ SY2156 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1894,plain,
! [SV409: $i,SV30: $i] :
( ( ! [SY2157: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV30 )
| ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV30 ) @ SV409 ) @ SY2157 @ SV30 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1895,plain,
! [SV410: $i,SV31: $i] :
( ( ! [SY2158: $i,SY2159: $i,SY2160: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV31 )
| ~ ( class_RealVector_Ometric__space @ SV410 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SY2158 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SY2159 @ SV410 @ SV31 @ SV31 ) @ SY2160 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SY2158 @ SY2160 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1896,plain,
! [SV411: $i,SV32: $i] :
( ( ! [SY2161: $i,SY2162: $i,SY2163: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV32 )
| ~ ( class_RealVector_Ometric__space @ SV411 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SY2161 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SY2162 @ SV411 @ SV32 @ SV32 ) @ SY2163 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SY2161 @ SY2163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1897,plain,
! [SV412: $i,SV33: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV33 )
| ( SV412
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ~ ( c_SEQ_OZseq @ ( c_COMBK @ SV412 @ SV33 @ tc_nat ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1898,plain,
! [SV413: $i,SV34: $i] :
( ( ! [SY2164: $i,SY2165: $i,SY2166: $i,SY2167: $i] :
( ~ ( class_RealVector_Ometric__space @ SV34 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
| ( SY2164 = SY2165 )
| ~ ( c_Lim_OLIM @ SY2166 @ SY2167 @ SY2165 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SY2166 @ SY2167 @ SY2164 @ SV413 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1899,plain,
! [SV414: $i,SV35: $i] :
( ( ! [SY2168: $i,SY2169: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV35 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SV414 @ SV35 @ tc_RealDef_Oreal @ SY2168 ) @ SY2169 @ SY2168 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV414 @ SY2169 @ SY2168 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1900,plain,
! [SV415: $i,SV36: $i] :
( ( ! [SY2170: $i,SY2171: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV36 )
| ( c_Limits_OZfun @ SV415 @ SY2170 @ SY2171 @ SV36 )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SV415 @ SV36 @ tc_RealDef_Oreal @ SY2171 ) @ SY2170 @ SY2171 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1901,plain,
! [SV416: $i,SV37: $i] :
( ( ! [SY2172: $i,SY2173: $i] :
( ~ ( class_RealVector_Ometric__space @ SV37 )
| ~ ( class_RealVector_Ometric__space @ SV416 )
| ( c_Lim_OisCont @ ( c_COMBK @ SY2172 @ SV416 @ SV37 ) @ SY2173 @ SV37 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1902,plain,
! [SV417: $i,SV38: $i] :
( ( ! [SY2174: $i,SY2175: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV38 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SV417 @ SV38 @ SV38 @ SY2174 ) @ SY2175 @ SY2174 @ SV38 )
| ~ ( c_Limits_OZfun @ SV417 @ SY2175 @ SY2174 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1903,plain,
! [SV418: $i,SV39: $i] :
( ( ! [SY2176: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV39 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ SV418 ) @ SY2176 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ SV418 ) ) @ SY2176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1904,plain,
! [SV419: $i,SV40: $i] :
( ( ! [SY2177: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV40 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ SY2177 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ SY2177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1905,plain,
! [SV420: $i,SV41: $i] :
( ( ! [SY2178: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV41 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV420 )
| ( c_Lim_OisUCont @ SY2178 @ SV41 @ SV420 )
| ~ ( c_RealVector_Obounded__linear @ SY2178 @ SV41 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1906,plain,
! [SV421: $i,SV42: $i] :
( ( ! [SY2179: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV42 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV42 ) @ SV421 ) @ SY2179 @ SV42 @ SV42 @ tc_nat ) @ SV42 )
| ~ ( c_SEQ_OZseq @ SY2179 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1907,plain,
! [SV422: $i,SV43: $i] :
( ( ! [SY2180: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV43 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV43 ) @ SV422 ) @ SY2180 @ SV43 @ SV43 @ tc_nat ) @ SV43 )
| ~ ( c_SEQ_OZseq @ SY2180 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1908,plain,
! [SV423: $i,SV44: $i] :
( ( ! [SY2181: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV44 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SY2181 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SY2181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1909,plain,
! [SV424: $i,SV45: $i] :
( ( ! [SY2182: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ SV45 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV424 ) @ SY2182 @ SV424 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV45 @ SY2182 @ SV424 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1910,plain,
! [SV46: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ SV46 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV46 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1911,plain,
! [SV425: $i,SV47: $i] :
( ( ! [SY2183: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV47 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV425 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV47 ) @ SV425 ) ) @ SY2183 ) )
= SY2183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1912,plain,
! [SV426: $i,SV48: $i] :
( ( ! [SY2184: $i,SY2185: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV48 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV48 )
| ~ ( class_RealVector_Ometric__space @ SV426 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SY2184 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SY2185 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SY2184 @ SY2185 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1913,plain,
! [SV427: $i,SV49: $i] :
( ( ! [SY2186: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV49 )
| ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SY2186 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SY2186 ) @ SV49 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1914,plain,
! [SV428: $i,SV50: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV50 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV50 ) @ SV428 ) @ SV428 )
= SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1915,plain,
! [SV429: $i,SV51: $i] :
( ( ! [SY2187: $i,SY2188: $i,SY2189: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV51 )
| ~ ( class_RealVector_Ometric__space @ SV429 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SY2187 ) @ SY2188 @ SV51 @ SV51 @ SV429 ) @ SY2189 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SY2188 @ SY2189 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1916,plain,
! [SV430: $i,SV52: $i] :
( ( ! [SY2190: $i,SY2191: $i,SY2192: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV52 )
| ~ ( class_RealVector_Ometric__space @ SV430 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SY2190 ) @ SY2191 @ SV52 @ SV52 @ SV430 ) @ SY2192 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SY2191 @ SY2192 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1917,plain,
! [SV431: $i,SV53: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV53 )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV53 ) @ SV431 ) @ SV53 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1918,plain,
! [SV54: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV54 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV54 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV54 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1919,plain,
! [SV55: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV55 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) )
= ( c_HOL_Ozero__class_Ozero @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1920,plain,
! [SV432: $i,SV56: $i] :
( ( ! [SY2193: $i,SY2194: $i,SY2195: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV56 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SY2193 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SY2194 ) @ SY2195 @ SY2193 @ SV56 )
| ~ ( c_Limits_Otendsto @ SV432 @ SY2194 @ SY2195 @ SY2193 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1921,plain,
! [SV433: $i,SV57: $i] :
( ( ! [SY2196: $i,SY2197: $i,SY2198: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV57 )
| ( c_Limits_Otendsto @ SV433 @ SY2196 @ SY2197 @ SY2198 @ SV57 )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SY2198 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SY2196 ) @ SY2197 @ SY2198 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1922,plain,
! [SV434: $i,SV58: $i] :
( ( ! [SY2199: $i,SY2200: $i,SY2201: $i,SY2202: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV58 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV434 )
| ~ ( class_RealVector_Ometric__space @ SY2199 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2200 @ SY2201 @ SV434 @ SV58 @ SY2199 ) @ SY2202 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SY2199 @ SV58 )
| ~ ( c_Lim_OLIM @ SY2201 @ SY2202 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SY2199 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SY2200 @ SV434 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1923,plain,
! [SV435: $i,SV59: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV59 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ SV435 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ SV435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1924,plain,
! [SV436: $i,SV61: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV61 )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV61 ) @ SV436 @ SV61 @ SV61 @ tc_nat ) @ SV61 )
| ~ ( c_Series_Osummable @ SV436 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1925,plain,
! [SV437: $i,SV62: $i] :
( ( ! [SY2203: $i,SY2204: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV62 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ SY2203 ) ) @ SY2204 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SY2203 ) @ SY2204 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1926,plain,
! [SV438: $i,SV63: $i] :
( ( ! [SY2205: $i,SY2206: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SY2205 ) ) @ SY2206 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SY2206 ) ) @ SY2205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1927,plain,
! [SV439: $i,SV64: $i] :
( ( ! [SY2207: $i,SY2208: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV64 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ SY2207 ) ) @ SY2208 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SY2207 ) @ SY2208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1928,plain,
! [SV440: $i,SV65: $i] :
( ( ! [SY2209: $i,SY2210: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SY2209 ) @ SY2210 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ SY2209 ) ) @ SY2210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1929,plain,
! [SV441: $i,SV66: $i] :
( ( ! [SY2211: $i,SY2212: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SY2211 ) @ SY2212 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SY2211 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ SY2212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1930,plain,
! [SV442: $i,SV67: $i] :
( ( ! [SY2213: $i,SY2214: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SY2213 ) @ SY2214 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ SY2213 ) ) @ SY2214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1931,plain,
! [SV443: $i,SV68: $i] :
( ( ! [SY2215: $i,SY2216: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV443 ) @ SY2215 ) ) @ SY2216 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV443 ) @ SY2216 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SY2215 ) @ SY2216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1932,plain,
! [SV444: $i,SV69: $i] :
( ( ! [SY2217: $i,SY2218: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY2217 ) @ SY2218 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SY2217 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SY2218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1933,plain,
! [SV445: $i,SV70: $i] :
( ( ! [SY2219: $i,SY2220: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV70 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SY2219 ) @ SY2220 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SY2219 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SY2220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1934,plain,
! [SV446: $i,SV71: $i] :
( ( ! [SY2221: $i,SY2222: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV71 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV446 ) @ SY2221 ) ) @ SY2222 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV446 ) @ SY2222 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SY2221 ) @ SY2222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1935,plain,
! [SV447: $i,SV72: $i] :
( ( ! [SY2223: $i,SY2224: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV72 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV447 ) @ SY2223 ) ) @ SY2224 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV447 ) @ SY2224 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SY2223 ) @ SY2224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1936,plain,
! [SV448: $i,SV73: $i] :
( ( ! [SY2225: $i,SY2226: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV73 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY2225 ) @ SY2226 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SY2225 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SY2226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1937,plain,
! [SV449: $i,SV74: $i] :
( ( ! [SY2227: $i,SY2228: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV74 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV449 ) @ SY2227 ) ) @ SY2228 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV449 ) @ SY2228 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SY2227 ) @ SY2228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1938,plain,
! [SV450: $i,SV75: $i] :
( ( ! [SY2229: $i,SY2230: $i] :
( ~ ( class_RealVector_Ometric__space @ SV75 )
| ~ ( class_HOL_Ozero @ SV75 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SY2229 @ SV75 @ SV450 ) @ SY2230 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SY2229
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1939,plain,
! [SV451: $i,SV76: $i] :
( ( ! [SY2231: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV76 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ ( c_Series_Osuminf @ SY2231 @ SV76 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ SY2231 @ SV76 @ SV76 @ tc_nat ) @ SV76 ) )
| ~ ( c_Series_Osummable @ SY2231 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1940,plain,
! [SV452: $i,SV77: $i] :
( ( ! [SY2232: $i,SY2233: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV77 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV452 ) @ SY2232 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SY2233 ) @ SY2232 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV452 ) @ SY2233 ) ) @ SY2232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1941,plain,
! [SV453: $i,SV78: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV78 )
| ( c_RealVector_Obounded__linear @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV78 ) @ SV453 @ SV78 @ SV78 @ SV78 ) @ SV78 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1942,plain,
! [SV454: $i,SV79: $i] :
( ( ! [SY2234: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV79 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ SV454 ) ) @ SY2234 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ SV454 ) @ SY2234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1943,plain,
! [SV455: $i,SV80: $i] :
( ( ! [SY2235: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV80 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ SV455 ) ) @ SY2235 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ SV455 ) @ SY2235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1944,plain,
! [SV456: $i,SV81: $i] :
( ( ! [SY2236: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ SY2236 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ SY2236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1945,plain,
! [SV457: $i,SV82: $i] :
( ( ! [SY2237: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ SY2237 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ SY2237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1946,plain,
! [SV458: $i,SV83: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV83 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SV458 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SV458 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ SV458 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1947,plain,
! [SV459: $i,SV84: $i] :
( ( ! [SY2238: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV84 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SV459 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SY2238 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ SV459 ) @ SY2238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1948,plain,
! [SV460: $i,SV85: $i] :
( ( ! [SY2239: $i,SY2240: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV85 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV85 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SY2239 ) @ SY2240 @ SY2239 @ SV85 )
| ~ ( c_Limits_OZfun @ SV460 @ SY2240 @ SY2239 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1949,plain,
! [SV461: $i,SV86: $i] :
( ( ! [SY2241: $i,SY2242: $i,SY2243: $i,SY2244: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV86 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SY2241 @ SV86 @ SV86 @ SY2242 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SY2243 ) @ SY2244 @ SY2242 @ SV86 )
| ~ ( c_Limits_Otendsto @ SY2241 @ SY2243 @ SY2244 @ SY2242 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1950,plain,
! [SV462: $i,SV87: $i] :
( ( ! [SY2245: $i,SY2246: $i,SY2247: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV87 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SY2245 @ SV87 @ SV87 @ SY2246 ) @ SY2247 @ SY2246 @ SV87 )
| ~ ( c_Limits_OZfun @ SY2245 @ SY2247 @ SY2246 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1951,plain,
! [SV463: $i,SV88: $i] :
( ( ! [SY2248: $i,SY2249: $i,SY2250: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV88 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SY2248 @ SV88 @ SV88 @ SY2249 ) @ SY2250 @ SY2249 @ SV88 )
| ~ ( c_Limits_OZfun @ SY2248 @ SY2250 @ SY2249 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1952,plain,
! [SV464: $i,SV89: $i] :
( ( ! [SY2251: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV89 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SY2251 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV464 ) @ SY2251 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SY2251 ) ) )
| ( SY2251
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
| ( SV464
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1953,plain,
! [SV465: $i,SV90: $i] :
( ( ! [SY2252: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SY2252 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV465 ) @ SY2252 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SY2252 ) ) )
| ( SY2252
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1954,plain,
! [SV91: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ SV91 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV91 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1955,plain,
! [SV466: $i,SV92: $i] :
( ( ! [SY2253: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ ( c_Series_Osuminf @ SY2253 @ SV92 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ SY2253 @ SV92 @ SV92 @ tc_nat ) @ SV92 ) )
| ~ ( c_Series_Osummable @ SY2253 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1956,plain,
! [SV467: $i,SV93: $i] :
( ( ! [SY2254: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV93 )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ SY2254 @ SV93 @ SV93 @ tc_nat ) @ SV93 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ ( c_Series_Osuminf @ SY2254 @ SV93 ) ) )
| ~ ( c_Series_Osummable @ SY2254 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1957,plain,
! [SV94: $i] :
( ( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ SV94 @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ SV94 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV94 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1958,plain,
! [SV468: $i,SV95: $i] :
( ( ! [SY2255: $i,SY2256: $i,SY2257: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV95 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SY2255 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY2256 ) @ SY2257 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SY2256 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY2255 ) @ SY2257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1959,plain,
! [SV469: $i,SV96: $i] :
( ( ! [SY2258: $i,SY2259: $i,SY2260: $i,SY2261: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV96 )
| ~ ( class_RealVector_Ometric__space @ SV469 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SY2258 ) @ SY2259 @ SV96 @ SV96 @ SV469 ) @ SY2260 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SY2258 ) @ SY2261 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SY2259 @ SY2260 @ SY2261 @ SV469 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1960,plain,
! [SV470: $i,SV97: $i] :
( ( ! [SY2262: $i,SY2263: $i] :
( ~ ( class_RealVector_Ometric__space @ SV97 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SV470 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SY2262 @ ( hAPP @ c_Complex_ORe @ SY2263 ) @ SV97 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV470 @ SY2262 @ SY2263 @ SV97 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1961,plain,
! [SV471: $i,SV98: $i] :
( ( ! [SY2264: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV98 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV98 ) @ SV471 @ SV98 @ SV98 @ SV98 ) @ SY2264 @ SV98 )
| ~ ( c_Deriv_Odifferentiable @ SV471 @ SY2264 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1962,plain,
! [SV472: $i,SV99: $i] :
( ( ! [SY2265: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV99 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV99 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ SV472 ) @ SY2265 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV472 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SY2265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1963,plain,
! [SV473: $i,SV100: $i] :
( ( ! [SY2266: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV100 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ SV473 ) @ SY2266 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SY2266 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV473 ) ) )
| ( SY2266
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1964,plain,
! [SV474: $i,SV101: $i] :
( ( ! [SY2267: $i,SY2268: $i,SY2269: $i] :
( ~ ( class_RealVector_Ometric__space @ SV101 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SY2267 @ SV101 @ SV474 ) @ SY2268 @ SY2269 @ SV474 @ SV101 )
| ( SY2267 = SY2269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1965,plain,
! [SV475: $i,SV102: $i] :
( ( ! [SY2270: $i,SY2271: $i,SY2272: $i] :
( ~ ( class_RealVector_Ometric__space @ SV102 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
| ( SY2270 = SY2271 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SY2270 @ SV102 @ SV475 ) @ SY2272 @ SY2271 @ SV475 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1966,plain,
! [SV476: $i,SV103: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV103 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ SV476 ) )
= SV476 )
| ( SV476
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1967,plain,
! [SV477: $i,SV104: $i] :
( ( ! [SY2273: $i,SY2274: $i,SY2275: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV104 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ ( c_Finite__Set_Osetsum @ SY2273 @ SY2274 @ SY2275 @ SV104 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ SY2273 @ SV104 @ SV104 @ SY2275 ) @ SY2274 @ SY2275 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1968,plain,
! [SV478: $i,SV105: $i] :
( ( ! [SY2276: $i,SY2277: $i,SY2278: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ ( c_Finite__Set_Osetsum @ SY2276 @ SY2277 @ SY2278 @ SV105 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ SY2276 @ SV105 @ SV105 @ SY2278 ) @ SY2277 @ SY2278 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1969,plain,
! [SV479: $i,SV106: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ SV106 ) ) @ SV479 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV106 ) @ ( hAPP @ c_Suc @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1970,plain,
! [SV480: $i,SV107: $i] :
( ( ! [SY2279: $i,SY2280: $i,SY2281: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
| ~ ( class_RealVector_Ometric__space @ SV480 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SY2279 @ SV107 @ SV107 @ SV480 ) @ SY2280 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SY2281 ) @ SV480 @ SV107 )
| ( SY2281
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SY2279 @ SY2280 @ SY2281 @ SV480 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1971,plain,
! [SV481: $i,SV108: $i] :
( ( ! [SY2282: $i,SY2283: $i] :
( ~ ( class_RealVector_Ometric__space @ SV108 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV481 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SY2282 @ SV481 @ SV481 @ SV108 ) @ SY2283 @ SV108 @ SV481 )
| ~ ( c_Lim_OisCont @ SY2282 @ SY2283 @ SV108 @ SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1972,plain,
! [SV482: $i,SV109: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV109 )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ SV482 @ SV109 @ SV109 @ tc_nat ) @ SV109 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ ( c_Series_Osuminf @ SV482 @ SV109 ) ) )
| ~ ( c_Series_Osummable @ SV482 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1973,plain,
! [SV483: $i,SV110: $i] :
( ( ! [SY2284: $i,SY2285: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ SY2284 ) ) @ SY2285 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ SY2284 ) @ SY2285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1974,plain,
! [SV484: $i,SV111: $i] :
( ( ! [SY2286: $i,SY2287: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ SY2286 ) ) @ SY2287 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ SY2286 ) @ SY2287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1975,plain,
! [SV485: $i,SV112: $i] :
( ( ! [SY2288: $i,SY2289: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SY2288 ) @ SY2289 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SY2288 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ SY2289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1976,plain,
! [SV113: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV113 ) )
= $true )
| ( ( c_Series_Osummable @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 @ tc_nat ) @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1977,plain,
! [SV486: $i,SV114: $i] :
( ( ! [SY2290: $i,SY2291: $i,SY2292: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV114 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV114 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SY2290 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SY2291 ) @ SY2292 @ SY2290 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SY2291 @ SY2292 @ SY2290 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1978,plain,
! [SV115: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV115 ) )
= $true )
| ( ( c_Series_Osums @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1979,plain,
! [SV487: $i,SV116: $i] :
( ( ! [SY2293: $i,SY2294: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV116 )
| ~ ( class_RealVector_Ometric__space @ SV487 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2293 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY2294 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SY2293 @ SY2294 ) @ SV116 @ SV487 )
| ~ ( c_Lim_OisCont @ SY2293 @ SY2294 @ SV116 @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1980,plain,
! [SV488: $i,SV117: $i] :
( ( ! [SY2295: $i,SY2296: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV117 )
| ~ ( class_RealVector_Ometric__space @ SV488 )
| ( c_Lim_OisCont @ SY2295 @ SY2296 @ SV117 @ SV488 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SY2295 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY2296 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SY2295 @ SY2296 ) @ SV117 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1981,plain,
! [SV489: $i,SV118: $i] :
( ( ! [SY2297: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV118 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SV489 @ SV118 @ SV118 @ SV118 ) @ SY2297 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SY2297 ) @ SV489 ) @ SV118 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1982,plain,
! [SV490: $i,SV119: $i] :
( ( ! [SY2298: $i,SY2299: $i] :
( ~ ( class_RealVector_Ometric__space @ SV119 )
| ~ ( class_RealVector_Ometric__space @ SV490 )
| ( c_Lim_OisCont @ SY2298 @ SY2299 @ SV119 @ SV490 )
| ~ ( c_Lim_OisUCont @ SY2298 @ SV119 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1983,plain,
! [SV491: $i,SV120: $i] :
( ( ! [SY2300: $i,SY2301: $i,SY2302: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV120 )
| ~ ( class_RealVector_Ometric__space @ SV491 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SY2300 ) @ SY2301 @ SV120 @ SV120 @ SV491 ) @ SY2302 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SY2301 @ SY2302 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1984,plain,
! [SV492: $i,SV121: $i] :
( ( ! [SY2303: $i,SY2304: $i,SY2305: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV121 )
| ~ ( class_RealVector_Ometric__space @ SV492 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SY2303 ) @ SY2304 @ SV121 @ SV121 @ SV492 ) @ SY2305 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SY2304 @ SY2305 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1985,plain,
! [SV493: $i,SV122: $i] :
( ( ! [SY2306: $i,SY2307: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV122 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SY2306 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SY2307 ) @ SV122 )
| ~ ( c_Series_Osums @ SY2306 @ SY2307 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1986,plain,
! [SV494: $i,SV124: $i] :
( ( ! [SY2308: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV124 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV124 ) @ SV494 ) @ SY2308 @ SV124 @ SV124 @ tc_nat ) @ SV124 )
| ~ ( c_Series_Osummable @ SY2308 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1987,plain,
! [SV495: $i,SV125: $i] :
( ( ! [SY2309: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV125 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ SY2309 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ SY2309 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1988,plain,
! [SV496: $i,SV126: $i] :
( ( ! [SY2310: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV126 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ SY2310 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ SY2310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1989,plain,
! [SV497: $i,SV127: $i] :
( ( ! [SY2311: $i,SY2312: $i,SY2313: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV127 )
| ~ ( class_RealVector_Ometric__space @ SV497 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SY2311 @ SV127 @ SV127 @ SV497 ) @ SY2312 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SY2313 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SY2311 @ SY2312 @ SY2313 @ SV497 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1990,plain,
! [SV128: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV128 ) )
= $true )
| ( ( ( c_Series_Osuminf @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ tc_nat ) @ SV128 )
= ( c_HOL_Ozero__class_Ozero @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1991,plain,
! [SV498: $i,SV129: $i] :
( ( ! [SY2314: $i,SY2315: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV129 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV498 )
| ( c_SEQ_OZseq @ ( c_COMBB @ SY2314 @ SY2315 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
| ~ ( c_SEQ_OZseq @ SY2315 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SY2314 @ SV129 @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1992,plain,
! [SV499: $i,SV130: $i] :
( ( ! [SY2316: $i,SY2317: $i,SY2318: $i,SY2319: $i,SY2320: $i] :
( ~ ( class_RealVector_Ometric__space @ SV130 )
| ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SY2316 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2317 @ SY2318 @ SV130 @ SV499 @ SY2316 ) @ SY2319 @ ( hAPP @ SY2317 @ SY2320 ) @ SY2316 @ SV499 )
| ~ ( c_Lim_OLIM @ SY2318 @ SY2319 @ SY2320 @ SY2316 @ SV130 )
| ~ ( c_Lim_OisCont @ SY2317 @ SY2320 @ SV130 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1993,plain,
! [SV500: $i,SV131: $i] :
( ( ! [SY2321: $i,SY2322: $i,SY2323: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV131 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV131 )
| ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SY2321 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SY2322 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SY2323 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SY2321 @ SY2322 @ SY2323 @ SV500 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1994,plain,
! [SV501: $i,SV132: $i] :
( ( ! [SY2324: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ SV132 @ SV501 @ SY2324 @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ SV132 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY2324 ) @ SV501 @ SY2324 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1995,plain,
! [SV502: $i,SV133: $i] :
( ( ! [SY2325: $i,SY2326: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV133 )
| ~ ( class_Int_Onumber__ring @ SV133 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SY2325 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SY2326 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SY2326 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SY2325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1996,plain,
! [SV503: $i,SV134: $i] :
( ( ! [SY2327: $i,SY2328: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV134 )
| ~ ( class_Int_Onumber__ring @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SY2327 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SY2328 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SY2328 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SY2327 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1997,plain,
! [SV504: $i,SV135: $i] :
( ( ! [SY2329: $i,SY2330: $i,SY2331: $i,SY2332: $i,SY2333: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV135 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SY2329 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2330 @ SY2331 @ SV135 @ SV504 @ SY2329 ) @ SY2332 @ ( hAPP @ SY2330 @ SY2333 ) @ SY2329 @ SV504 )
| ~ ( c_Lim_OLIM @ SY2331 @ SY2332 @ SY2333 @ SY2329 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SY2330 @ SV135 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1998,plain,
! [SV505: $i,SV136: $i] :
( ( ! [SY2334: $i,SY2335: $i,SY2336: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV136 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SY2334 @ SV136 @ SV136 @ SY2335 ) @ SY2336 @ SY2335 @ SV136 )
| ~ ( c_Limits_OZfun @ SY2334 @ SY2336 @ SY2335 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1999,plain,
! [SV506: $i,SV137: $i] :
( ( ! [SY2337: $i,SY2338: $i,SY2339: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV137 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SY2337 @ SV137 @ SV137 @ SY2338 ) @ SY2339 @ SY2338 @ SV137 )
| ~ ( c_Limits_OZfun @ SY2337 @ SY2339 @ SY2338 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2000,plain,
! [SV507: $i,SV138: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV138 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV138 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ SV507 ) )
= SV507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2001,plain,
! [SV508: $i,SV139: $i] :
( ( ! [SY2340: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV139 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SV508 @ SV139 @ SV139 @ SV139 ) @ SY2340 @ SV139 )
| ( ( hAPP @ SV508 @ SY2340 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
| ~ ( c_Deriv_Odifferentiable @ SV508 @ SY2340 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2002,plain,
! [SV509: $i,SV140: $i] :
( ( ! [SY2341: $i,SY2342: $i,SY2343: $i,SY2344: $i,SY2345: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV140 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SY2341 @ SY2342 @ SV509 @ SV140 @ SY2343 ) @ ( hAPP @ SY2341 @ SY2344 ) @ SY2345 @ SY2343 @ SV140 )
| ~ ( c_Limits_Otendsto @ SY2342 @ SY2344 @ SY2345 @ SY2343 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SY2341 @ SV509 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2003,plain,
! [SV510: $i,SV141: $i] :
( ( ! [SY2346: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV141 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SV510 ) @ SY2346 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SY2346 ) @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2004,plain,
! [SV142: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV142 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Ozero__class_Ozero @ SV142 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV142 ) )
= ( c_HOL_Ozero__class_Ozero @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(2005,plain,
! [SV511: $i,SV143: $i] :
( ( ! [SY2347: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SV511 ) @ SY2347 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SY2347 ) @ SV511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2006,plain,
! [SV512: $i,SV144: $i] :
( ( ! [SY2348: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV144 )
| ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV144 ) @ SV512 @ SV144 @ SV144 @ SV144 ) @ SY2348 @ SV144 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2007,plain,
! [SV513: $i,SV145: $i] :
( ( ! [SY2349: $i,SY2350: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV145 )
| ~ ( class_RealVector_Ometric__space @ SV513 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SY2349 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SY2350 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SY2349 @ SY2350 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2008,plain,
! [SV514: $i,SV146: $i] :
( ( ! [SY2351: $i,SY2352: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV146 )
| ~ ( class_RealVector_Ometric__space @ SV514 )
| ( c_Lim_OLIM @ SY2351 @ SY2352 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SY2351 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SY2352 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2009,plain,
! [SV515: $i,SV147: $i] :
( ( ! [SY2353: $i,SY2354: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY2353 ) @ SY2354 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY2353 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ SY2354 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2010,plain,
! [SV516: $i,SV148: $i] :
( ( ! [SY2355: $i,SY2356: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ SY2355 ) ) @ SY2356 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY2355 ) @ SY2356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2011,plain,
! [SV517: $i,SV149: $i] :
( ( ! [SY2357: $i,SY2358: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV149 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY2357 ) @ SY2358 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ SY2357 ) ) @ SY2358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2012,plain,
! [SV518: $i,SV150: $i] :
( ( ! [SY2359: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ SV518 ) ) @ SY2359 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV518 ) @ SY2359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2013,plain,
! [SV519: $i,SV151: $i] :
( ( ! [SY2360: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV151 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV519 ) @ SY2360 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV519 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV151 ) @ SY2360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2014,plain,
! [SV520: $i,SV152: $i] :
( ( ! [SY2361: $i,SY2362: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY2361 ) @ SY2362 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY2361 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ SY2362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2015,plain,
! [SV521: $i,SV153: $i] :
( ( ! [SY2363: $i,SY2364: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ SY2363 ) ) @ SY2364 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY2363 ) @ SY2364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2016,plain,
! [SV522: $i,SV154: $i] :
( ( ! [SY2365: $i,SY2366: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV154 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SY2365 ) @ SY2366 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ SY2365 ) ) @ SY2366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2017,plain,
! [SV523: $i,SV155: $i] :
( ( ! [SY2367: $i,SY2368: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV155 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SY2367 ) ) @ SY2368 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SY2368 ) ) @ SY2367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2018,plain,
! [SV524: $i,SV156: $i] :
( ( ! [SY2369: $i,SY2370: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY2369 ) @ SY2370 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY2369 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ SY2370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2019,plain,
! [SV525: $i,SV157: $i] :
( ( ! [SY2371: $i,SY2372: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SY2371 ) ) @ SY2372 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY2371 ) @ SY2372 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2020,plain,
! [SV526: $i,SV158: $i] :
( ( ! [SY2373: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV158 ) @ SV526 ) @ SY2373 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV158 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV158 ) @ SV526 ) ) @ SY2373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2021,plain,
! [SV527: $i,SV159: $i] :
( ( ! [SY2374: $i,SY2375: $i,SY2376: $i,SY2377: $i] :
( ( hAPP @ ( c_COMBC @ SV159 @ SV527 @ SY2374 @ SY2375 @ SY2376 ) @ SY2377 )
= ( hAPP @ ( hAPP @ SV159 @ SY2377 ) @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2022,plain,
! [SV528: $i,SV160: $i] :
( ( ! [SY2378: $i,SY2379: $i] :
( ( hAPP @ ( c_COMBK @ SV160 @ SV528 @ SY2378 ) @ SY2379 )
= SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2023,plain,
! [SV529: $i,SV161: $i] :
( ( ! [SY2380: $i,SY2381: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV161 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV529 )
| ( c_Series_Osummable @ ( c_COMBB @ SY2380 @ SY2381 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
| ~ ( c_Series_Osummable @ SY2381 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SY2380 @ SV161 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2024,plain,
! [SV530: $i,SV162: $i] :
( ( ! [SY2382: $i,SY2383: $i,SY2384: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SY2382 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SY2383 ) @ SY2384 @ SY2382 @ SV162 )
| ( SY2383
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SV530 @ SY2383 @ SY2384 @ SY2382 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2025,plain,
! [SV531: $i,SV163: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV163 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV163 ) @ SV531 ) @ ( c_HOL_Ozero__class_Ozero @ SV163 ) )
= ( c_HOL_Ozero__class_Ozero @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2026,plain,
! [SV532: $i,SV164: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV164 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV532 )
= ( c_HOL_Ozero__class_Ozero @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2027,plain,
! [SV533: $i,SV165: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV165 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV165 ) @ SV533 ) @ ( c_HOL_Ozero__class_Ozero @ SV165 ) )
= ( c_HOL_Ozero__class_Ozero @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2028,plain,
! [SV534: $i,SV166: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV166 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV166 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV534 )
= ( c_HOL_Ozero__class_Ozero @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2029,plain,
! [SV535: $i,SV167: $i] :
( ( ! [SY2385: $i,SY2386: $i,SY2387: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV167 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV535 ) @ SY2385 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SY2386 ) @ SY2385 ) ) @ SY2387 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ SV535 ) @ SY2386 ) ) @ SY2385 ) ) @ SY2387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2030,plain,
! [SV536: $i,SV168: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV168 )
| ( c_SEQ_OLIMSEQ @ SV536 @ ( c_SEQ_Olim @ SV536 @ SV168 ) @ SV168 )
| ~ ( c_SEQ_Oconvergent @ SV536 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2031,plain,
! [SV537: $i,SV169: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV169 )
| ( c_SEQ_Oconvergent @ SV537 @ SV169 )
| ~ ( c_SEQ_OLIMSEQ @ SV537 @ ( c_SEQ_Olim @ SV537 @ SV169 ) @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2032,plain,
! [SV538: $i,SV170: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV170 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV170 ) @ SV538 ) ) @ SV538 )
= ( c_HOL_Ozero__class_Ozero @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2033,plain,
! [SV539: $i,SV171: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV171 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV171 ) @ SV539 ) ) @ SV539 )
= ( c_HOL_Ozero__class_Ozero @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2034,plain,
! [SV540: $i,SV172: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV172 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV172 ) @ SV540 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV172 ) @ SV540 ) )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2035,plain,
! [SV541: $i,SV173: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV173 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV173 ) @ SV541 ) ) @ SV541 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2036,plain,
! [SV542: $i,SV174: $i] :
( ( ! [SY2388: $i,SY2389: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV174 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV542 )
| ( c_Lim_OisCont @ SY2388 @ SY2389 @ SV174 @ SV542 )
| ~ ( c_RealVector_Obounded__linear @ SY2388 @ SV174 @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2037,plain,
! [SV543: $i,SV175: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV175 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV175 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SV543 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SV543 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
| ~ ( c_Series_Osummable @ SV543 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2038,plain,
! [SV544: $i,SV176: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV176 )
| ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ SV544 @ SV176 @ SV176 @ tc_nat ) @ SV176 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ ( c_SEQ_Olim @ SV544 @ SV176 ) ) )
| ~ ( c_SEQ_Oconvergent @ SV544 @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2039,plain,
! [SV545: $i,SV177: $i] :
( ( ! [SY2390: $i,SY2391: $i,SY2392: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV177 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ ( c_Finite__Set_Osetsum @ SY2390 @ SY2391 @ SY2392 @ SV177 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ SY2390 @ SV177 @ SV177 @ SY2392 ) @ SY2391 @ SY2392 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2040,plain,
! [SV178: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ SV178 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV178 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(2041,plain,
! [SV546: $i,SV179: $i] :
( ( ! [SY2393: $i,SY2394: $i,SY2395: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV179 )
| ~ ( class_RealVector_Ometric__space @ SV546 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SY2393 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SY2394 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SY2395 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SY2393 @ SY2394 @ SY2395 @ SV546 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2042,plain,
! [SV547: $i,SV180: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV180 )
| ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV180 ) @ SV547 @ SV180 @ SV180 @ tc_nat ) @ SV180 )
| ~ ( c_SEQ_Oconvergent @ SV547 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2043,plain,
! [SV548: $i,SV181: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV181 )
| ( c_SEQ_Oconvergent @ SV548 @ SV181 )
| ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV181 ) @ SV548 @ SV181 @ SV181 @ tc_nat ) @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2044,plain,
! [SV549: $i,SV182: $i] :
( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV182 )
| ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 ) @ SV182 @ SV182 )
| ( SV549
= ( c_HOL_Ozero__class_Ozero @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2045,plain,
! [SV550: $i,SV183: $i] :
( ( ! [SY2396: $i,SY2397: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SY2396 ) @ SY2397 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SY2396 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SY2397 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2046,plain,
! [SV551: $i,SV184: $i] :
( ( ! [SY2398: $i,SY2399: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ SY2398 ) @ SY2399 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SY2398 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SY2399 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2047,plain,
! [SV552: $i,SV185: $i] :
( ( ! [SY2400: $i,SY2401: $i,SY2402: $i,SY2403: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV185 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV552 )
| ( c_Limits_OZfun @ ( c_COMBB @ SY2400 @ SY2401 @ SV552 @ SV185 @ SY2402 ) @ SY2403 @ SY2402 @ SV185 )
| ~ ( c_Limits_OZfun @ SY2401 @ SY2403 @ SY2402 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SY2400 @ SV552 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2048,plain,
! [SV553: $i,SV186: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 )
| ( c_Lim_OisUCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV186 ) @ SV553 @ SV186 @ SV186 @ SV186 ) @ SV186 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2049,plain,
! [SV187: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV187 ) )
= $true )
| ( ( c_SEQ_OZseq @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV187 @ tc_nat ) @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(2050,plain,
! [SV554: $i,SV188: $i] :
( ( ! [SY2404: $i,SY2405: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV188 )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ SV554 @ SV188 @ SV188 @ SY2404 ) @ SY2405 @ SY2404 @ SV188 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ ( c_Finite__Set_Osetsum @ SV554 @ SY2405 @ SY2404 @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2051,plain,
! [SV555: $i,SV189: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV189 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SV555 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2052,plain,
! [SV556: $i,SV190: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV190 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SV556 )
= SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2053,plain,
! [SV557: $i,SV191: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV191 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SV557 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2054,plain,
! [SV558: $i,SV192: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV192 )
| ~ ( class_Int_Onumber__ring @ SV192 )
| ( SV558
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV558 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2055,plain,
! [SV559: $i,SV193: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SV559 )
= SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2056,plain,
! [SV560: $i,SV194: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV194 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ ( c_HOL_Ozero__class_Ozero @ SV194 ) ) @ SV560 )
= SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2057,plain,
! [SV561: $i,SV195: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV195 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV195 ) @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) )
= SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2058,plain,
! [SV562: $i,SV196: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV196 ) @ ( c_HOL_Ozero__class_Ozero @ SV196 ) ) @ SV562 )
= SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2059,plain,
! [SV563: $i,SV197: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV197 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ SV563 ) )
= SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2060,plain,
! [SV564: $i,SV198: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV198 )
| ( SV564
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ SV564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2061,plain,
! [SV565: $i,SV199: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV199 )
| ( SV565
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ SV565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2062,plain,
! [SV566: $i,SV200: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV200 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ SV566 ) )
= SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2063,plain,
! [SV567: $i,SV201: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV201 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ SV567 ) )
= SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2064,plain,
! [SV568: $i,SV202: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV202 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV202 )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SV568 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
| ~ ( c_Series_Osummable @ SV568 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2065,plain,
! [SV569: $i,SV203: $i] :
( ( ! [SY2406: $i,SY2407: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV203 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SY2406 ) @ SY2407 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SY2406 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ SY2407 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2066,plain,
! [SV570: $i,SV204: $i] :
( ( ! [SY2408: $i,SY2409: $i] :
( ~ ( class_RealVector_Oreal__algebra @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ SY2408 ) ) @ SY2409 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ SY2408 ) @ SY2409 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2067,plain,
! [SV571: $i,SV205: $i] :
( ( ! [SY2410: $i,SY2411: $i] :
( ~ ( class_RealVector_Oreal__algebra @ SV205 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SY2410 ) @ SY2411 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SY2410 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ SY2411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2068,plain,
! [SV572: $i,SV206: $i] :
( ( ! [SY2412: $i,SY2413: $i] :
( ~ ( class_RealVector_Ometric__space @ SV206 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SY2412 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SY2413 @ SV206 @ SV572 )
| ~ ( c_Lim_OisCont @ SY2412 @ SY2413 @ SV206 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2069,plain,
! [SV573: $i,SV207: $i] :
( ( ! [SY2414: $i,SY2415: $i,SY2416: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV207 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV573 )
| ( ( hAPP @ SY2414 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SY2415 ) @ SY2416 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SY2415 ) @ ( hAPP @ SY2414 @ SY2416 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SY2414 @ SV207 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2070,plain,
! [SV574: $i,SV208: $i] :
( ( ! [SY2417: $i,SY2418: $i] :
( ~ ( class_RealVector_Ometric__space @ SV208 )
| ~ ( class_RealVector_Ometric__space @ SV574 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SY2417 @ SY2418 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
| ~ ( c_SEQ_OCauchy @ SY2418 @ SV208 )
| ~ ( c_Lim_OisUCont @ SY2417 @ SV208 @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2071,plain,
! [SV575: $i,SV209: $i] :
( ( ! [SY2419: $i,SY2420: $i,SY2421: $i] :
( ~ ( class_RealVector_Ometric__space @ SV209 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV575 )
| ( c_Lim_OLIM @ SY2419 @ SY2420 @ SY2421 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SY2419 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SY2420 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SY2421 @ SV575 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2072,plain,
! [SV576: $i,SV210: $i] :
( ( ! [SY2422: $i,SY2423: $i,SY2424: $i] :
( ~ ( class_RealVector_Ometric__space @ SV210 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV576 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2422 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SY2423 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SY2424 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SY2422 @ SY2423 @ SY2424 @ SV576 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2073,plain,
! [SV577: $i,SV211: $i] :
( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV211 )
| ~ ( class_RealVector_Ometric__space @ SV577 )
| ( c_Lim_OLIM @ SY2425 @ SY2426 @ ( hAPP @ SY2425 @ SY2426 ) @ SV211 @ SV577 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SY2425 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SY2426 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SY2425 @ SY2426 ) @ SV211 @ SV577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2074,plain,
! [SV578: $i,SV212: $i] :
( ( ! [SY2427: $i,SY2428: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV212 )
| ~ ( class_RealVector_Ometric__space @ SV578 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2427 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SY2428 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SY2427 @ SY2428 ) @ SV212 @ SV578 )
| ~ ( c_Lim_OLIM @ SY2427 @ SY2428 @ ( hAPP @ SY2427 @ SY2428 ) @ SV212 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2075,plain,
! [SV579: $i,SV213: $i] :
( ( ! [SY2429: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV213 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV213 ) @ SV579 ) @ SY2429 @ SV213 @ SV213 @ tc_nat ) @ SV213 )
| ~ ( c_Series_Osummable @ SY2429 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2076,plain,
! [SV580: $i,SV214: $i] :
( ( ! [SY2430: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV214 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV214 ) @ SV580 ) @ SY2430 @ SV214 @ SV214 @ tc_nat ) @ SV214 )
| ~ ( c_Series_Osummable @ SY2430 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2077,plain,
! [SV581: $i,SV215: $i] :
( ( ! [SY2431: $i,SY2432: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV215 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SY2431 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SY2432 ) @ SV215 )
| ~ ( c_Series_Osums @ SY2431 @ SY2432 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2078,plain,
! [SV582: $i,SV216: $i] :
( ( ! [SY2433: $i,SY2434: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SY2433 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SY2434 ) @ SV216 )
| ~ ( c_Series_Osums @ SY2433 @ SY2434 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2079,plain,
! [SV583: $i,SV217: $i] :
( ( ! [SY2435: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV217 )
| ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 @ SV583 ) @ SY2435 @ SV583 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2080,plain,
! [SV584: $i,SV218: $i] :
( ( ! [SY2436: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV218 )
| ( c_Series_Osummable @ SV584 @ SV218 )
| ~ ( c_Series_Osums @ SV584 @ SY2436 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2081,plain,
! [SV585: $i,SV219: $i] :
( ( ! [SY2437: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV219 )
| ( c_Series_Osummable @ SV585 @ SV219 )
| ~ ( c_Series_Osums @ SV585 @ SY2437 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2082,plain,
! [SV586: $i,SV220: $i] :
( ( ! [SY2438: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV220 )
| ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV220 ) @ SV586 ) @ SY2438 @ SV220 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2083,plain,
! [SV587: $i,SV221: $i] :
( ( ! [SY2439: $i,SY2440: $i,SY2441: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV221 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SY2439 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SY2440 ) @ SY2441 @ SY2439 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV587 @ SY2440 @ SY2441 @ SY2439 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2084,plain,
! [SV588: $i,SV222: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ SV222 ) ) @ SV588 )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV222 ) @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2085,plain,
! [SV589: $i,SV223: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV223 ) @ ( hAPP @ c_Suc @ SV589 ) )
= ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV223 ) @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2086,plain,
! [SV590: $i,SV224: $i] :
( ( ! [SY2442: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV224 )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 @ SV590 ) @ SY2442 @ SV590 @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2087,plain,
! [SV591: $i,SV225: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV225 )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV225 ) @ SV591 ) )
= ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2088,plain,
! [SV592: $i,SV226: $i] :
( ( ! [SY2443: $i,SY2444: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV226 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SY2443 ) @ SY2444 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SY2443 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ SY2444 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2089,plain,
! [SV593: $i,SV227: $i] :
( ( ! [SY2445: $i,SY2446: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV227 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SY2445 ) @ SY2446 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SY2445 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ SY2446 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2090,plain,
! [SV594: $i,SV228: $i] :
( ( ! [SY2447: $i,SY2448: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SY2447 ) @ SY2448 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SY2447 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ SY2448 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2091,plain,
! [SV595: $i,SV229: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV229 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV229 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SV595 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
| ~ ( c_SEQ_OZseq @ SV595 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2092,plain,
! [SV596: $i,SV230: $i] :
( ( ! [SY2449: $i,SY2450: $i] :
( ~ ( class_RealVector_Otopological__space @ SV230 )
| ( c_Limits_Otendsto @ ( c_COMBK @ SV596 @ SV230 @ SY2449 ) @ SV596 @ SY2450 @ SY2449 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2093,plain,
! [SV597: $i,SV231: $i] :
( ( ! [SY2451: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV231 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SV597 ) @ SY2451 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SY2451 ) @ SV597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2094,plain,
! [SV598: $i,SV232: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV232 ) @ SV598 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV598 ) @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2095,plain,
! [SV599: $i,SV233: $i] :
( ( ! [SY2452: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SV599 ) @ SY2452 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SY2452 ) @ SV599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2096,plain,
! [SV600: $i,SV234: $i] :
( ( ! [SY2453: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV234 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV600 ) @ SY2453 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SY2453 ) @ SV600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2097,plain,
! [SV235: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV235 ) )
= $true )
| ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV235 ) @ ( c_HOL_Ozero__class_Ozero @ SV235 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(2098,plain,
! [SV601: $i,SV236: $i] :
( ( ! [SY2454: $i,SY2455: $i] :
( ~ ( class_RealVector_Ometric__space @ SV236 )
| ~ ( class_RealVector_Ometric__space @ SV601 )
| ( c_Lim_OLIM @ ( c_COMBK @ SY2454 @ SV236 @ SV601 ) @ SY2455 @ SY2454 @ SV601 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2099,plain,
! [SV602: $i,SV237: $i] :
( ( ! [SY2456: $i,SY2457: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV237 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV237 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SV602 @ SY2456 @ SY2457 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SV602 @ tc_RealDef_Oreal @ SV237 @ SY2457 ) @ SY2456 @ SY2457 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2100,plain,
! [SV603: $i,SV238: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV238 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ SV603 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ SV603 ) ) )
| ( SV603
= ( c_HOL_Ozero__class_Ozero @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2101,plain,
! [SV604: $i,SV239: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) ) @ SV604 )
= ( c_HOL_Ozero__class_Ozero @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2102,plain,
! [SV605: $i,SV240: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV240 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV240 ) @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV240 ) )
= ( c_HOL_Ozero__class_Ozero @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2103,plain,
! [SV606: $i,SV241: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV241 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV241 ) @ ( c_HOL_Ozero__class_Ozero @ SV241 ) ) @ SV606 )
= ( c_HOL_Ozero__class_Ozero @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2104,plain,
! [SV607: $i,SV242: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV242 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV242 ) @ ( c_HOL_Ozero__class_Ozero @ SV242 ) ) @ SV607 )
= ( c_HOL_Ozero__class_Ozero @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2105,plain,
! [SV608: $i,SV243: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV243 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV243 ) @ SV608 ) @ ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2106,plain,
! [SV609: $i,SV244: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV244 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV244 ) @ SV609 ) @ ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= ( c_HOL_Ozero__class_Ozero @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2107,plain,
! [SV610: $i,SV245: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV245 ) @ ( c_HOL_Ozero__class_Ozero @ SV245 ) ) @ SV610 )
= ( c_HOL_Ozero__class_Ozero @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2108,plain,
! [SV611: $i,SV246: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV246 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) ) @ SV611 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2109,plain,
! [SV612: $i,SV247: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV247 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV247 ) @ SV612 ) @ ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2110,plain,
! [SV613: $i,SV248: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV248 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV248 ) @ ( c_HOL_Ozero__class_Ozero @ SV248 ) ) @ SV613 )
= ( c_HOL_Ozero__class_Ozero @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2111,plain,
! [SV614: $i,SV249: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV249 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV249 ) @ SV614 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= ( c_HOL_Ozero__class_Ozero @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2112,plain,
! [SV615: $i,SV250: $i] :
( ( ! [SY2458: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV250 )
| ( c_Series_Osummable @ ( c_COMBB @ SV615 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2458 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV250 @ tc_nat ) @ SV250 )
| ~ ( c_Series_Osummable @ SV615 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2113,plain,
! [SV616: $i,SV251: $i] :
( ( ! [SY2459: $i,SY2460: $i,SY2461: $i,SY2462: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV251 )
| ~ ( class_RealVector_Ometric__space @ SV616 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SY2459 ) @ SY2460 @ SV251 @ SV251 @ SV616 ) @ SY2461 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SY2459 ) @ SY2462 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SY2460 @ SY2461 @ SY2462 @ SV616 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2114,plain,
! [SV617: $i,SV252: $i] :
( ( ! [SY2463: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV252 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV252 ) @ SV617 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ SY2463 ) @ SV617 ) )
= SY2463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2115,plain,
! [SV618: $i,SV253: $i] :
( ( ! [SY2464: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV253 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV253 ) @ SV618 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ SV618 ) @ SY2464 ) )
= SY2464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2116,plain,
! [SV619: $i,SV254: $i] :
( ( ! [SY2465: $i,SY2466: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ SV254 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV619 ) @ ( hAPP @ c_Complex_ORe @ SY2465 ) @ SY2466 @ SV619 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV254 @ SY2465 @ SY2466 @ SV619 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2117,plain,
! [SV620: $i,SV255: $i] :
( ( ! [SY2467: $i,SY2468: $i,SY2469: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV255 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV620 )
| ( c_Series_Osums @ ( c_COMBB @ SY2467 @ SY2468 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SY2467 @ SY2469 ) @ SV620 )
| ~ ( c_Series_Osums @ SY2468 @ SY2469 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SY2467 @ SV255 @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2118,plain,
! [SV621: $i,SV256: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV256 )
| ( c_SEQ_OLIMSEQ @ SV621 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
| ~ ( c_Series_Osummable @ SV621 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2119,plain,
! [SV622: $i,SV257: $i] :
( ( ! [SY2470: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV257 )
| ( SV622
= ( c_Series_Osuminf @ SY2470 @ SV257 ) )
| ~ ( c_Series_Osums @ SY2470 @ SV622 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2120,plain,
! [SV623: $i,SV258: $i] :
( ( ! [SY2471: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV258 )
| ( ( c_Series_Osuminf @ SV623 @ SV258 )
= SY2471 )
| ~ ( c_Series_Osums @ SV623 @ SY2471 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2121,plain,
! [SV624: $i,SV259: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ SV259 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SV624 ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ SV259 @ SV624 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2122,plain,
! [SV260: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV260 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV260 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV260 ) @ ( c_HOL_Ozero__class_Ozero @ SV260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(2123,plain,
! [SV625: $i,SV262: $i] :
( ( ~ ( class_SEQ_Ocomplete__space @ SV262 )
| ( c_SEQ_OCauchy @ SV625 @ SV262 )
| ~ ( c_SEQ_Oconvergent @ SV625 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2124,plain,
! [SV626: $i,SV263: $i] :
( ( ~ ( class_SEQ_Ocomplete__space @ SV263 )
| ( c_SEQ_Oconvergent @ SV626 @ SV263 )
| ~ ( c_SEQ_OCauchy @ SV626 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2125,plain,
! [SV627: $i,SV264: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV264 )
| ( c_Lim_OisUCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV264 ) @ SV627 ) @ SV264 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2126,plain,
! [SV628: $i,SV265: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV265 )
| ( c_SEQ_OCauchy @ SV628 @ SV265 )
| ~ ( c_SEQ_Oconvergent @ SV628 @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2127,plain,
! [SV266: $i] :
( ( ( c_SEQ_Oconvergent @ SV266 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV266 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(2128,plain,
! [SV629: $i,SV267: $i] :
( ( ! [SY2472: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV267 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SV629 ) ) @ SY2472 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ SV629 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SY2472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2129,plain,
! [SV630: $i,SV268: $i] :
( ( ! [SY2473: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV268 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV630 @ SV268 @ SV268 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SY2473 ) @ SV268 )
| ~ ( c_Series_Osums @ SV630 @ SY2473 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2130,plain,
! [SV269: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV269 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV269 ) @ ( c_HOL_Ozero__class_Ozero @ SV269 ) )
= ( c_HOL_Ozero__class_Ozero @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(2131,plain,
! [SV270: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV270 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV270 ) @ ( c_HOL_Ozero__class_Ozero @ SV270 ) )
= ( c_HOL_Ozero__class_Ozero @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(2132,plain,
! [SV631: $i,SV271: $i] :
( ( ! [SY2474: $i,SY2475: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV271 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV631 )
| ( c_Lim_OLIM @ SY2474 @ SY2475 @ ( hAPP @ SY2474 @ SY2475 ) @ SV271 @ SV631 )
| ~ ( c_RealVector_Obounded__linear @ SY2474 @ SV271 @ SV631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2133,plain,
! [SV632: $i,SV272: $i] :
( ( ! [SY2476: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV272 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV272 ) @ SV632 ) @ SY2476 @ SV272 @ SV272 @ tc_nat ) @ SV272 )
| ~ ( c_SEQ_OZseq @ SY2476 @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2134,plain,
! [SV633: $i,SV273: $i] :
( ( ! [SY2477: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV273 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV273 ) @ SV633 ) @ SY2477 @ SV273 @ SV273 @ tc_nat ) @ SV273 )
| ~ ( c_SEQ_OZseq @ SY2477 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2135,plain,
! [SV634: $i,SV274: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV274 )
| ( c_Series_Osums @ SV634 @ ( c_Series_Osuminf @ SV634 @ SV274 ) @ SV274 )
| ~ ( c_Series_Osummable @ SV634 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2136,plain,
! [SV635: $i,SV275: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV275 )
| ~ ( c_Series_Osummable @ SV635 @ SV275 )
| ( c_Series_Osums @ SV635 @ ( c_Series_Osuminf @ SV635 @ SV275 ) @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2137,plain,
! [SV636: $i,SV276: $i] :
( ( ! [SY2478: $i,SY2479: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV276 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV636 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SY2478 @ SY2479 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
| ~ ( c_SEQ_OCauchy @ SY2479 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SY2478 @ SV276 @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2138,plain,
! [SV637: $i,SV277: $i] :
( ( ! [SY2480: $i,SY2481: $i] :
( ~ ( class_RealVector_Ometric__space @ SV277 )
| ~ ( class_RealVector_Ometric__space @ SV637 )
| ( c_Lim_OisCont @ SY2480 @ SY2481 @ SV277 @ SV637 )
| ~ ( c_Lim_OLIM @ SY2480 @ SY2481 @ ( hAPP @ SY2480 @ SY2481 ) @ SV277 @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2139,plain,
! [SV638: $i,SV278: $i] :
( ( ! [SY2482: $i,SY2483: $i] :
( ~ ( class_RealVector_Ometric__space @ SV278 )
| ~ ( class_RealVector_Ometric__space @ SV638 )
| ( c_Lim_OLIM @ SY2482 @ SY2483 @ ( hAPP @ SY2482 @ SY2483 ) @ SV278 @ SV638 )
| ~ ( c_Lim_OisCont @ SY2482 @ SY2483 @ SV278 @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2140,plain,
! [SV639: $i,SV279: $i] :
( ( ! [SY2484: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV279 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV639 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SY2484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2141,plain,
! [SV640: $i,SV280: $i] :
( ( ! [SY2485: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV280 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SV640 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SY2485 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2142,plain,
! [SV641: $i,SV281: $i] :
( ( ! [SY2486: $i,SY2487: $i,SY2488: $i,SY2489: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV281 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SY2486 @ SV281 @ SV281 @ SY2487 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SY2488 ) @ SY2489 @ SY2487 @ SV281 )
| ~ ( c_Limits_Otendsto @ SY2486 @ SY2488 @ SY2489 @ SY2487 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2143,plain,
! [SV642: $i,SV282: $i] :
( ( ! [SY2490: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV282 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV282 ) @ SV642 ) @ SY2490 @ SV282 @ SV282 @ tc_nat ) @ SV282 )
| ~ ( c_SEQ_OCauchy @ SY2490 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2144,plain,
! [SV283: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV283 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV283 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV283 ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV283 ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) )
= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(2145,plain,
! [SV643: $i,SV284: $i] :
( ( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ SV284 @ SV643 ) )
= SV284 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2146,plain,
! [SV644: $i,SV285: $i] :
( ( ! [SY2491: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV285 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV285 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SY2491 ) @ SV285 )
| ~ ( c_Series_Osums @ SV644 @ SY2491 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2147,plain,
! [SV645: $i,SV286: $i] :
( ( ! [SY2492: $i,SY2493: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV286 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV645 )
| ( ( hAPP @ SY2492 @ ( c_Series_Osuminf @ SY2493 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SY2492 @ SY2493 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
| ~ ( c_Series_Osummable @ SY2493 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SY2492 @ SV286 @ SV645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2148,plain,
! [SV646: $i,SV287: $i] :
( ( ! [SY2494: $i,SY2495: $i] :
( ~ ( class_RealVector_Ometric__space @ SV287 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV646 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SY2494 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SY2495 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SY2494 @ SY2495 @ SV287 @ SV646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2149,plain,
! [SV647: $i,SV288: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV288 )
| ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV288 ) @ SV647 ) @ SV288 @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2150,plain,
! [SV648: $i,SV289: $i] :
( ( ! [SY2496: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV289 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ SV648 ) @ SY2496 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SY2496 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SV648 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2151,plain,
! [SV649: $i,SV290: $i] :
( ( ! [SY2497: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV290 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ SV649 ) @ SY2497 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SV649 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SY2497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2152,plain,
! [SV650: $i,SV292: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ SV292 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SV650 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV292 @ SV650 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2153,plain,
! [SV651: $i,SV293: $i] :
( ( ! [SY2498: $i,SY2499: $i,SY2500: $i,SY2501: $i] :
( ( c_Set_Oimage @ SV293 @ ( c_Set_Oimage @ SV651 @ SY2498 @ SY2499 @ SY2500 ) @ SY2500 @ SY2501 )
= ( c_Set_Oimage @ ( c_COMBB @ SV293 @ SV651 @ SY2500 @ SY2501 @ SY2499 ) @ SY2498 @ SY2499 @ SY2501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2154,plain,
! [SV652: $i,SV294: $i] :
( ( ! [SY2502: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV294 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV652 @ SV294 @ SV294 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SY2502 ) @ SV294 )
| ~ ( c_SEQ_OLIMSEQ @ SV652 @ SY2502 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2155,plain,
! [SV653: $i,SV295: $i] :
( ( ! [SY2503: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV295 )
| ( c_SEQ_OLIMSEQ @ SV653 @ SY2503 @ SV295 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV653 @ SV295 @ SV295 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SY2503 ) @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2156,plain,
! [SV296: $i] :
( ( v_thesis____ = $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ SV296 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(2157,plain,
! [SV654: $i,SV297: $i] :
( ( ! [SY2504: $i] :
( ~ ( class_RealVector_Ometric__space @ SV297 )
| ( c_SEQ_Oconvergent @ SV654 @ SV297 )
| ~ ( c_SEQ_OLIMSEQ @ SV654 @ SY2504 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2158,plain,
! [SV655: $i,SV298: $i] :
( ( ! [SY2505: $i] :
( ~ ( class_RealVector_Ometric__space @ SV298 )
| ( c_SEQ_Oconvergent @ SV655 @ SV298 )
| ~ ( c_SEQ_OLIMSEQ @ SV655 @ SY2505 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2159,plain,
! [SV656: $i,SV299: $i] :
( ( ! [SY2506: $i] :
( ~ ( class_RealVector_Ometric__space @ SV299 )
| ( SV656 = SY2506 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV656 @ SV299 @ tc_nat ) @ SY2506 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2160,plain,
! [SV657: $i,SV300: $i] :
( ( ! [SY2507: $i,SY2508: $i,SY2509: $i,SY2510: $i,SY2511: $i] :
( ~ ( class_RealVector_Ometric__space @ SV300 )
| ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SY2507 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2508 @ SY2509 @ SV300 @ SV657 @ SY2507 ) @ SY2510 @ ( hAPP @ SY2508 @ SY2511 ) @ SY2507 @ SV657 )
| ~ ( c_Lim_OLIM @ SY2509 @ SY2510 @ SY2511 @ SY2507 @ SV300 )
| ~ ( c_Lim_OLIM @ SY2508 @ SY2511 @ ( hAPP @ SY2508 @ SY2511 ) @ SV300 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2161,plain,
! [SV658: $i,SV301: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV301 )
| ( c_SEQ_OLIMSEQ @ SV658 @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV301 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV301 ) @ SV658 @ SV301 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2162,plain,
! [SV659: $i,SV302: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV302 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV302 ) @ SV659 @ SV302 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV659 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2163,plain,
! [SV660: $i,SV303: $i] :
( ( ! [SY2512: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV303 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV660 @ SV303 @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SY2512 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV660 @ SY2512 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2164,plain,
! [SV661: $i,SV304: $i] :
( ( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ SV304 @ SV661 ) )
= SV661 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2165,plain,
! [SV662: $i,SV305: $i] :
( ( ! [SY2513: $i,SY2514: $i] :
( ~ ( class_RealVector_Ometric__space @ SV305 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV662 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2513 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SY2514 @ SV305 )
| ~ ( c_SEQ_OLIMSEQ @ SV662 @ SY2514 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2166,plain,
! [SV663: $i,SV306: $i] :
( ( ! [SY2515: $i,SY2516: $i] :
( ~ ( class_RealVector_Ometric__space @ SV306 )
| ( c_SEQ_OLIMSEQ @ SV663 @ SY2515 @ SV306 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV663 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2516 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SY2515 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2167,plain,
! [SV664: $i,SV307: $i] :
( ( ! [SY2517: $i] :
( ~ ( class_RealVector_Ometric__space @ SV307 )
| ( ( c_SEQ_Olim @ SV664 @ SV307 )
= SY2517 )
| ~ ( c_SEQ_OLIMSEQ @ SV664 @ SY2517 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2168,plain,
! [SV665: $i,SV308: $i] :
( ( ! [SY2518: $i,SY2519: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ SV308 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV665 ) @ ( hAPP @ c_Complex_OIm @ SY2518 ) @ SY2519 @ SV665 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV308 @ SY2518 @ SY2519 @ SV665 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2169,plain,
! [SV309: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ SV309 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV309 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2170,plain,
! [SV666: $i,SV310: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV310 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV666 @ SV310 @ tc_nat ) @ SV666 @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2171,plain,
! [SV667: $i,SV311: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV311 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV667 @ SV311 @ tc_nat ) @ SV667 @ SV311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2172,plain,
! [SV668: $i,SV312: $i] :
( ( ! [SY2520: $i,SY2521: $i,SY2522: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV312 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV668 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY2520 @ SY2521 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SY2520 @ SY2522 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SY2521 @ SY2522 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SY2520 @ SV312 @ SV668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2173,plain,
! [SV669: $i,SV313: $i] :
( ( ! [SY2523: $i,SY2524: $i,SY2525: $i,SY2526: $i] :
( ~ ( class_RealVector_Ometric__space @ SV313 )
| ~ ( class_RealVector_Ometric__space @ SV669 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SY2523 @ SY2524 @ SV669 @ SV313 @ tc_nat ) @ SY2525 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SY2524 @ SY2526 @ SV669 )
| ( ( hAPP @ SY2524 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SY2524 @ SY2526 @ SV669 ) )
= SY2526 )
| ~ ( c_Lim_OLIM @ SY2523 @ SY2526 @ SY2525 @ SV669 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2174,plain,
! [SV670: $i,SV314: $i] :
( ( ! [SY2527: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ SV314 @ SV670 @ SY2527 @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ SV314 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SY2527 ) @ SV670 @ SY2527 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2175,plain,
! [SV671: $i,SV315: $i] :
( ( ! [SY2528: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV315 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV315 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SY2528 ) @ SV315 )
| ~ ( c_SEQ_OLIMSEQ @ SV671 @ SY2528 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2176,plain,
! [SV672: $i,SV316: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ SV316 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SV672 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV316 @ SV672 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2177,plain,
! [SV317: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ SV317 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV317 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(2178,plain,
! [SV673: $i,SV318: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ SV318 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SV673 ) @ tc_RealDef_Oreal )
| ~ ( c_Series_Osums @ SV318 @ SV673 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2179,plain,
! [SV674: $i,SV319: $i] :
( ( ! [SY2529: $i] :
( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ SV319 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV674 ) @ SY2529 @ SV674 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV319 @ SY2529 @ SV674 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2180,plain,
! [SV675: $i,SV320: $i] :
( ( ! [SY2530: $i,SY2531: $i,SY2532: $i,SY2533: $i] :
( ~ ( class_RealVector_Ometric__space @ SV320 )
| ~ ( class_RealVector_Ometric__space @ SV675 )
| ~ ( class_RealVector_Ometric__space @ SY2530 )
| ( c_Lim_OisCont @ ( c_COMBB @ SY2531 @ SY2532 @ SY2530 @ SV675 @ SV320 ) @ SY2533 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SY2531 @ ( hAPP @ SY2532 @ SY2533 ) @ SY2530 @ SV675 )
| ~ ( c_Lim_OisCont @ SY2532 @ SY2533 @ SV320 @ SY2530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2181,plain,
! [SV676: $i,SV321: $i] :
( ( ! [SY2534: $i,SY2535: $i] :
( ~ ( class_RealVector_Ometric__space @ SV321 )
| ( SV676 = SY2534 )
| ~ ( c_SEQ_OLIMSEQ @ SY2535 @ SY2534 @ SV321 )
| ~ ( c_SEQ_OLIMSEQ @ SY2535 @ SV676 @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2182,plain,
! [SV677: $i,SV322: $i] :
( ( ! [SY2536: $i,SY2537: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV322 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SY2536 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SY2537 ) @ SV322 )
| ~ ( c_SEQ_OLIMSEQ @ SY2536 @ SY2537 @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2183,plain,
! [SV678: $i,SV323: $i] :
( ( ! [SY2538: $i,SY2539: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV323 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SY2538 @ SV323 @ SV323 @ SV323 ) @ SY2539 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SY2538 @ SY2539 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SY2538 @ SY2539 ) @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2184,plain,
! [SV679: $i,SV324: $i] :
( ( ! [SY2540: $i,SY2541: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV324 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SY2540 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SY2541 ) @ SV324 )
| ~ ( c_SEQ_OLIMSEQ @ SY2540 @ SY2541 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2185,plain,
! [SV680: $i,SV326: $i] :
( ( ! [SY2542: $i] :
( ~ ( class_RealVector_Ometric__space @ SV326 )
| ( c_SEQ_OCauchy @ SV680 @ SV326 )
| ~ ( c_SEQ_OLIMSEQ @ SV680 @ SY2542 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2186,plain,
! [SV681: $i,SV327: $i] :
( ( ! [SY2543: $i] :
( ~ ( class_RealVector_Ometric__space @ SV327 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV681 @ c_Suc @ tc_nat @ SV327 @ tc_nat ) @ SY2543 @ SV327 )
| ~ ( c_SEQ_OLIMSEQ @ SV681 @ SY2543 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2187,plain,
! [SV682: $i,SV328: $i] :
( ( ! [SY2544: $i] :
( ~ ( class_RealVector_Ometric__space @ SV328 )
| ( c_SEQ_OLIMSEQ @ SV682 @ SY2544 @ SV328 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV682 @ c_Suc @ tc_nat @ SV328 @ tc_nat ) @ SY2544 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2188,plain,
! [SV683: $i,SV329: $i] :
( ( ! [SY2545: $i,SY2546: $i,SY2547: $i,SY2548: $i] :
( ( hAPP @ ( c_COMBB @ SV329 @ SV683 @ SY2545 @ SY2546 @ SY2547 ) @ SY2548 )
= ( hAPP @ SV329 @ ( hAPP @ SV683 @ SY2548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2189,plain,
! [SV684: $i,SV330: $i] :
( ( ! [SY2549: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV330 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV684 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SY2549 ) @ SV330 )
| ( SY2549
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ~ ( c_SEQ_OLIMSEQ @ SV684 @ SY2549 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2190,plain,
! [SV685: $i,SV331: $i] :
( ( ! [SY2550: $i,SY2551: $i] :
( ~ ( class_RealVector_Ometric__space @ SV331 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SV685 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SY2550 @ ( hAPP @ c_Complex_OIm @ SY2551 ) @ SV331 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV685 @ SY2550 @ SY2551 @ SV331 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2191,plain,
! [SV332: $i] :
( ( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ SV332 @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ SV332 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV332 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(2192,plain,
! [SV333: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ SV333 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV333 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(2193,plain,
! [SV686: $i,SV334: $i] :
( ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV334 @ SV686 ) )
| ~ ( class_Lattices_Oboolean__algebra @ SV686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2194,plain,
! [SV687: $i,SV335: $i] :
( ( ! [SY2552: $i,SY2553: $i,SY2554: $i,SY2555: $i] :
( ( hAPP @ ( c_COMBC @ SV335 @ SV687 @ SY2552 @ SY2553 @ SY2554 ) @ SY2555 )
= ( hAPP @ ( hAPP @ SV335 @ SY2555 ) @ SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2195,plain,
! [SV688: $i,SV336: $i] :
( ( ! [SY2556: $i,SY2557: $i,SY2558: $i,SY2559: $i] :
( ( hAPP @ ( c_COMBB @ SV336 @ SV688 @ SY2556 @ SY2557 @ SY2558 ) @ SY2559 )
= ( hAPP @ SV336 @ ( hAPP @ SV688 @ SY2559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2196,plain,
! [SV689: $i,SV337: $i] :
( ( c_fequal @ SV337 @ SV337 @ SV689 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2197,plain,
! [SV690: $i,SV338: $i] :
( ( ! [SY2560: $i] :
( ( SV338 = SV690 )
| ~ ( c_fequal @ SV338 @ SV690 @ SY2560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2198,plain,
! [SV691: $i,SV339: $i] :
( ( ! [SY2561: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV339 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV691 ) @ SV691 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SY2561 ) @ SY2561 ) )
| ( SV691
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SY2561 ) )
| ( SV691 = SY2561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2199,plain,
! [SV692: $i,SV340: $i] :
( ( ! [SY2562: $i,SY2563: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV692 ) @ SY2562 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY2563 ) @ SY2562 ) )
| ( SV692 = SY2563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2200,plain,
! [SV341: $i] :
( ( ( hAPP @ c_Suc @ SV341 )
= SV341 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(2201,plain,
! [SV693: $i,SV342: $i] :
( ( ! [SY2564: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV342 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SV693 ) @ SY2564 )
!= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV693
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SY2564
= ( c_HOL_Ozero__class_Ozero @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2202,plain,
! [SV694: $i,SV343: $i] :
( ( ! [SY2565: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SY2565 ) )
| ( SV694 = SY2565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2203,plain,
! [SV695: $i,SV344: $i] :
( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV344 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV344 ) @ SV695 )
!= ( c_HOL_Ozero__class_Ozero @ SV344 ) )
| ( SV695
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2204,plain,
! [SV696: $i,SV345: $i] :
( ( ! [SY2566: $i,SY2567: $i,SY2568: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV345 )
| ~ ( class_Int_Onumber__ring @ SV345 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SY2566 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2567 ) @ SY2568 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SY2568 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2567 ) @ SY2566 ) ) )
| ( SY2566 = SY2568 )
| ( SV696 = SY2567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2205,plain,
! [SV697: $i,SV346: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV346 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV346 ) @ SV697 ) @ SV697 )
!= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
| ( SV697
= ( c_HOL_Ozero__class_Ozero @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2206,plain,
! [SV698: $i,SV347: $i] :
( ( ! [SY2569: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV347 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SY2569 ) )
| ( SV698 = SY2569 )
| ( SY2569
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2207,plain,
! [SV699: $i,SV348: $i] :
( ( ! [SY2570: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV348 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ SV699 ) @ SY2570 )
!= ( c_HOL_Ozero__class_Ozero @ SV348 ) )
| ( SV699
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV348 ) @ SY2570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2208,plain,
! [SV700: $i,SV349: $i] :
( ( ! [SY2571: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV349 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV700 ) @ SV700 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SY2571 ) @ SY2571 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
| ( SV700
= ( c_HOL_Ozero__class_Ozero @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2209,plain,
! [SV701: $i,SV350: $i] :
( ( ! [SY2572: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SV701 ) @ SY2572 )
!= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SY2572
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2210,plain,
! [SV702: $i,SV351: $i] :
( ( ! [SY2573: $i,SY2574: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SV351 @ SV702 )
!= ( c_Complex_Ocomplex_OComplex @ SY2573 @ SY2574 ) )
| ( SV702 = SY2574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2211,plain,
! [SV703: $i,SV352: $i] :
( ( ! [SY2575: $i,SY2576: $i,SY2577: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV352 )
| ~ ( class_Int_Onumber__ring @ SV352 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SY2575 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2576 ) @ SY2577 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SY2577 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2576 ) @ SY2575 ) ) )
| ( SY2575 = SY2577 )
| ( SV703 = SY2576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2212,plain,
! [SV704: $i,SV353: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV353 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV353 ) @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2213,plain,
! [SV705: $i,SV354: $i] :
( ( ! [SY2578: $i,SY2579: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV354 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SY2578 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SY2579 ) )
| ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SY2578 = SY2579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2214,plain,
! [SV706: $i,SV355: $i] :
( ( ! [SY2580: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SV706 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SY2580 ) )
| ( SV706 = SY2580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2215,plain,
! [SV707: $i,SV356: $i] :
( ( ( ( hAPP @ c_Suc @ SV356 )
!= ( hAPP @ c_Suc @ SV707 ) )
| ( SV356 = SV707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2216,plain,
! [SV708: $i,SV357: $i] :
( ( ! [SY2581: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV357 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SV708 ) @ SY2581 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SY2581
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV708
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2217,plain,
! [SV709: $i,SV358: $i] :
( ( ! [SY2582: $i,SY2583: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SY2582 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SY2583 ) )
| ( SY2582 = SY2583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2218,plain,
! [SV710: $i,SV359: $i] :
( ( ! [SY2584: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV359 ) @ SV710 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2584 ) @ SV710 ) )
| ( SV359 = SY2584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2219,plain,
! [SV711: $i,SV360: $i] :
( ( ! [SY2585: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV360 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV711 ) @ SY2585 )
!= ( c_HOL_Ozero__class_Ozero @ SV360 ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV360 ) @ SV711 )
= SY2585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2220,plain,
! [SV712: $i,SV361: $i] :
( ( ! [SY2586: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV361 )
| ~ ( class_Int_Onumber__ring @ SV361 )
| ( SV712
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SY2586 ) )
| ( SY2586
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2221,plain,
! [SV713: $i,SV362: $i] :
( ( ! [SY2587: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV362 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SV713 ) @ SY2587 )
!= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SY2587
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2222,plain,
! [SV714: $i,SV363: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV363 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV363 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SV714 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( SV714
= ( c_HOL_Ozero__class_Ozero @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2223,plain,
! [SV715: $i,SV364: $i] :
( ( ! [SY2588: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV364 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV715 ) @ SV715 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SY2588 ) @ SY2588 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
| ( SY2588
= ( c_HOL_Ozero__class_Ozero @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2224,plain,
! [SV716: $i,SV365: $i] :
( ( ! [SY2589: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV365 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV716 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SY2589 ) )
| ( SV716 = SY2589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2225,plain,
! [SV717: $i,SV366: $i] :
( ( ! [SY2590: $i,SY2591: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV366 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SY2590 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SY2591 ) @ SY2590 ) )
| ( SY2590
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SV717 = SY2591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2226,plain,
! [SV718: $i,SV367: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV367 )
| ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV367 ) @ SV718 )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2227,plain,
! [SV719: $i,SV368: $i] :
( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV368 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV368 ) @ SV719 )
!= SV719 )
| ( SV719
= ( c_HOL_Ozero__class_Ozero @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2228,plain,
! [SV720: $i,SV369: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV369 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV369 ) @ SV720 )
!= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
| ( SV720
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2229,plain,
! [SV721: $i,SV370: $i] :
( ( ! [SY2592: $i,SY2593: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SV370 @ SV721 )
!= ( c_Complex_Ocomplex_OComplex @ SY2592 @ SY2593 ) )
| ( SV370 = SY2592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2230,plain,
! [SV722: $i,SV371: $i] :
( ( ( ( hAPP @ c_Complex_OIm @ SV371 )
!= ( hAPP @ c_Complex_OIm @ SV722 ) )
| ( ( hAPP @ c_Complex_ORe @ SV371 )
!= ( hAPP @ c_Complex_ORe @ SV722 ) )
| ( SV371 = SV722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2231,plain,
! [SV723: $i,SV372: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV372 )
| ( ( c_HOL_Ozero__class_Ozero @ SV372 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV372 ) @ SV723 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV372 )
= SV723 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2232,plain,
! [SV724: $i,SV373: $i] :
( ( ! [SY2594: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV373 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SY2594 ) )
| ( SV724 = SY2594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2233,plain,
! [SV725: $i,SV374: $i] :
( ( ! [SY2595: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV374 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV725 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SY2595 ) )
| ( SV725 = SY2595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2234,plain,
! [SV726: $i,SV375: $i] :
( ( ! [SY2596: $i,SY2597: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV375 )
| ~ ( class_Int_Onumber__ring @ SV375 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SY2596 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SY2597 ) )
| ( SY2596 = SY2597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2235,plain,
! [SV727: $i,SV376: $i] :
( ( ! [SY2598: $i] :
( ~ ( class_RealVector_Oreal__algebra__1 @ SV376 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV727 )
!= ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SY2598 ) )
| ( SV727 = SY2598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2236,plain,
! [SV728: $i,SV377: $i] :
( ( ! [SY2599: $i,SY2600: $i,SY2601: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SY2599 ) @ SY2600 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SY2599 ) @ SY2601 ) ) )
| ( SY2600 = SY2601 )
| ( SY2599
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2237,plain,
! [SV378: $i] :
( ( SV378
= ( hAPP @ c_Suc @ SV378 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2238,plain,
! [SV729: $i,SV379: $i] :
( ( ! [SY2602: $i,SY2603: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SY2602 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SY2603 ) )
| ( SY2602 = SY2603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2239,plain,
! [SV730: $i,SV380: $i] :
( ( ( ( hAPP @ c_Suc @ SV380 )
!= ( hAPP @ c_Suc @ SV730 ) )
| ( SV380 = SV730 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2240,plain,
! [SV731: $i,SV381: $i] :
( ( ! [SY2604: $i,SY2605: $i,SY2606: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV381 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2604 ) @ SY2605 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2604 ) @ SY2606 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SY2605 )
= SY2606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2241,plain,
! [SV732: $i,SV382: $i] :
( ( ! [SY2607: $i,SY2608: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV382 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SY2607 ) @ SY2608 ) )
!= SY2607 )
| ( SV732
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SY2608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2242,plain,
! [SV1: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ SV1 @ tc_RealDef_Oreal )
= $false )
| ( v_thesis____ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(2243,plain,
! [SV733: $i,SV383: $i,SV2: $i] :
( ( ! [SY2609: $i,SY2610: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV2 )
| ~ ( class_RealVector_Ometric__space @ SV383 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SY2609 @ SV383 @ SV2 @ SV2 ) @ SY2610 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SV733 @ SY2610 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2244,plain,
! [SV734: $i,SV384: $i,SV3: $i] :
( ( ! [SY2611: $i,SY2612: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV3 )
| ~ ( class_RealVector_Ometric__space @ SV384 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SY2611 @ SV384 @ SV3 @ SV3 ) @ SY2612 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SV734 @ SY2612 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2245,plain,
! [SV735: $i,SV385: $i,SV4: $i] :
( ( ! [SY2613: $i,SY2614: $i,SY2615: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV4 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SY2613 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SY2614 ) @ SY2613 ) @ SY2615 @ SV735 @ SV4 )
| ~ ( c_Limits_Otendsto @ SV385 @ SY2614 @ SY2615 @ SV735 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2246,plain,
! [SV736: $i,SV386: $i,SV5: $i] :
( ( ! [SY2616: $i,SY2617: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV5 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SV736 ) @ SY2616 @ SV736 @ SV5 @ SV5 ) @ SY2617 @ SV736 @ SV5 )
| ~ ( c_Limits_OZfun @ SV386 @ SY2617 @ SV736 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2247,plain,
! [SV737: $i,SV387: $i,SV6: $i] :
( ( ! [SY2618: $i,SY2619: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV6 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SV737 ) @ SY2618 @ SV737 @ SV6 @ SV6 ) @ SY2619 @ SV737 @ SV6 )
| ~ ( c_Limits_OZfun @ SV387 @ SY2619 @ SV737 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2248,plain,
! [SV738: $i,SV388: $i,SV7: $i] :
( ( ! [SY2620: $i,SY2621: $i,SY2622: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV7 )
| ~ ( class_RealVector_Ometric__space @ SV388 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SY2620 @ SV388 @ SV7 @ SV7 ) @ SY2621 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SY2622 ) @ SY2620 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SY2621 @ SY2622 @ SV388 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2249,plain,
! [SV739: $i,SV389: $i,SV8: $i] :
( ( ! [SY2623: $i,SY2624: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV8 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ ( c_Finite__Set_Osetsum @ SV389 @ SV739 @ SY2623 @ SV8 ) ) @ SY2624 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ SV389 @ SV8 @ ( tc_fun @ SV8 @ SV8 ) @ SY2623 ) @ SY2624 @ SY2623 @ SV8 @ SV8 ) @ SV739 @ SY2623 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2250,plain,
! [SV740: $i,SV390: $i,SV9: $i] :
( ( ! [SY2625: $i,SY2626: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ ( c_Finite__Set_Osetsum @ SV390 @ SV740 @ SY2625 @ SV9 ) ) @ SY2626 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ SV390 @ SV9 @ ( tc_fun @ SV9 @ SV9 ) @ SY2625 ) @ SY2626 @ SY2625 @ SV9 @ SV9 ) @ SV740 @ SY2625 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2251,plain,
! [SV741: $i,SV391: $i,SV10: $i] :
( ( ! [SY2627: $i,SY2628: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ ( c_Finite__Set_Osetsum @ SV391 @ SV741 @ SY2627 @ tc_RealDef_Oreal ) ) @ SY2628 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ SV391 @ tc_RealDef_Oreal @ ( tc_fun @ SV10 @ SV10 ) @ SY2627 ) @ SY2628 @ SY2627 @ SV10 @ SV10 ) @ SV741 @ SY2627 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2252,plain,
! [SV742: $i,SV392: $i,SV11: $i] :
( ( ! [SY2629: $i,SY2630: $i,SY2631: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV11 )
| ~ ( class_RealVector_Ometric__space @ SV392 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SY2629 @ SV392 @ SV11 @ SV11 ) @ SY2630 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SY2631 ) @ SY2629 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SY2630 @ SY2631 @ SV392 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2253,plain,
! [SV743: $i,SV393: $i,SV12: $i] :
( ( ! [SY2632: $i,SY2633: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV12 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SV743 ) @ SY2632 @ SV743 @ SV12 @ SV12 ) @ SY2633 @ SV743 @ SV12 )
| ~ ( c_Limits_OZfun @ SV393 @ SY2633 @ SV743 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2254,plain,
! [SV744: $i,SV394: $i,SV13: $i] :
( ( ! [SY2634: $i,SY2635: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV13 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SV744 ) @ SY2634 @ SV744 @ SV13 @ SV13 ) @ SY2635 @ SV744 @ SV13 )
| ~ ( c_Limits_OZfun @ SV394 @ SY2635 @ SV744 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2255,plain,
! [SV745: $i,SV395: $i,SV14: $i] :
( ( ! [SY2636: $i,SY2637: $i,SY2638: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV14 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SY2636 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SY2637 ) @ SY2636 ) @ SY2638 @ SV745 @ SV14 )
| ~ ( c_Limits_Otendsto @ SV395 @ SY2637 @ SY2638 @ SV745 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2256,plain,
! [SV396: $i,SV15: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV15 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV15 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SV396 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
| ~ ( c_SEQ_OCauchy @ SV396 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2257,plain,
! [SV397: $i,SV16: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV16 ) )
= $true )
| ( ( c_Lim_OisUCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV16 ) @ SV397 ) @ SV16 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2258,plain,
! [SV398: $i,SV17: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV17 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV17 ) @ SV398 @ SV17 @ SV17 @ tc_nat ) @ SV17 )
| ~ ( c_SEQ_OZseq @ SV398 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2259,plain,
! [SV746: $i,SV399: $i,SV18: $i] :
( ( ! [SY2639: $i,SY2640: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY2639 ) @ SY2640 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SY2639 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ SY2640 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2260,plain,
! [SV747: $i,SV400: $i,SV19: $i] :
( ( ! [SY2641: $i,SY2642: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ SV747 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY2641 ) @ SY2642 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV747 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SY2641 ) @ SY2642 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2261,plain,
! [SV748: $i,SV401: $i,SV20: $i] :
( ( ! [SY2643: $i,SY2644: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV748 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SY2643 ) @ SY2644 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SY2643 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV748 ) @ SY2644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2262,plain,
! [SV402: $i,SV21: $i] :
( ( ( ~ ( class_SEQ_Obanach @ SV21 ) )
= $true )
| ( ( ( c_Series_Osummable @ SV402 @ SV21 )
| ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV21 ) @ SV402 @ SV21 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2263,plain,
! [SV22: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV22 )
= $false )
| ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV22 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2264,plain,
! [SV23: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV23 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV23 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV23 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2265,plain,
! [SV749: $i,SV403: $i,SV24: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV24 )
| ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SV749 ) @ SV24 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2266,plain,
! [SV750: $i,SV404: $i,SV25: $i] :
( ( ! [SY2645: $i] :
( ~ ( class_RealVector_Ometric__space @ SV25 )
| ~ ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SY2645 @ SV25 @ SV404 )
| ( ( hAPP @ SV750 @ SY2645 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SV750 @ SY2645 @ SV25 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2267,plain,
! [SV751: $i,SV405: $i,SV26: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV26 )
| ( c_Deriv_Odifferentiable @ ( c_COMBK @ SV405 @ SV26 @ SV26 ) @ SV751 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2268,plain,
! [SV406: $i,SV27: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV27 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ SV406 @ SV27 )
| ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV27 ) @ SV406 @ SV27 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2269,plain,
! [SV407: $i,SV28: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV28 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV28 ) @ SV407 @ SV28 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ SV407 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2270,plain,
! [SV752: $i,SV408: $i,SV29: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV29 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV29 ) @ SV408 ) @ SV752 @ SV29 @ SV29 @ tc_nat ) @ SV29 )
| ~ ( c_SEQ_OCauchy @ SV752 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2271,plain,
! [SV753: $i,SV409: $i,SV30: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV30 )
| ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV30 ) @ SV409 ) @ SV753 @ SV30 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2272,plain,
! [SV754: $i,SV410: $i,SV31: $i] :
( ( ! [SY2646: $i,SY2647: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV31 )
| ~ ( class_RealVector_Ometric__space @ SV410 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SY2646 @ SV410 @ SV31 @ SV31 ) @ SY2647 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SV754 @ SY2647 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2273,plain,
! [SV755: $i,SV411: $i,SV32: $i] :
( ( ! [SY2648: $i,SY2649: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV32 )
| ~ ( class_RealVector_Ometric__space @ SV411 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SY2648 @ SV411 @ SV32 @ SV32 ) @ SY2649 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SV755 @ SY2649 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2274,plain,
! [SV412: $i,SV33: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV33 ) )
= $true )
| ( ( ( SV412
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ~ ( c_SEQ_OZseq @ ( c_COMBK @ SV412 @ SV33 @ tc_nat ) @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2275,plain,
! [SV756: $i,SV413: $i,SV34: $i] :
( ( ! [SY2650: $i,SY2651: $i,SY2652: $i] :
( ~ ( class_RealVector_Ometric__space @ SV34 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
| ( SV756 = SY2650 )
| ~ ( c_Lim_OLIM @ SY2651 @ SY2652 @ SY2650 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SY2651 @ SY2652 @ SV756 @ SV413 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2276,plain,
! [SV757: $i,SV414: $i,SV35: $i] :
( ( ! [SY2653: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV35 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SV414 @ SV35 @ tc_RealDef_Oreal @ SV757 ) @ SY2653 @ SV757 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV414 @ SY2653 @ SV757 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2277,plain,
! [SV758: $i,SV415: $i,SV36: $i] :
( ( ! [SY2654: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV36 )
| ( c_Limits_OZfun @ SV415 @ SV758 @ SY2654 @ SV36 )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SV415 @ SV36 @ tc_RealDef_Oreal @ SY2654 ) @ SV758 @ SY2654 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2278,plain,
! [SV759: $i,SV416: $i,SV37: $i] :
( ( ! [SY2655: $i] :
( ~ ( class_RealVector_Ometric__space @ SV37 )
| ~ ( class_RealVector_Ometric__space @ SV416 )
| ( c_Lim_OisCont @ ( c_COMBK @ SV759 @ SV416 @ SV37 ) @ SY2655 @ SV37 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2279,plain,
! [SV760: $i,SV417: $i,SV38: $i] :
( ( ! [SY2656: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV38 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SV417 @ SV38 @ SV38 @ SV760 ) @ SY2656 @ SV760 @ SV38 )
| ~ ( c_Limits_OZfun @ SV417 @ SY2656 @ SV760 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2280,plain,
! [SV761: $i,SV418: $i,SV39: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV39 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ SV418 ) @ SV761 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ SV418 ) ) @ SV761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2281,plain,
! [SV762: $i,SV419: $i,SV40: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV40 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ SV762 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ SV762 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2282,plain,
! [SV763: $i,SV420: $i,SV41: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV41 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV420 )
| ( c_Lim_OisUCont @ SV763 @ SV41 @ SV420 )
| ~ ( c_RealVector_Obounded__linear @ SV763 @ SV41 @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2283,plain,
! [SV764: $i,SV421: $i,SV42: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV42 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV42 ) @ SV421 ) @ SV764 @ SV42 @ SV42 @ tc_nat ) @ SV42 )
| ~ ( c_SEQ_OZseq @ SV764 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2284,plain,
! [SV765: $i,SV422: $i,SV43: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV43 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV43 ) @ SV422 ) @ SV765 @ SV43 @ SV43 @ tc_nat ) @ SV43 )
| ~ ( c_SEQ_OZseq @ SV765 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2285,plain,
! [SV766: $i,SV423: $i,SV44: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV44 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SV766 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SV766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2286,plain,
! [SV767: $i,SV424: $i,SV45: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ SV45 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV424 ) @ SV767 @ SV424 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV45 @ SV767 @ SV424 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2287,plain,
! [SV46: $i] :
( ( ( c_SEQ_OCauchy @ SV46 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_ORe @ SV46 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(2288,plain,
! [SV768: $i,SV425: $i,SV47: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV47 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV425 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV47 ) @ SV425 ) ) @ SV768 ) )
= SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2289,plain,
! [SV769: $i,SV426: $i,SV48: $i] :
( ( ! [SY2657: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV48 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV48 )
| ~ ( class_RealVector_Ometric__space @ SV426 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SY2657 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SY2657 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2290,plain,
! [SV770: $i,SV427: $i,SV49: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV49 )
| ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SV770 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SV770 ) @ SV49 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2291,plain,
! [SV428: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV50 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV50 ) @ SV428 ) @ SV428 )
= SV428 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2292,plain,
! [SV771: $i,SV429: $i,SV51: $i] :
( ( ! [SY2658: $i,SY2659: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV51 )
| ~ ( class_RealVector_Ometric__space @ SV429 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SY2658 @ SV51 @ SV51 @ SV429 ) @ SY2659 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SY2658 @ SY2659 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2293,plain,
! [SV772: $i,SV430: $i,SV52: $i] :
( ( ! [SY2660: $i,SY2661: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV52 )
| ~ ( class_RealVector_Ometric__space @ SV430 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SY2660 @ SV52 @ SV52 @ SV430 ) @ SY2661 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SY2660 @ SY2661 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2294,plain,
! [SV431: $i,SV53: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV53 ) )
= $true )
| ( ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV53 ) @ SV431 ) @ SV53 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2295,plain,
! [SV54: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV54 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV54 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV54 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2296,plain,
! [SV55: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV55 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) )
= ( c_HOL_Ozero__class_Ozero @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2297,plain,
! [SV773: $i,SV432: $i,SV56: $i] :
( ( ! [SY2662: $i,SY2663: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV56 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SV773 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SY2662 ) @ SY2663 @ SV773 @ SV56 )
| ~ ( c_Limits_Otendsto @ SV432 @ SY2662 @ SY2663 @ SV773 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2298,plain,
! [SV774: $i,SV433: $i,SV57: $i] :
( ( ! [SY2664: $i,SY2665: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV57 )
| ( c_Limits_Otendsto @ SV433 @ SV774 @ SY2664 @ SY2665 @ SV57 )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SY2665 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV774 ) @ SY2664 @ SY2665 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2299,plain,
! [SV775: $i,SV434: $i,SV58: $i] :
( ( ! [SY2666: $i,SY2667: $i,SY2668: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV58 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV434 )
| ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2666 @ SY2667 @ SV434 @ SV58 @ SV775 ) @ SY2668 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SY2667 @ SY2668 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SY2666 @ SV434 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2300,plain,
! [SV435: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV59 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ SV435 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ SV435 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2301,plain,
! [SV436: $i,SV61: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV61 ) )
= $true )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV61 ) @ SV436 @ SV61 @ SV61 @ tc_nat ) @ SV61 )
| ~ ( c_Series_Osummable @ SV436 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2302,plain,
! [SV776: $i,SV437: $i,SV62: $i] :
( ( ! [SY2669: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV62 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ SV776 ) ) @ SY2669 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV776 ) @ SY2669 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2303,plain,
! [SV777: $i,SV438: $i,SV63: $i] :
( ( ! [SY2670: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SV777 ) ) @ SY2670 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SY2670 ) ) @ SV777 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2304,plain,
! [SV778: $i,SV439: $i,SV64: $i] :
( ( ! [SY2671: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV64 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ SV778 ) ) @ SY2671 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV778 ) @ SY2671 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2305,plain,
! [SV779: $i,SV440: $i,SV65: $i] :
( ( ! [SY2672: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV779 ) @ SY2672 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ SV779 ) ) @ SY2672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2306,plain,
! [SV780: $i,SV441: $i,SV66: $i] :
( ( ! [SY2673: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ SY2673 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ SY2673 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2307,plain,
! [SV781: $i,SV442: $i,SV67: $i] :
( ( ! [SY2674: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV781 ) @ SY2674 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ SV781 ) ) @ SY2674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2308,plain,
! [SV782: $i,SV443: $i,SV68: $i] :
( ( ! [SY2675: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV443 ) @ SV782 ) ) @ SY2675 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV443 ) @ SY2675 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV782 ) @ SY2675 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2309,plain,
! [SV783: $i,SV444: $i,SV69: $i] :
( ( ! [SY2676: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV783 ) @ SY2676 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SV783 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SY2676 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2310,plain,
! [SV784: $i,SV445: $i,SV70: $i] :
( ( ! [SY2677: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV70 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV784 ) @ SY2677 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SV784 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SY2677 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2311,plain,
! [SV785: $i,SV446: $i,SV71: $i] :
( ( ! [SY2678: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV71 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV446 ) @ SV785 ) ) @ SY2678 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV446 ) @ SY2678 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV785 ) @ SY2678 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2312,plain,
! [SV786: $i,SV447: $i,SV72: $i] :
( ( ! [SY2679: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV72 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV447 ) @ SV786 ) ) @ SY2679 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV447 ) @ SY2679 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV786 ) @ SY2679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2313,plain,
! [SV787: $i,SV448: $i,SV73: $i] :
( ( ! [SY2680: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV73 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV787 ) @ SY2680 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SV787 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SY2680 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2314,plain,
! [SV788: $i,SV449: $i,SV74: $i] :
( ( ! [SY2681: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV74 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV449 ) @ SV788 ) ) @ SY2681 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV449 ) @ SY2681 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV788 ) @ SY2681 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2315,plain,
! [SV789: $i,SV450: $i,SV75: $i] :
( ( ! [SY2682: $i] :
( ~ ( class_RealVector_Ometric__space @ SV75 )
| ~ ( class_HOL_Ozero @ SV75 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SY2682 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2316,plain,
! [SV790: $i,SV451: $i,SV76: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV76 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ ( c_Series_Osuminf @ SV790 @ SV76 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ SV790 @ SV76 @ SV76 @ tc_nat ) @ SV76 ) )
| ~ ( c_Series_Osummable @ SV790 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2317,plain,
! [SV791: $i,SV452: $i,SV77: $i] :
( ( ! [SY2683: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV77 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV452 ) @ SV791 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SY2683 ) @ SV791 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV452 ) @ SY2683 ) ) @ SV791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2318,plain,
! [SV453: $i,SV78: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV78 ) )
= $true )
| ( ( c_RealVector_Obounded__linear @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV78 ) @ SV453 @ SV78 @ SV78 @ SV78 ) @ SV78 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2319,plain,
! [SV792: $i,SV454: $i,SV79: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV79 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ SV454 ) ) @ SV792 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ SV454 ) @ SV792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2320,plain,
! [SV793: $i,SV455: $i,SV80: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV80 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ SV455 ) ) @ SV793 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ SV455 ) @ SV793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2321,plain,
! [SV794: $i,SV456: $i,SV81: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ SV794 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ SV794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2322,plain,
! [SV795: $i,SV457: $i,SV82: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ SV795 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ SV795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2323,plain,
! [SV458: $i,SV83: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV83 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SV458 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SV458 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ SV458 ) @ SV458 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2324,plain,
! [SV796: $i,SV459: $i,SV84: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV84 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SV459 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SV796 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ SV459 ) @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2325,plain,
! [SV797: $i,SV460: $i,SV85: $i] :
( ( ! [SY2684: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV85 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV85 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SY2684 @ SV797 @ SV85 )
| ~ ( c_Limits_OZfun @ SV460 @ SY2684 @ SV797 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2326,plain,
! [SV798: $i,SV461: $i,SV86: $i] :
( ( ! [SY2685: $i,SY2686: $i,SY2687: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV86 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SY2685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SY2686 ) @ SY2687 @ SY2685 @ SV86 )
| ~ ( c_Limits_Otendsto @ SV798 @ SY2686 @ SY2687 @ SY2685 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2327,plain,
! [SV799: $i,SV462: $i,SV87: $i] :
( ( ! [SY2688: $i,SY2689: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV87 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SV799 @ SV87 @ SV87 @ SY2688 ) @ SY2689 @ SY2688 @ SV87 )
| ~ ( c_Limits_OZfun @ SV799 @ SY2689 @ SY2688 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2328,plain,
! [SV800: $i,SV463: $i,SV88: $i] :
( ( ! [SY2690: $i,SY2691: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV88 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SV800 @ SV88 @ SV88 @ SY2690 ) @ SY2691 @ SY2690 @ SV88 )
| ~ ( c_Limits_OZfun @ SV800 @ SY2691 @ SY2690 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2329,plain,
! [SV801: $i,SV464: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV89 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV464 ) @ SV801 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) ) )
| ( SV801
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
| ( SV464
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2330,plain,
! [SV802: $i,SV465: $i,SV90: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV465 ) @ SV802 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) ) )
| ( SV802
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2331,plain,
! [SV91: $i] :
( ( ( c_SEQ_OZseq @ SV91 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_ORe @ SV91 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2332,plain,
! [SV803: $i,SV466: $i,SV92: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ ( c_Series_Osuminf @ SV803 @ SV92 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ SV803 @ SV92 @ SV92 @ tc_nat ) @ SV92 ) )
| ~ ( c_Series_Osummable @ SV803 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2333,plain,
! [SV804: $i,SV467: $i,SV93: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV93 )
| ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ SV804 @ SV93 @ SV93 @ tc_nat ) @ SV93 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ ( c_Series_Osuminf @ SV804 @ SV93 ) ) )
| ~ ( c_Series_Osummable @ SV804 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2334,plain,
! [SV94: $i] :
( ( ( c_Series_Osummable @ SV94 @ tc_Complex_Ocomplex )
= $false )
| ( ( ( hAPP @ c_Complex_ORe @ ( c_Series_Osuminf @ SV94 @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_ORe @ SV94 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2335,plain,
! [SV805: $i,SV468: $i,SV95: $i] :
( ( ! [SY2692: $i,SY2693: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV95 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV805 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY2692 ) @ SY2693 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SY2692 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV805 ) @ SY2693 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2336,plain,
! [SV806: $i,SV469: $i,SV96: $i] :
( ( ! [SY2694: $i,SY2695: $i,SY2696: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV96 )
| ~ ( class_RealVector_Ometric__space @ SV469 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SY2694 @ SV96 @ SV96 @ SV469 ) @ SY2695 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SY2696 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SY2694 @ SY2695 @ SY2696 @ SV469 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2337,plain,
! [SV807: $i,SV470: $i,SV97: $i] :
( ( ! [SY2697: $i] :
( ~ ( class_RealVector_Ometric__space @ SV97 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SV470 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SV807 @ ( hAPP @ c_Complex_ORe @ SY2697 ) @ SV97 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV470 @ SV807 @ SY2697 @ SV97 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2338,plain,
! [SV808: $i,SV471: $i,SV98: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV98 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV98 ) @ SV471 @ SV98 @ SV98 @ SV98 ) @ SV808 @ SV98 )
| ~ ( c_Deriv_Odifferentiable @ SV471 @ SV808 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2339,plain,
! [SV809: $i,SV472: $i,SV99: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV99 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV99 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ SV472 ) @ SV809 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV472 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2340,plain,
! [SV810: $i,SV473: $i,SV100: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV100 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ SV473 ) @ SV810 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV810 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV473 ) ) )
| ( SV810
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2341,plain,
! [SV811: $i,SV474: $i,SV101: $i] :
( ( ! [SY2698: $i,SY2699: $i] :
( ~ ( class_RealVector_Ometric__space @ SV101 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SY2698 @ SY2699 @ SV474 @ SV101 )
| ( SV811 = SY2699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2342,plain,
! [SV812: $i,SV475: $i,SV102: $i] :
( ( ! [SY2700: $i,SY2701: $i] :
( ~ ( class_RealVector_Ometric__space @ SV102 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
| ( SV812 = SY2700 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SY2701 @ SY2700 @ SV475 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2343,plain,
! [SV476: $i,SV103: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV103 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ SV476 ) )
= SV476 )
| ( SV476
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2344,plain,
! [SV813: $i,SV477: $i,SV104: $i] :
( ( ! [SY2702: $i,SY2703: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV104 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ ( c_Finite__Set_Osetsum @ SV813 @ SY2702 @ SY2703 @ SV104 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ SV813 @ SV104 @ SV104 @ SY2703 ) @ SY2702 @ SY2703 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2345,plain,
! [SV814: $i,SV478: $i,SV105: $i] :
( ( ! [SY2704: $i,SY2705: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ ( c_Finite__Set_Osetsum @ SV814 @ SY2704 @ SY2705 @ SV105 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ SV814 @ SV105 @ SV105 @ SY2705 ) @ SY2704 @ SY2705 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2346,plain,
! [SV815: $i,SV480: $i,SV107: $i] :
( ( ! [SY2706: $i,SY2707: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
| ~ ( class_RealVector_Ometric__space @ SV480 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SY2706 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SY2707 ) @ SV480 @ SV107 )
| ( SY2707
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SY2706 @ SY2707 @ SV480 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2347,plain,
! [SV816: $i,SV481: $i,SV108: $i] :
( ( ! [SY2708: $i] :
( ~ ( class_RealVector_Ometric__space @ SV108 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV481 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SY2708 @ SV108 @ SV481 )
| ~ ( c_Lim_OisCont @ SV816 @ SY2708 @ SV108 @ SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2348,plain,
! [SV482: $i,SV109: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV109 ) )
= $true )
| ( ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ SV482 @ SV109 @ SV109 @ tc_nat ) @ SV109 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ ( c_Series_Osuminf @ SV482 @ SV109 ) ) )
| ~ ( c_Series_Osummable @ SV482 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2349,plain,
! [SV817: $i,SV483: $i,SV110: $i] :
( ( ! [SY2709: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ SV817 ) ) @ SY2709 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ SV817 ) @ SY2709 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2350,plain,
! [SV818: $i,SV484: $i,SV111: $i] :
( ( ! [SY2710: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ SV818 ) ) @ SY2710 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ SV818 ) @ SY2710 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2351,plain,
! [SV819: $i,SV485: $i,SV112: $i] :
( ( ! [SY2711: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ SY2711 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ SY2711 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2352,plain,
! [SV113: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV113 )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 @ tc_nat ) @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2353,plain,
! [SV820: $i,SV486: $i,SV114: $i] :
( ( ! [SY2712: $i,SY2713: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV114 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV114 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SY2712 ) @ SY2713 @ SV820 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SY2712 @ SY2713 @ SV820 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2354,plain,
! [SV115: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV115 )
= $false )
| ( ( c_Series_Osums @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2355,plain,
! [SV821: $i,SV487: $i,SV116: $i] :
( ( ! [SY2714: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV116 )
| ~ ( class_RealVector_Ometric__space @ SV487 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY2714 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SY2714 ) @ SV116 @ SV487 )
| ~ ( c_Lim_OisCont @ SV821 @ SY2714 @ SV116 @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2356,plain,
! [SV822: $i,SV488: $i,SV117: $i] :
( ( ! [SY2715: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV117 )
| ~ ( class_RealVector_Ometric__space @ SV488 )
| ( c_Lim_OisCont @ SV822 @ SY2715 @ SV117 @ SV488 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY2715 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SY2715 ) @ SV117 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2357,plain,
! [SV823: $i,SV489: $i,SV118: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV118 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SV489 @ SV118 @ SV118 @ SV118 ) @ SV823 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SV823 ) @ SV489 ) @ SV118 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2358,plain,
! [SV824: $i,SV490: $i,SV119: $i] :
( ( ! [SY2716: $i] :
( ~ ( class_RealVector_Ometric__space @ SV119 )
| ~ ( class_RealVector_Ometric__space @ SV490 )
| ( c_Lim_OisCont @ SV824 @ SY2716 @ SV119 @ SV490 )
| ~ ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2359,plain,
! [SV825: $i,SV491: $i,SV120: $i] :
( ( ! [SY2717: $i,SY2718: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV120 )
| ~ ( class_RealVector_Ometric__space @ SV491 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SY2717 @ SV120 @ SV120 @ SV491 ) @ SY2718 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SY2717 @ SY2718 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2360,plain,
! [SV826: $i,SV492: $i,SV121: $i] :
( ( ! [SY2719: $i,SY2720: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV121 )
| ~ ( class_RealVector_Ometric__space @ SV492 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SY2719 @ SV121 @ SV121 @ SV492 ) @ SY2720 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SY2719 @ SY2720 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2361,plain,
! [SV827: $i,SV493: $i,SV122: $i] :
( ( ! [SY2721: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV122 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV827 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SY2721 ) @ SV122 )
| ~ ( c_Series_Osums @ SV827 @ SY2721 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2362,plain,
! [SV828: $i,SV494: $i,SV124: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV124 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV124 ) @ SV494 ) @ SV828 @ SV124 @ SV124 @ tc_nat ) @ SV124 )
| ~ ( c_Series_Osummable @ SV828 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2363,plain,
! [SV829: $i,SV495: $i,SV125: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV125 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ SV829 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ SV829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2364,plain,
! [SV830: $i,SV496: $i,SV126: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV126 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ SV830 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ SV830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2365,plain,
! [SV831: $i,SV497: $i,SV127: $i] :
( ( ! [SY2722: $i,SY2723: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV127 )
| ~ ( class_RealVector_Ometric__space @ SV497 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SY2722 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SY2723 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SV831 @ SY2722 @ SY2723 @ SV497 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2366,plain,
! [SV128: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV128 )
= $false )
| ( ( ( c_Series_Osuminf @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ tc_nat ) @ SV128 )
= ( c_HOL_Ozero__class_Ozero @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2367,plain,
! [SV832: $i,SV498: $i,SV129: $i] :
( ( ! [SY2724: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV129 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV498 )
| ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SY2724 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
| ~ ( c_SEQ_OZseq @ SY2724 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2368,plain,
! [SV833: $i,SV499: $i,SV130: $i] :
( ( ! [SY2725: $i,SY2726: $i,SY2727: $i,SY2728: $i] :
( ~ ( class_RealVector_Ometric__space @ SV130 )
| ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2725 @ SY2726 @ SV130 @ SV499 @ SV833 ) @ SY2727 @ ( hAPP @ SY2725 @ SY2728 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SY2726 @ SY2727 @ SY2728 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SY2725 @ SY2728 @ SV130 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2369,plain,
! [SV834: $i,SV500: $i,SV131: $i] :
( ( ! [SY2729: $i,SY2730: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV131 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV131 )
| ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SY2729 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SY2730 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SY2729 @ SY2730 @ SV500 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2370,plain,
! [SV835: $i,SV501: $i,SV132: $i] :
( ( ( hAPP @ c_Complex_ORe @ ( c_Finite__Set_Osetsum @ SV132 @ SV501 @ SV835 @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_ORe @ SV132 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV835 ) @ SV501 @ SV835 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2371,plain,
! [SV836: $i,SV502: $i,SV133: $i] :
( ( ! [SY2731: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV133 )
| ~ ( class_Int_Onumber__ring @ SV133 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SY2731 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SY2731 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2372,plain,
! [SV837: $i,SV503: $i,SV134: $i] :
( ( ! [SY2732: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV134 )
| ~ ( class_Int_Onumber__ring @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SY2732 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SY2732 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2373,plain,
! [SV838: $i,SV504: $i,SV135: $i] :
( ( ! [SY2733: $i,SY2734: $i,SY2735: $i,SY2736: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV135 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2733 @ SY2734 @ SV135 @ SV504 @ SV838 ) @ SY2735 @ ( hAPP @ SY2733 @ SY2736 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SY2734 @ SY2735 @ SY2736 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SY2733 @ SV135 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2374,plain,
! [SV839: $i,SV505: $i,SV136: $i] :
( ( ! [SY2737: $i,SY2738: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV136 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SV839 @ SV136 @ SV136 @ SY2737 ) @ SY2738 @ SY2737 @ SV136 )
| ~ ( c_Limits_OZfun @ SV839 @ SY2738 @ SY2737 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2375,plain,
! [SV840: $i,SV506: $i,SV137: $i] :
( ( ! [SY2739: $i,SY2740: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV137 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SV840 @ SV137 @ SV137 @ SY2739 ) @ SY2740 @ SY2739 @ SV137 )
| ~ ( c_Limits_OZfun @ SV840 @ SY2740 @ SY2739 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2376,plain,
! [SV507: $i,SV138: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV138 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV138 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ SV507 ) )
= SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2000]) ).
thf(2377,plain,
! [SV841: $i,SV508: $i,SV139: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV139 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SV508 @ SV139 @ SV139 @ SV139 ) @ SV841 @ SV139 )
| ( ( hAPP @ SV508 @ SV841 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
| ~ ( c_Deriv_Odifferentiable @ SV508 @ SV841 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2378,plain,
! [SV842: $i,SV509: $i,SV140: $i] :
( ( ! [SY2741: $i,SY2742: $i,SY2743: $i,SY2744: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV140 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SY2741 @ SV509 @ SV140 @ SY2742 ) @ ( hAPP @ SV842 @ SY2743 ) @ SY2744 @ SY2742 @ SV140 )
| ~ ( c_Limits_Otendsto @ SY2741 @ SY2743 @ SY2744 @ SY2742 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2379,plain,
! [SV843: $i,SV510: $i,SV141: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV141 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SV510 ) @ SV843 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SV843 ) @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2380,plain,
! [SV142: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV142 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Ozero__class_Ozero @ SV142 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV142 ) )
= ( c_HOL_Ozero__class_Ozero @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2381,plain,
! [SV844: $i,SV511: $i,SV143: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SV511 ) @ SV844 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SV844 ) @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2382,plain,
! [SV845: $i,SV512: $i,SV144: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV144 )
| ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV144 ) @ SV512 @ SV144 @ SV144 @ SV144 ) @ SV845 @ SV144 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2383,plain,
! [SV846: $i,SV513: $i,SV145: $i] :
( ( ! [SY2745: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV145 )
| ~ ( class_RealVector_Ometric__space @ SV513 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SY2745 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV846 @ SY2745 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2384,plain,
! [SV847: $i,SV514: $i,SV146: $i] :
( ( ! [SY2746: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV146 )
| ~ ( class_RealVector_Ometric__space @ SV514 )
| ( c_Lim_OLIM @ SV847 @ SY2746 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SY2746 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2385,plain,
! [SV848: $i,SV515: $i,SV147: $i] :
( ( ! [SY2747: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ SY2747 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ SY2747 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2386,plain,
! [SV849: $i,SV516: $i,SV148: $i] :
( ( ! [SY2748: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ SV849 ) ) @ SY2748 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV849 ) @ SY2748 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2387,plain,
! [SV850: $i,SV517: $i,SV149: $i] :
( ( ! [SY2749: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV149 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV850 ) @ SY2749 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ SV850 ) ) @ SY2749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2388,plain,
! [SV851: $i,SV518: $i,SV150: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ SV518 ) ) @ SV851 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV518 ) @ SV851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2389,plain,
! [SV852: $i,SV519: $i,SV151: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV151 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV519 ) @ SV852 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV519 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV151 ) @ SV852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2390,plain,
! [SV853: $i,SV520: $i,SV152: $i] :
( ( ! [SY2750: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ SY2750 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ SY2750 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2391,plain,
! [SV854: $i,SV521: $i,SV153: $i] :
( ( ! [SY2751: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ SV854 ) ) @ SY2751 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV854 ) @ SY2751 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2392,plain,
! [SV855: $i,SV522: $i,SV154: $i] :
( ( ! [SY2752: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV154 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV855 ) @ SY2752 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ SV855 ) ) @ SY2752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2393,plain,
! [SV856: $i,SV523: $i,SV155: $i] :
( ( ! [SY2753: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV155 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SV856 ) ) @ SY2753 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SY2753 ) ) @ SV856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2394,plain,
! [SV857: $i,SV524: $i,SV156: $i] :
( ( ! [SY2754: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ SY2754 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ SY2754 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2395,plain,
! [SV858: $i,SV525: $i,SV157: $i] :
( ( ! [SY2755: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV858 ) ) @ SY2755 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV858 ) @ SY2755 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2396,plain,
! [SV859: $i,SV526: $i,SV158: $i] :
( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV158 ) @ SV526 ) @ SV859 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV158 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV158 ) @ SV526 ) ) @ SV859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2397,plain,
! [SV860: $i,SV527: $i,SV159: $i] :
( ( ! [SY2756: $i,SY2757: $i,SY2758: $i] :
( ( hAPP @ ( c_COMBC @ SV159 @ SV527 @ SV860 @ SY2756 @ SY2757 ) @ SY2758 )
= ( hAPP @ ( hAPP @ SV159 @ SY2758 ) @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2398,plain,
! [SV861: $i,SV528: $i,SV160: $i] :
( ( ! [SY2759: $i] :
( ( hAPP @ ( c_COMBK @ SV160 @ SV528 @ SV861 ) @ SY2759 )
= SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2399,plain,
! [SV862: $i,SV529: $i,SV161: $i] :
( ( ! [SY2760: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV161 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV529 )
| ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SY2760 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
| ~ ( c_Series_Osummable @ SY2760 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2400,plain,
! [SV863: $i,SV530: $i,SV162: $i] :
( ( ! [SY2761: $i,SY2762: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SY2761 ) @ SY2762 @ SV863 @ SV162 )
| ( SY2761
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SV530 @ SY2761 @ SY2762 @ SV863 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2401,plain,
! [SV531: $i,SV163: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV163 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV163 ) @ SV531 ) @ ( c_HOL_Ozero__class_Ozero @ SV163 ) )
= ( c_HOL_Ozero__class_Ozero @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2402,plain,
! [SV532: $i,SV164: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV164 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV532 )
= ( c_HOL_Ozero__class_Ozero @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2403,plain,
! [SV533: $i,SV165: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV165 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV165 ) @ SV533 ) @ ( c_HOL_Ozero__class_Ozero @ SV165 ) )
= ( c_HOL_Ozero__class_Ozero @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2404,plain,
! [SV534: $i,SV166: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV166 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV166 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV534 )
= ( c_HOL_Ozero__class_Ozero @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2405,plain,
! [SV864: $i,SV535: $i,SV167: $i] :
( ( ! [SY2763: $i,SY2764: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV167 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV535 ) @ SV864 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SY2763 ) @ SV864 ) ) @ SY2764 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ SV535 ) @ SY2763 ) ) @ SV864 ) ) @ SY2764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2406,plain,
! [SV536: $i,SV168: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV168 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ SV536 @ ( c_SEQ_Olim @ SV536 @ SV168 ) @ SV168 )
| ~ ( c_SEQ_Oconvergent @ SV536 @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2407,plain,
! [SV537: $i,SV169: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV169 ) )
= $true )
| ( ( ( c_SEQ_Oconvergent @ SV537 @ SV169 )
| ~ ( c_SEQ_OLIMSEQ @ SV537 @ ( c_SEQ_Olim @ SV537 @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2408,plain,
! [SV538: $i,SV170: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV170 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV170 ) @ SV538 ) ) @ SV538 )
= ( c_HOL_Ozero__class_Ozero @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2409,plain,
! [SV539: $i,SV171: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV171 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV171 ) @ SV539 ) ) @ SV539 )
= ( c_HOL_Ozero__class_Ozero @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2410,plain,
! [SV540: $i,SV172: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV172 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV172 ) @ SV540 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV172 ) @ SV540 ) )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2411,plain,
! [SV541: $i,SV173: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV173 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV173 ) @ SV541 ) ) @ SV541 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2412,plain,
! [SV865: $i,SV542: $i,SV174: $i] :
( ( ! [SY2765: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV174 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV542 )
| ( c_Lim_OisCont @ SV865 @ SY2765 @ SV174 @ SV542 )
| ~ ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2413,plain,
! [SV543: $i,SV175: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV175 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV175 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SV543 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SV543 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
| ~ ( c_Series_Osummable @ SV543 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2414,plain,
! [SV544: $i,SV176: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV176 ) )
= $true )
| ( ( ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ SV544 @ SV176 @ SV176 @ tc_nat ) @ SV176 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ ( c_SEQ_Olim @ SV544 @ SV176 ) ) )
| ~ ( c_SEQ_Oconvergent @ SV544 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2415,plain,
! [SV866: $i,SV545: $i,SV177: $i] :
( ( ! [SY2766: $i,SY2767: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV177 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ ( c_Finite__Set_Osetsum @ SV866 @ SY2766 @ SY2767 @ SV177 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ SV866 @ SV177 @ SV177 @ SY2767 ) @ SY2766 @ SY2767 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2416,plain,
! [SV178: $i] :
( ( ( c_Series_Osummable @ SV178 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_ORe @ SV178 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2417,plain,
! [SV867: $i,SV546: $i,SV179: $i] :
( ( ! [SY2768: $i,SY2769: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV179 )
| ~ ( class_RealVector_Ometric__space @ SV546 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SY2768 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SY2769 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV867 @ SY2768 @ SY2769 @ SV546 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2418,plain,
! [SV547: $i,SV180: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV180 ) )
= $true )
| ( ( ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV180 ) @ SV547 @ SV180 @ SV180 @ tc_nat ) @ SV180 )
| ~ ( c_SEQ_Oconvergent @ SV547 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2419,plain,
! [SV548: $i,SV181: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV181 ) )
= $true )
| ( ( ( c_SEQ_Oconvergent @ SV548 @ SV181 )
| ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV181 ) @ SV548 @ SV181 @ SV181 @ tc_nat ) @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2420,plain,
! [SV549: $i,SV182: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV182 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 ) @ SV182 @ SV182 )
| ( SV549
= ( c_HOL_Ozero__class_Ozero @ SV182 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2421,plain,
! [SV868: $i,SV550: $i,SV183: $i] :
( ( ! [SY2770: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV868 ) @ SY2770 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SV868 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SY2770 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2422,plain,
! [SV869: $i,SV551: $i,SV184: $i] :
( ( ! [SY2771: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ SV869 ) @ SY2771 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SV869 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SY2771 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2423,plain,
! [SV870: $i,SV552: $i,SV185: $i] :
( ( ! [SY2772: $i,SY2773: $i,SY2774: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV185 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV552 )
| ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SY2772 @ SV552 @ SV185 @ SY2773 ) @ SY2774 @ SY2773 @ SV185 )
| ~ ( c_Limits_OZfun @ SY2772 @ SY2774 @ SY2773 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2424,plain,
! [SV553: $i,SV186: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 ) )
= $true )
| ( ( c_Lim_OisUCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV186 ) @ SV553 @ SV186 @ SV186 @ SV186 ) @ SV186 @ SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2425,plain,
! [SV187: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV187 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV187 @ tc_nat ) @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2426,plain,
! [SV871: $i,SV554: $i,SV188: $i] :
( ( ! [SY2775: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV188 )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ SV554 @ SV188 @ SV188 @ SV871 ) @ SY2775 @ SV871 @ SV188 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ ( c_Finite__Set_Osetsum @ SV554 @ SY2775 @ SV871 @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2427,plain,
! [SV555: $i,SV189: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV189 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SV555 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SV555 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2428,plain,
! [SV556: $i,SV190: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV190 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SV556 )
= SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2429,plain,
! [SV557: $i,SV191: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV191 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SV557 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SV557 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2430,plain,
! [SV558: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV192 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV192 )
| ( SV558
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV558 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2431,plain,
! [SV559: $i,SV193: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SV559 )
= SV559 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2432,plain,
! [SV560: $i,SV194: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV194 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ ( c_HOL_Ozero__class_Ozero @ SV194 ) ) @ SV560 )
= SV560 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2433,plain,
! [SV561: $i,SV195: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV195 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV195 ) @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) )
= SV561 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2434,plain,
! [SV562: $i,SV196: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV196 ) @ ( c_HOL_Ozero__class_Ozero @ SV196 ) ) @ SV562 )
= SV562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2435,plain,
! [SV563: $i,SV197: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV197 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ SV563 ) )
= SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2436,plain,
! [SV564: $i,SV198: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV198 ) )
= $true )
| ( ( SV564
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ SV564 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2437,plain,
! [SV565: $i,SV199: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV199 ) )
= $true )
| ( ( SV565
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ SV565 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2438,plain,
! [SV566: $i,SV200: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV200 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ SV566 ) )
= SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2439,plain,
! [SV567: $i,SV201: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV201 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ SV567 ) )
= SV567 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2440,plain,
! [SV568: $i,SV202: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV202 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV202 )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SV568 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
| ~ ( c_Series_Osummable @ SV568 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2441,plain,
! [SV872: $i,SV569: $i,SV203: $i] :
( ( ! [SY2776: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV203 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ SY2776 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ SY2776 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2442,plain,
! [SV873: $i,SV570: $i,SV204: $i] :
( ( ! [SY2777: $i] :
( ~ ( class_RealVector_Oreal__algebra @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ SV873 ) ) @ SY2777 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ SV873 ) @ SY2777 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2443,plain,
! [SV874: $i,SV571: $i,SV205: $i] :
( ( ! [SY2778: $i] :
( ~ ( class_RealVector_Oreal__algebra @ SV205 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ SY2778 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ SY2778 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2444,plain,
! [SV875: $i,SV572: $i,SV206: $i] :
( ( ! [SY2779: $i] :
( ~ ( class_RealVector_Ometric__space @ SV206 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SY2779 @ SV206 @ SV572 )
| ~ ( c_Lim_OisCont @ SV875 @ SY2779 @ SV206 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2445,plain,
! [SV876: $i,SV573: $i,SV207: $i] :
( ( ! [SY2780: $i,SY2781: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV207 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV573 )
| ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SY2780 ) @ SY2781 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SY2780 ) @ ( hAPP @ SV876 @ SY2781 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2446,plain,
! [SV877: $i,SV574: $i,SV208: $i] :
( ( ! [SY2782: $i] :
( ~ ( class_RealVector_Ometric__space @ SV208 )
| ~ ( class_RealVector_Ometric__space @ SV574 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SY2782 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
| ~ ( c_SEQ_OCauchy @ SY2782 @ SV208 )
| ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2447,plain,
! [SV878: $i,SV575: $i,SV209: $i] :
( ( ! [SY2783: $i,SY2784: $i] :
( ~ ( class_RealVector_Ometric__space @ SV209 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV575 )
| ( c_Lim_OLIM @ SV878 @ SY2783 @ SY2784 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SY2783 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SY2784 @ SV575 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2448,plain,
! [SV879: $i,SV576: $i,SV210: $i] :
( ( ! [SY2785: $i,SY2786: $i] :
( ~ ( class_RealVector_Ometric__space @ SV210 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV576 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SY2785 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SY2786 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SV879 @ SY2785 @ SY2786 @ SV576 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2449,plain,
! [SV880: $i,SV577: $i,SV211: $i] :
( ( ! [SY2787: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV211 )
| ~ ( class_RealVector_Ometric__space @ SV577 )
| ( c_Lim_OLIM @ SV880 @ SY2787 @ ( hAPP @ SV880 @ SY2787 ) @ SV211 @ SV577 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SY2787 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SY2787 ) @ SV211 @ SV577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2450,plain,
! [SV881: $i,SV578: $i,SV212: $i] :
( ( ! [SY2788: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV212 )
| ~ ( class_RealVector_Ometric__space @ SV578 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SY2788 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SY2788 ) @ SV212 @ SV578 )
| ~ ( c_Lim_OLIM @ SV881 @ SY2788 @ ( hAPP @ SV881 @ SY2788 ) @ SV212 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2451,plain,
! [SV882: $i,SV579: $i,SV213: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV213 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV213 ) @ SV579 ) @ SV882 @ SV213 @ SV213 @ tc_nat ) @ SV213 )
| ~ ( c_Series_Osummable @ SV882 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2452,plain,
! [SV883: $i,SV580: $i,SV214: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV214 )
| ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV214 ) @ SV580 ) @ SV883 @ SV214 @ SV214 @ tc_nat ) @ SV214 )
| ~ ( c_Series_Osummable @ SV883 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2453,plain,
! [SV884: $i,SV581: $i,SV215: $i] :
( ( ! [SY2789: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV215 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV884 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SY2789 ) @ SV215 )
| ~ ( c_Series_Osums @ SV884 @ SY2789 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2454,plain,
! [SV885: $i,SV582: $i,SV216: $i] :
( ( ! [SY2790: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV885 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SY2790 ) @ SV216 )
| ~ ( c_Series_Osums @ SV885 @ SY2790 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2455,plain,
! [SV886: $i,SV583: $i,SV217: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV217 )
| ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 @ SV583 ) @ SV886 @ SV583 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2456,plain,
! [SV887: $i,SV584: $i,SV218: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV218 )
| ( c_Series_Osummable @ SV584 @ SV218 )
| ~ ( c_Series_Osums @ SV584 @ SV887 @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2457,plain,
! [SV888: $i,SV585: $i,SV219: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV219 )
| ( c_Series_Osummable @ SV585 @ SV219 )
| ~ ( c_Series_Osums @ SV585 @ SV888 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2458,plain,
! [SV889: $i,SV586: $i,SV220: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV220 )
| ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV220 ) @ SV586 ) @ SV889 @ SV220 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2459,plain,
! [SV890: $i,SV587: $i,SV221: $i] :
( ( ! [SY2791: $i,SY2792: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV221 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SV890 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SY2791 ) @ SY2792 @ SV890 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV587 @ SY2791 @ SY2792 @ SV890 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2460,plain,
! [SV891: $i,SV590: $i,SV224: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV224 )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 @ SV590 ) @ SV891 @ SV590 @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2461,plain,
! [SV591: $i,SV225: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV225 ) )
= $true )
| ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV225 ) @ SV591 ) )
= ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2462,plain,
! [SV892: $i,SV592: $i,SV226: $i] :
( ( ! [SY2793: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV226 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ SY2793 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ SY2793 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2463,plain,
! [SV893: $i,SV593: $i,SV227: $i] :
( ( ! [SY2794: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV227 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ SY2794 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ SY2794 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2464,plain,
! [SV894: $i,SV594: $i,SV228: $i] :
( ( ! [SY2795: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ SY2795 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ SY2795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2465,plain,
! [SV595: $i,SV229: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV229 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV229 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SV595 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
| ~ ( c_SEQ_OZseq @ SV595 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2466,plain,
! [SV895: $i,SV596: $i,SV230: $i] :
( ( ! [SY2796: $i] :
( ~ ( class_RealVector_Otopological__space @ SV230 )
| ( c_Limits_Otendsto @ ( c_COMBK @ SV596 @ SV230 @ SV895 ) @ SV596 @ SY2796 @ SV895 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2467,plain,
! [SV896: $i,SV597: $i,SV231: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV231 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SV597 ) @ SV896 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SV896 ) @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2468,plain,
! [SV897: $i,SV599: $i,SV233: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SV599 ) @ SV897 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SV897 ) @ SV599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2469,plain,
! [SV898: $i,SV600: $i,SV234: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV234 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV600 ) @ SV898 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV898 ) @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2470,plain,
! [SV235: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV235 )
= $false )
| ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV235 ) @ ( c_HOL_Ozero__class_Ozero @ SV235 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2471,plain,
! [SV899: $i,SV601: $i,SV236: $i] :
( ( ! [SY2797: $i] :
( ~ ( class_RealVector_Ometric__space @ SV236 )
| ~ ( class_RealVector_Ometric__space @ SV601 )
| ( c_Lim_OLIM @ ( c_COMBK @ SV899 @ SV236 @ SV601 ) @ SY2797 @ SV899 @ SV601 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2472,plain,
! [SV900: $i,SV602: $i,SV237: $i] :
( ( ! [SY2798: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV237 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV237 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SV602 @ SV900 @ SY2798 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SV602 @ tc_RealDef_Oreal @ SV237 @ SY2798 ) @ SV900 @ SY2798 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2473,plain,
! [SV603: $i,SV238: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV238 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ SV603 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ SV603 ) ) )
| ( SV603
= ( c_HOL_Ozero__class_Ozero @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2474,plain,
! [SV604: $i,SV239: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV239 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) ) @ SV604 )
= ( c_HOL_Ozero__class_Ozero @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2475,plain,
! [SV605: $i,SV240: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV240 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV240 ) @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV240 ) )
= ( c_HOL_Ozero__class_Ozero @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2476,plain,
! [SV606: $i,SV241: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV241 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV241 ) @ ( c_HOL_Ozero__class_Ozero @ SV241 ) ) @ SV606 )
= ( c_HOL_Ozero__class_Ozero @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2477,plain,
! [SV607: $i,SV242: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV242 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV242 ) @ ( c_HOL_Ozero__class_Ozero @ SV242 ) ) @ SV607 )
= ( c_HOL_Ozero__class_Ozero @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2478,plain,
! [SV608: $i,SV243: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV243 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV243 ) @ SV608 ) @ ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2479,plain,
! [SV609: $i,SV244: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV244 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV244 ) @ SV609 ) @ ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2480,plain,
! [SV610: $i,SV245: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV245 ) @ ( c_HOL_Ozero__class_Ozero @ SV245 ) ) @ SV610 )
= ( c_HOL_Ozero__class_Ozero @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2481,plain,
! [SV611: $i,SV246: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV246 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) ) @ SV611 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2482,plain,
! [SV612: $i,SV247: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV247 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV247 ) @ SV612 ) @ ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2483,plain,
! [SV613: $i,SV248: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV248 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV248 ) @ ( c_HOL_Ozero__class_Ozero @ SV248 ) ) @ SV613 )
= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2484,plain,
! [SV614: $i,SV249: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV249 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV249 ) @ SV614 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2485,plain,
! [SV901: $i,SV615: $i,SV250: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV250 )
| ( c_Series_Osummable @ ( c_COMBB @ SV615 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV901 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV250 @ tc_nat ) @ SV250 )
| ~ ( c_Series_Osummable @ SV615 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2486,plain,
! [SV902: $i,SV616: $i,SV251: $i] :
( ( ! [SY2799: $i,SY2800: $i,SY2801: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV251 )
| ~ ( class_RealVector_Ometric__space @ SV616 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SY2799 @ SV251 @ SV251 @ SV616 ) @ SY2800 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SY2801 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SY2799 @ SY2800 @ SY2801 @ SV616 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2487,plain,
! [SV903: $i,SV617: $i,SV252: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV252 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV252 ) @ SV617 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ SV903 ) @ SV617 ) )
= SV903 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2488,plain,
! [SV904: $i,SV618: $i,SV253: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV253 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV253 ) @ SV618 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ SV618 ) @ SV904 ) )
= SV904 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2489,plain,
! [SV905: $i,SV619: $i,SV254: $i] :
( ( ! [SY2802: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ SV254 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV619 ) @ ( hAPP @ c_Complex_ORe @ SV905 ) @ SY2802 @ SV619 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV254 @ SV905 @ SY2802 @ SV619 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2490,plain,
! [SV906: $i,SV620: $i,SV255: $i] :
( ( ! [SY2803: $i,SY2804: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV255 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV620 )
| ( c_Series_Osums @ ( c_COMBB @ SV906 @ SY2803 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SY2804 ) @ SV620 )
| ~ ( c_Series_Osums @ SY2803 @ SY2804 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2491,plain,
! [SV621: $i,SV256: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV256 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ SV621 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
| ~ ( c_Series_Osummable @ SV621 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2492,plain,
! [SV907: $i,SV622: $i,SV257: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV257 )
| ( SV622
= ( c_Series_Osuminf @ SV907 @ SV257 ) )
| ~ ( c_Series_Osums @ SV907 @ SV622 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2493,plain,
! [SV908: $i,SV623: $i,SV258: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV258 )
| ( ( c_Series_Osuminf @ SV623 @ SV258 )
= SV908 )
| ~ ( c_Series_Osums @ SV623 @ SV908 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2494,plain,
! [SV624: $i,SV259: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ SV259 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SV624 ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Series_Osums @ SV259 @ SV624 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2121]) ).
thf(2495,plain,
! [SV260: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV260 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV260 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV260 ) @ ( c_HOL_Ozero__class_Ozero @ SV260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2496,plain,
! [SV625: $i,SV262: $i] :
( ( ( ~ ( class_SEQ_Ocomplete__space @ SV262 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ SV625 @ SV262 )
| ~ ( c_SEQ_Oconvergent @ SV625 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2497,plain,
! [SV626: $i,SV263: $i] :
( ( ( ~ ( class_SEQ_Ocomplete__space @ SV263 ) )
= $true )
| ( ( ( c_SEQ_Oconvergent @ SV626 @ SV263 )
| ~ ( c_SEQ_OCauchy @ SV626 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2498,plain,
! [SV627: $i,SV264: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV264 ) )
= $true )
| ( ( c_Lim_OisUCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV264 ) @ SV627 ) @ SV264 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2499,plain,
! [SV628: $i,SV265: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV265 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ SV628 @ SV265 )
| ~ ( c_SEQ_Oconvergent @ SV628 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2500,plain,
! [SV266: $i] :
( ( ( c_SEQ_OCauchy @ SV266 @ tc_RealDef_Oreal )
= $false )
| ( ( c_SEQ_Oconvergent @ SV266 @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2501,plain,
! [SV909: $i,SV629: $i,SV267: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV267 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SV629 ) ) @ SV909 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ SV629 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SV909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2502,plain,
! [SV910: $i,SV630: $i,SV268: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV268 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV630 @ SV268 @ SV268 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV910 ) @ SV268 )
| ~ ( c_Series_Osums @ SV630 @ SV910 @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2503,plain,
! [SV269: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV269 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV269 ) @ ( c_HOL_Ozero__class_Ozero @ SV269 ) )
= ( c_HOL_Ozero__class_Ozero @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2504,plain,
! [SV270: $i] :
( ( ( class_OrderedGroup_Oordered__ab__group__add @ SV270 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV270 ) @ ( c_HOL_Ozero__class_Ozero @ SV270 ) )
= ( c_HOL_Ozero__class_Ozero @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2505,plain,
! [SV911: $i,SV631: $i,SV271: $i] :
( ( ! [SY2805: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV271 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV631 )
| ( c_Lim_OLIM @ SV911 @ SY2805 @ ( hAPP @ SV911 @ SY2805 ) @ SV271 @ SV631 )
| ~ ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2506,plain,
! [SV912: $i,SV632: $i,SV272: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV272 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV272 ) @ SV632 ) @ SV912 @ SV272 @ SV272 @ tc_nat ) @ SV272 )
| ~ ( c_SEQ_OZseq @ SV912 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2507,plain,
! [SV913: $i,SV633: $i,SV273: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV273 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV273 ) @ SV633 ) @ SV913 @ SV273 @ SV273 @ tc_nat ) @ SV273 )
| ~ ( c_SEQ_OZseq @ SV913 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2508,plain,
! [SV634: $i,SV274: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV274 ) )
= $true )
| ( ( ( c_Series_Osums @ SV634 @ ( c_Series_Osuminf @ SV634 @ SV274 ) @ SV274 )
| ~ ( c_Series_Osummable @ SV634 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2509,plain,
! [SV635: $i,SV275: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV275 ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV635 @ SV275 )
| ( c_Series_Osums @ SV635 @ ( c_Series_Osuminf @ SV635 @ SV275 ) @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2510,plain,
! [SV914: $i,SV636: $i,SV276: $i] :
( ( ! [SY2806: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV276 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV636 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SY2806 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
| ~ ( c_SEQ_OCauchy @ SY2806 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2511,plain,
! [SV915: $i,SV637: $i,SV277: $i] :
( ( ! [SY2807: $i] :
( ~ ( class_RealVector_Ometric__space @ SV277 )
| ~ ( class_RealVector_Ometric__space @ SV637 )
| ( c_Lim_OisCont @ SV915 @ SY2807 @ SV277 @ SV637 )
| ~ ( c_Lim_OLIM @ SV915 @ SY2807 @ ( hAPP @ SV915 @ SY2807 ) @ SV277 @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2512,plain,
! [SV916: $i,SV638: $i,SV278: $i] :
( ( ! [SY2808: $i] :
( ~ ( class_RealVector_Ometric__space @ SV278 )
| ~ ( class_RealVector_Ometric__space @ SV638 )
| ( c_Lim_OLIM @ SV916 @ SY2808 @ ( hAPP @ SV916 @ SY2808 ) @ SV278 @ SV638 )
| ~ ( c_Lim_OisCont @ SV916 @ SY2808 @ SV278 @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2513,plain,
! [SV917: $i,SV639: $i,SV279: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV279 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV639 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2514,plain,
! [SV918: $i,SV640: $i,SV280: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV280 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SV640 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SV918 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2515,plain,
! [SV919: $i,SV641: $i,SV281: $i] :
( ( ! [SY2809: $i,SY2810: $i,SY2811: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV281 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SY2809 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SY2810 ) @ SY2811 @ SY2809 @ SV281 )
| ~ ( c_Limits_Otendsto @ SV919 @ SY2810 @ SY2811 @ SY2809 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2516,plain,
! [SV920: $i,SV642: $i,SV282: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV282 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV282 ) @ SV642 ) @ SV920 @ SV282 @ SV282 @ tc_nat ) @ SV282 )
| ~ ( c_SEQ_OCauchy @ SV920 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2517,plain,
! [SV283: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV283 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV283 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV283 ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV283 ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV283 ) ) )
= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2518,plain,
! [SV921: $i,SV644: $i,SV285: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV285 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV285 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SV921 ) @ SV285 )
| ~ ( c_Series_Osums @ SV644 @ SV921 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2519,plain,
! [SV922: $i,SV645: $i,SV286: $i] :
( ( ! [SY2812: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV286 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV645 )
| ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SY2812 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SY2812 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
| ~ ( c_Series_Osummable @ SY2812 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2520,plain,
! [SV923: $i,SV646: $i,SV287: $i] :
( ( ! [SY2813: $i] :
( ~ ( class_RealVector_Ometric__space @ SV287 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV646 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SY2813 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SV923 @ SY2813 @ SV287 @ SV646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2521,plain,
! [SV647: $i,SV288: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV288 ) )
= $true )
| ( ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV288 ) @ SV647 ) @ SV288 @ SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2522,plain,
! [SV924: $i,SV648: $i,SV289: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV289 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ SV648 ) @ SV924 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SV924 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SV648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2523,plain,
! [SV925: $i,SV649: $i,SV290: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV290 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ SV649 ) @ SV925 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SV649 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SV925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2524,plain,
! [SV650: $i,SV292: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ SV292 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SV650 ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV292 @ SV650 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2525,plain,
! [SV926: $i,SV651: $i,SV293: $i] :
( ( ! [SY2814: $i,SY2815: $i,SY2816: $i] :
( ( c_Set_Oimage @ SV293 @ ( c_Set_Oimage @ SV651 @ SV926 @ SY2814 @ SY2815 ) @ SY2815 @ SY2816 )
= ( c_Set_Oimage @ ( c_COMBB @ SV293 @ SV651 @ SY2815 @ SY2816 @ SY2814 ) @ SV926 @ SY2814 @ SY2816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2526,plain,
! [SV927: $i,SV652: $i,SV294: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV294 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV652 @ SV294 @ SV294 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV927 ) @ SV294 )
| ~ ( c_SEQ_OLIMSEQ @ SV652 @ SV927 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2527,plain,
! [SV928: $i,SV653: $i,SV295: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV295 )
| ( c_SEQ_OLIMSEQ @ SV653 @ SV928 @ SV295 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV653 @ SV295 @ SV295 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV928 ) @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2528,plain,
! [SV296: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ ( c_COMBB @ v_s @ ( c_COMBB @ v_f____ @ v_ga____ @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ SV296 @ tc_RealDef_Oreal )
= $false )
| ( v_thesis____ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2529,plain,
! [SV929: $i,SV654: $i,SV297: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV297 )
| ( c_SEQ_Oconvergent @ SV654 @ SV297 )
| ~ ( c_SEQ_OLIMSEQ @ SV654 @ SV929 @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2530,plain,
! [SV930: $i,SV655: $i,SV298: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV298 )
| ( c_SEQ_Oconvergent @ SV655 @ SV298 )
| ~ ( c_SEQ_OLIMSEQ @ SV655 @ SV930 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2531,plain,
! [SV931: $i,SV656: $i,SV299: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV299 )
| ( SV656 = SV931 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV656 @ SV299 @ tc_nat ) @ SV931 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2532,plain,
! [SV932: $i,SV657: $i,SV300: $i] :
( ( ! [SY2817: $i,SY2818: $i,SY2819: $i,SY2820: $i] :
( ~ ( class_RealVector_Ometric__space @ SV300 )
| ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SY2817 @ SY2818 @ SV300 @ SV657 @ SV932 ) @ SY2819 @ ( hAPP @ SY2817 @ SY2820 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SY2818 @ SY2819 @ SY2820 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SY2817 @ SY2820 @ ( hAPP @ SY2817 @ SY2820 ) @ SV300 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2533,plain,
! [SV658: $i,SV301: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV301 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ SV658 @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV301 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV301 ) @ SV658 @ SV301 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2161]) ).
thf(2534,plain,
! [SV659: $i,SV302: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV302 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV302 ) @ SV659 @ SV302 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV659 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2535,plain,
! [SV933: $i,SV660: $i,SV303: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV303 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV660 @ SV303 @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV933 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV660 @ SV933 @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2536,plain,
! [SV934: $i,SV662: $i,SV305: $i] :
( ( ! [SY2821: $i] :
( ~ ( class_RealVector_Ometric__space @ SV305 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV662 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV934 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SY2821 @ SV305 )
| ~ ( c_SEQ_OLIMSEQ @ SV662 @ SY2821 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2537,plain,
! [SV935: $i,SV663: $i,SV306: $i] :
( ( ! [SY2822: $i] :
( ~ ( class_RealVector_Ometric__space @ SV306 )
| ( c_SEQ_OLIMSEQ @ SV663 @ SV935 @ SV306 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV663 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2822 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SV935 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2538,plain,
! [SV936: $i,SV664: $i,SV307: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV307 )
| ( ( c_SEQ_Olim @ SV664 @ SV307 )
= SV936 )
| ~ ( c_SEQ_OLIMSEQ @ SV664 @ SV936 @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2539,plain,
! [SV937: $i,SV665: $i,SV308: $i] :
( ( ! [SY2823: $i] :
( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ SV308 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV665 ) @ ( hAPP @ c_Complex_OIm @ SV937 ) @ SY2823 @ SV665 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV308 @ SV937 @ SY2823 @ SV665 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2540,plain,
! [SV309: $i] :
( ( ( c_SEQ_OZseq @ SV309 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ c_Complex_OIm @ SV309 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2541,plain,
! [SV666: $i,SV310: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV310 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV666 @ SV310 @ tc_nat ) @ SV666 @ SV310 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2542,plain,
! [SV667: $i,SV311: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV311 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV667 @ SV311 @ tc_nat ) @ SV667 @ SV311 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2543,plain,
! [SV938: $i,SV668: $i,SV312: $i] :
( ( ! [SY2824: $i,SY2825: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV312 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV668 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SY2824 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SY2825 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SY2824 @ SY2825 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2544,plain,
! [SV939: $i,SV669: $i,SV313: $i] :
( ( ! [SY2826: $i,SY2827: $i,SY2828: $i] :
( ~ ( class_RealVector_Ometric__space @ SV313 )
| ~ ( class_RealVector_Ometric__space @ SV669 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SY2826 @ SV669 @ SV313 @ tc_nat ) @ SY2827 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SY2826 @ SY2828 @ SV669 )
| ( ( hAPP @ SY2826 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SY2826 @ SY2828 @ SV669 ) )
= SY2828 )
| ~ ( c_Lim_OLIM @ SV939 @ SY2828 @ SY2827 @ SV669 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2545,plain,
! [SV940: $i,SV670: $i,SV314: $i] :
( ( ( hAPP @ c_Complex_OIm @ ( c_Finite__Set_Osetsum @ SV314 @ SV670 @ SV940 @ tc_Complex_Ocomplex ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ c_Complex_OIm @ SV314 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV940 ) @ SV670 @ SV940 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2546,plain,
! [SV941: $i,SV671: $i,SV315: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV315 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV315 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SV941 ) @ SV315 )
| ~ ( c_SEQ_OLIMSEQ @ SV671 @ SV941 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2547,plain,
! [SV672: $i,SV316: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ SV316 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SV672 ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV316 @ SV672 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2548,plain,
! [SV317: $i] :
( ( ( c_SEQ_OCauchy @ SV317 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ c_Complex_OIm @ SV317 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2549,plain,
! [SV673: $i,SV318: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ SV318 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SV673 ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Series_Osums @ SV318 @ SV673 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2550,plain,
! [SV942: $i,SV674: $i,SV319: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ SV319 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV674 ) @ SV942 @ SV674 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV319 @ SV942 @ SV674 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2551,plain,
! [SV943: $i,SV675: $i,SV320: $i] :
( ( ! [SY2829: $i,SY2830: $i,SY2831: $i] :
( ~ ( class_RealVector_Ometric__space @ SV320 )
| ~ ( class_RealVector_Ometric__space @ SV675 )
| ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SY2829 @ SY2830 @ SV943 @ SV675 @ SV320 ) @ SY2831 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SY2829 @ ( hAPP @ SY2830 @ SY2831 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SY2830 @ SY2831 @ SV320 @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2552,plain,
! [SV944: $i,SV676: $i,SV321: $i] :
( ( ! [SY2832: $i] :
( ~ ( class_RealVector_Ometric__space @ SV321 )
| ( SV676 = SV944 )
| ~ ( c_SEQ_OLIMSEQ @ SY2832 @ SV944 @ SV321 )
| ~ ( c_SEQ_OLIMSEQ @ SY2832 @ SV676 @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2553,plain,
! [SV945: $i,SV677: $i,SV322: $i] :
( ( ! [SY2833: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV322 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV945 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SY2833 ) @ SV322 )
| ~ ( c_SEQ_OLIMSEQ @ SV945 @ SY2833 @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2554,plain,
! [SV946: $i,SV678: $i,SV323: $i] :
( ( ! [SY2834: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV323 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SY2834 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV946 @ SY2834 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SY2834 ) @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2555,plain,
! [SV947: $i,SV679: $i,SV324: $i] :
( ( ! [SY2835: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV324 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV947 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SY2835 ) @ SV324 )
| ~ ( c_SEQ_OLIMSEQ @ SV947 @ SY2835 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2556,plain,
! [SV948: $i,SV680: $i,SV326: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV326 )
| ( c_SEQ_OCauchy @ SV680 @ SV326 )
| ~ ( c_SEQ_OLIMSEQ @ SV680 @ SV948 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2557,plain,
! [SV949: $i,SV681: $i,SV327: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV327 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV681 @ c_Suc @ tc_nat @ SV327 @ tc_nat ) @ SV949 @ SV327 )
| ~ ( c_SEQ_OLIMSEQ @ SV681 @ SV949 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2558,plain,
! [SV950: $i,SV682: $i,SV328: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV328 )
| ( c_SEQ_OLIMSEQ @ SV682 @ SV950 @ SV328 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV682 @ c_Suc @ tc_nat @ SV328 @ tc_nat ) @ SV950 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2559,plain,
! [SV951: $i,SV683: $i,SV329: $i] :
( ( ! [SY2836: $i,SY2837: $i,SY2838: $i] :
( ( hAPP @ ( c_COMBB @ SV329 @ SV683 @ SV951 @ SY2836 @ SY2837 ) @ SY2838 )
= ( hAPP @ SV329 @ ( hAPP @ SV683 @ SY2838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2560,plain,
! [SV952: $i,SV684: $i,SV330: $i] :
( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV330 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV684 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV952 ) @ SV330 )
| ( SV952
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ~ ( c_SEQ_OLIMSEQ @ SV684 @ SV952 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2561,plain,
! [SV953: $i,SV685: $i,SV331: $i] :
( ( ! [SY2839: $i] :
( ~ ( class_RealVector_Ometric__space @ SV331 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SV685 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SV953 @ ( hAPP @ c_Complex_OIm @ SY2839 ) @ SV331 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV685 @ SV953 @ SY2839 @ SV331 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2562,plain,
! [SV332: $i] :
( ( ( c_Series_Osummable @ SV332 @ tc_Complex_Ocomplex )
= $false )
| ( ( ( hAPP @ c_Complex_OIm @ ( c_Series_Osuminf @ SV332 @ tc_Complex_Ocomplex ) )
= ( c_Series_Osuminf @ ( c_COMBB @ c_Complex_OIm @ SV332 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2563,plain,
! [SV333: $i] :
( ( ( c_Series_Osummable @ SV333 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ c_Complex_OIm @ SV333 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2564,plain,
! [SV686: $i,SV334: $i] :
( ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV334 @ SV686 ) )
= $true )
| ( ( ~ ( class_Lattices_Oboolean__algebra @ SV686 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2565,plain,
! [SV954: $i,SV687: $i,SV335: $i] :
( ( ! [SY2840: $i,SY2841: $i,SY2842: $i] :
( ( hAPP @ ( c_COMBC @ SV335 @ SV687 @ SV954 @ SY2840 @ SY2841 ) @ SY2842 )
= ( hAPP @ ( hAPP @ SV335 @ SY2842 ) @ SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2566,plain,
! [SV955: $i,SV688: $i,SV336: $i] :
( ( ! [SY2843: $i,SY2844: $i,SY2845: $i] :
( ( hAPP @ ( c_COMBB @ SV336 @ SV688 @ SV955 @ SY2843 @ SY2844 ) @ SY2845 )
= ( hAPP @ SV336 @ ( hAPP @ SV688 @ SY2845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2567,plain,
! [SV956: $i,SV690: $i,SV338: $i] :
( ( ( SV338 = SV690 )
| ~ ( c_fequal @ SV338 @ SV690 @ SV956 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2568,plain,
! [SV957: $i,SV691: $i,SV339: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV339 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV691 ) @ SV691 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV957 ) @ SV957 ) )
| ( SV691
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SV957 ) )
| ( SV691 = SV957 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2569,plain,
! [SV958: $i,SV692: $i,SV340: $i] :
( ( ! [SY2846: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV692 ) @ SV958 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY2846 ) @ SV958 ) )
| ( SV692 = SY2846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2570,plain,
! [SV959: $i,SV693: $i,SV342: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV342 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SV693 ) @ SV959 )
!= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV693
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV959
= ( c_HOL_Ozero__class_Ozero @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2571,plain,
! [SV960: $i,SV694: $i,SV343: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SV960 ) )
| ( SV694 = SV960 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2572,plain,
! [SV695: $i,SV344: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV344 ) )
= $true )
| ( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV344 ) @ SV695 )
!= ( c_HOL_Ozero__class_Ozero @ SV344 ) )
| ( SV695
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2573,plain,
! [SV961: $i,SV696: $i,SV345: $i] :
( ( ! [SY2847: $i,SY2848: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV345 )
| ~ ( class_Int_Onumber__ring @ SV345 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2847 ) @ SY2848 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SY2848 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SY2847 ) @ SV961 ) ) )
| ( SV961 = SY2848 )
| ( SV696 = SY2847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2574,plain,
! [SV697: $i,SV346: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV346 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV346 ) @ SV697 ) @ SV697 )
!= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
| ( SV697
= ( c_HOL_Ozero__class_Ozero @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2575,plain,
! [SV962: $i,SV698: $i,SV347: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV347 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV962 ) )
| ( SV698 = SV962 )
| ( SV962
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2576,plain,
! [SV963: $i,SV699: $i,SV348: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV348 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ SV699 ) @ SV963 )
!= ( c_HOL_Ozero__class_Ozero @ SV348 ) )
| ( SV699
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV348 ) @ SV963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2577,plain,
! [SV964: $i,SV700: $i,SV349: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV349 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV700 ) @ SV700 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV964 ) @ SV964 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
| ( SV700
= ( c_HOL_Ozero__class_Ozero @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2578,plain,
! [SV965: $i,SV701: $i,SV350: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SV701 ) @ SV965 )
!= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV965
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2579,plain,
! [SV966: $i,SV702: $i,SV351: $i] :
( ( ! [SY2849: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SV351 @ SV702 )
!= ( c_Complex_Ocomplex_OComplex @ SV966 @ SY2849 ) )
| ( SV702 = SY2849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2580,plain,
! [SV967: $i,SV703: $i,SV352: $i] :
( ( ! [SY2850: $i,SY2851: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV352 )
| ~ ( class_Int_Onumber__ring @ SV352 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2850 ) @ SY2851 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SY2851 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SY2850 ) @ SV967 ) ) )
| ( SV967 = SY2851 )
| ( SV703 = SY2850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2581,plain,
! [SV704: $i,SV353: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV353 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV353 ) @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ SV353 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2582,plain,
! [SV968: $i,SV705: $i,SV354: $i] :
( ( ! [SY2852: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV354 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV968 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SY2852 ) )
| ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV968 = SY2852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2583,plain,
! [SV969: $i,SV706: $i,SV355: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SV706 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SV969 ) )
| ( SV706 = SV969 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2584,plain,
! [SV707: $i,SV356: $i] :
( ( ( ( hAPP @ c_Suc @ SV356 )
!= ( hAPP @ c_Suc @ SV707 ) )
= $true )
| ( ( SV356 = SV707 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2585,plain,
! [SV970: $i,SV708: $i,SV357: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV357 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SV708 ) @ SV970 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV970
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV708
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2586,plain,
! [SV971: $i,SV709: $i,SV358: $i] :
( ( ! [SY2853: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV971 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SY2853 ) )
| ( SV971 = SY2853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2587,plain,
! [SV972: $i,SV710: $i,SV359: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV359 ) @ SV710 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV972 ) @ SV710 ) )
| ( SV359 = SV972 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2588,plain,
! [SV973: $i,SV711: $i,SV360: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV360 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV711 ) @ SV973 )
!= ( c_HOL_Ozero__class_Ozero @ SV360 ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV360 ) @ SV711 )
= SV973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2589,plain,
! [SV974: $i,SV712: $i,SV361: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV361 )
| ~ ( class_Int_Onumber__ring @ SV361 )
| ( SV712
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2590,plain,
! [SV975: $i,SV713: $i,SV362: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV362 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SV713 ) @ SV975 )
!= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV975
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2591,plain,
! [SV714: $i,SV363: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV363 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV363 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SV714 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( SV714
= ( c_HOL_Ozero__class_Ozero @ SV363 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2592,plain,
! [SV976: $i,SV715: $i,SV364: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV364 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV715 ) @ SV715 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV976 ) @ SV976 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
| ( SV976
= ( c_HOL_Ozero__class_Ozero @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2593,plain,
! [SV977: $i,SV716: $i,SV365: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV365 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV716 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV977 ) )
| ( SV716 = SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2594,plain,
! [SV978: $i,SV717: $i,SV366: $i] :
( ( ! [SY2854: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV366 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SV978 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SY2854 ) @ SV978 ) )
| ( SV978
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SV717 = SY2854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2595,plain,
! [SV718: $i,SV367: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV367 ) )
= $true )
| ( ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV367 ) @ SV718 )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2596,plain,
! [SV719: $i,SV368: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ SV368 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV368 ) @ SV719 )
!= SV719 )
| ( SV719
= ( c_HOL_Ozero__class_Ozero @ SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2597,plain,
! [SV720: $i,SV369: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV369 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV369 ) @ SV720 )
!= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
| ( SV720
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2598,plain,
! [SV979: $i,SV721: $i,SV370: $i] :
( ( ! [SY2855: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ SV370 @ SV721 )
!= ( c_Complex_Ocomplex_OComplex @ SV979 @ SY2855 ) )
| ( SV370 = SV979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2599,plain,
! [SV722: $i,SV371: $i] :
( ( ( ( hAPP @ c_Complex_OIm @ SV371 )
!= ( hAPP @ c_Complex_OIm @ SV722 ) )
= $true )
| ( ( ( ( hAPP @ c_Complex_ORe @ SV371 )
!= ( hAPP @ c_Complex_ORe @ SV722 ) )
| ( SV371 = SV722 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2600,plain,
! [SV723: $i,SV372: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV372 ) )
= $true )
| ( ( ( ( c_HOL_Ozero__class_Ozero @ SV372 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV372 ) @ SV723 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV372 )
= SV723 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2601,plain,
! [SV980: $i,SV724: $i,SV373: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV373 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV980 ) )
| ( SV724 = SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2602,plain,
! [SV981: $i,SV725: $i,SV374: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV374 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV725 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV981 ) )
| ( SV725 = SV981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2603,plain,
! [SV982: $i,SV726: $i,SV375: $i] :
( ( ! [SY2856: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV375 )
| ~ ( class_Int_Onumber__ring @ SV375 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SY2856 ) )
| ( SV982 = SY2856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2604,plain,
! [SV983: $i,SV727: $i,SV376: $i] :
( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV376 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV727 )
!= ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV983 ) )
| ( SV727 = SV983 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2605,plain,
! [SV984: $i,SV728: $i,SV377: $i] :
( ( ! [SY2857: $i,SY2858: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SY2857 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SY2858 ) ) )
| ( SY2857 = SY2858 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2606,plain,
! [SV985: $i,SV729: $i,SV379: $i] :
( ( ! [SY2859: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV985 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SY2859 ) )
| ( SV985 = SY2859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2607,plain,
! [SV730: $i,SV380: $i] :
( ( ( ( hAPP @ c_Suc @ SV380 )
!= ( hAPP @ c_Suc @ SV730 ) )
= $true )
| ( ( SV380 = SV730 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2608,plain,
! [SV986: $i,SV731: $i,SV381: $i] :
( ( ! [SY2860: $i,SY2861: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV381 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SY2860 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SY2861 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SY2860 )
= SY2861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2609,plain,
! [SV987: $i,SV732: $i,SV382: $i] :
( ( ! [SY2862: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV382 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV987 ) @ SY2862 ) )
!= SV987 )
| ( SV732
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SY2862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2610,plain,
! [SV988: $i,SV733: $i,SV383: $i,SV2: $i] :
( ( ! [SY2863: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV2 )
| ~ ( class_RealVector_Ometric__space @ SV383 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SY2863 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SV733 @ SY2863 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2611,plain,
! [SV989: $i,SV734: $i,SV384: $i,SV3: $i] :
( ( ! [SY2864: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV3 )
| ~ ( class_RealVector_Ometric__space @ SV384 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SY2864 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SV734 @ SY2864 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2612,plain,
! [SV990: $i,SV735: $i,SV385: $i,SV4: $i] :
( ( ! [SY2865: $i,SY2866: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV4 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SV990 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SY2865 ) @ SV990 ) @ SY2866 @ SV735 @ SV4 )
| ~ ( c_Limits_Otendsto @ SV385 @ SY2865 @ SY2866 @ SV735 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2613,plain,
! [SV991: $i,SV736: $i,SV386: $i,SV5: $i] :
( ( ! [SY2867: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV5 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SV736 ) @ SV991 @ SV736 @ SV5 @ SV5 ) @ SY2867 @ SV736 @ SV5 )
| ~ ( c_Limits_OZfun @ SV386 @ SY2867 @ SV736 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2614,plain,
! [SV992: $i,SV737: $i,SV387: $i,SV6: $i] :
( ( ! [SY2868: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV6 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SV737 ) @ SV992 @ SV737 @ SV6 @ SV6 ) @ SY2868 @ SV737 @ SV6 )
| ~ ( c_Limits_OZfun @ SV387 @ SY2868 @ SV737 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2615,plain,
! [SV993: $i,SV738: $i,SV388: $i,SV7: $i] :
( ( ! [SY2869: $i,SY2870: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV7 )
| ~ ( class_RealVector_Ometric__space @ SV388 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SY2869 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SY2870 ) @ SV993 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SY2869 @ SY2870 @ SV388 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2616,plain,
! [SV994: $i,SV739: $i,SV389: $i,SV8: $i] :
( ( ! [SY2871: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV8 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ ( c_Finite__Set_Osetsum @ SV389 @ SV739 @ SV994 @ SV8 ) ) @ SY2871 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ SV389 @ SV8 @ ( tc_fun @ SV8 @ SV8 ) @ SV994 ) @ SY2871 @ SV994 @ SV8 @ SV8 ) @ SV739 @ SV994 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2617,plain,
! [SV995: $i,SV740: $i,SV390: $i,SV9: $i] :
( ( ! [SY2872: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ ( c_Finite__Set_Osetsum @ SV390 @ SV740 @ SV995 @ SV9 ) ) @ SY2872 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ SV390 @ SV9 @ ( tc_fun @ SV9 @ SV9 ) @ SV995 ) @ SY2872 @ SV995 @ SV9 @ SV9 ) @ SV740 @ SV995 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2618,plain,
! [SV996: $i,SV741: $i,SV391: $i,SV10: $i] :
( ( ! [SY2873: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ ( c_Finite__Set_Osetsum @ SV391 @ SV741 @ SV996 @ tc_RealDef_Oreal ) ) @ SY2873 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ SV391 @ tc_RealDef_Oreal @ ( tc_fun @ SV10 @ SV10 ) @ SV996 ) @ SY2873 @ SV996 @ SV10 @ SV10 ) @ SV741 @ SV996 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2619,plain,
! [SV997: $i,SV742: $i,SV392: $i,SV11: $i] :
( ( ! [SY2874: $i,SY2875: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV11 )
| ~ ( class_RealVector_Ometric__space @ SV392 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SY2874 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SY2875 ) @ SV997 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SY2874 @ SY2875 @ SV392 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2620,plain,
! [SV998: $i,SV743: $i,SV393: $i,SV12: $i] :
( ( ! [SY2876: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV12 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SV743 ) @ SV998 @ SV743 @ SV12 @ SV12 ) @ SY2876 @ SV743 @ SV12 )
| ~ ( c_Limits_OZfun @ SV393 @ SY2876 @ SV743 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2621,plain,
! [SV999: $i,SV744: $i,SV394: $i,SV13: $i] :
( ( ! [SY2877: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV13 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SV744 ) @ SV999 @ SV744 @ SV13 @ SV13 ) @ SY2877 @ SV744 @ SV13 )
| ~ ( c_Limits_OZfun @ SV394 @ SY2877 @ SV744 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2622,plain,
! [SV1000: $i,SV745: $i,SV395: $i,SV14: $i] :
( ( ! [SY2878: $i,SY2879: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV14 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SV1000 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SY2878 ) @ SV1000 ) @ SY2879 @ SV745 @ SV14 )
| ~ ( c_Limits_Otendsto @ SV395 @ SY2878 @ SY2879 @ SV745 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2623,plain,
! [SV396: $i,SV15: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV15 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV15 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SV396 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
| ~ ( c_SEQ_OCauchy @ SV396 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2624,plain,
! [SV397: $i,SV16: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV16 )
= $false )
| ( ( c_Lim_OisUCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV16 ) @ SV397 ) @ SV16 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2625,plain,
! [SV398: $i,SV17: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV17 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV17 ) @ SV398 @ SV17 @ SV17 @ tc_nat ) @ SV17 )
| ~ ( c_SEQ_OZseq @ SV398 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2626,plain,
! [SV1001: $i,SV746: $i,SV399: $i,SV18: $i] :
( ( ! [SY2880: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ SY2880 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ SY2880 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2627,plain,
! [SV1002: $i,SV747: $i,SV400: $i,SV19: $i] :
( ( ! [SY2881: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ SV747 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SY2881 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV747 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SY2881 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2628,plain,
! [SV1003: $i,SV748: $i,SV401: $i,SV20: $i] :
( ( ! [SY2882: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV748 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV1003 ) @ SY2882 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV1003 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV748 ) @ SY2882 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2629,plain,
! [SV402: $i,SV21: $i] :
( ( ( class_SEQ_Obanach @ SV21 )
= $false )
| ( ( ( c_Series_Osummable @ SV402 @ SV21 )
| ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV21 ) @ SV402 @ SV21 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2630,plain,
! [SV23: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV23 ) )
= $true )
| ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV23 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2631,plain,
! [SV749: $i,SV403: $i,SV24: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV24 ) )
= $true )
| ( ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SV749 ) @ SV24 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2632,plain,
! [SV1004: $i,SV750: $i,SV404: $i,SV25: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV25 )
| ~ ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
| ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2633,plain,
! [SV751: $i,SV405: $i,SV26: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV26 ) )
= $true )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBK @ SV405 @ SV26 @ SV26 ) @ SV751 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2634,plain,
! [SV406: $i,SV27: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV27 )
= $false )
| ( ( ( c_SEQ_OZseq @ SV406 @ SV27 )
| ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV27 ) @ SV406 @ SV27 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2635,plain,
! [SV407: $i,SV28: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV28 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV28 ) @ SV407 @ SV28 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OZseq @ SV407 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2636,plain,
! [SV752: $i,SV408: $i,SV29: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV29 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV29 ) @ SV408 ) @ SV752 @ SV29 @ SV29 @ tc_nat ) @ SV29 )
| ~ ( c_SEQ_OCauchy @ SV752 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2637,plain,
! [SV753: $i,SV409: $i,SV30: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV30 ) )
= $true )
| ( ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV30 ) @ SV409 ) @ SV753 @ SV30 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2638,plain,
! [SV1005: $i,SV754: $i,SV410: $i,SV31: $i] :
( ( ! [SY2883: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV31 )
| ~ ( class_RealVector_Ometric__space @ SV410 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SY2883 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SV754 @ SY2883 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2639,plain,
! [SV1006: $i,SV755: $i,SV411: $i,SV32: $i] :
( ( ! [SY2884: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV32 )
| ~ ( class_RealVector_Ometric__space @ SV411 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SY2884 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SV755 @ SY2884 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2640,plain,
! [SV412: $i,SV33: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV33 )
= $false )
| ( ( ( SV412
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ~ ( c_SEQ_OZseq @ ( c_COMBK @ SV412 @ SV33 @ tc_nat ) @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2641,plain,
! [SV1007: $i,SV756: $i,SV413: $i,SV34: $i] :
( ( ! [SY2885: $i,SY2886: $i] :
( ~ ( class_RealVector_Ometric__space @ SV34 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
| ( SV756 = SV1007 )
| ~ ( c_Lim_OLIM @ SY2885 @ SY2886 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SY2885 @ SY2886 @ SV756 @ SV413 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2642,plain,
! [SV1008: $i,SV757: $i,SV414: $i,SV35: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV35 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SV414 @ SV35 @ tc_RealDef_Oreal @ SV757 ) @ SV1008 @ SV757 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV414 @ SV1008 @ SV757 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2643,plain,
! [SV1009: $i,SV758: $i,SV415: $i,SV36: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV36 )
| ( c_Limits_OZfun @ SV415 @ SV758 @ SV1009 @ SV36 )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SV415 @ SV36 @ tc_RealDef_Oreal @ SV1009 ) @ SV758 @ SV1009 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2644,plain,
! [SV1010: $i,SV759: $i,SV416: $i,SV37: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV37 )
| ~ ( class_RealVector_Ometric__space @ SV416 )
| ( c_Lim_OisCont @ ( c_COMBK @ SV759 @ SV416 @ SV37 ) @ SV1010 @ SV37 @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2645,plain,
! [SV1011: $i,SV760: $i,SV417: $i,SV38: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV38 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SV417 @ SV38 @ SV38 @ SV760 ) @ SV1011 @ SV760 @ SV38 )
| ~ ( c_Limits_OZfun @ SV417 @ SV1011 @ SV760 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2646,plain,
! [SV761: $i,SV418: $i,SV39: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV39 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ SV418 ) @ SV761 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ SV418 ) ) @ SV761 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2647,plain,
! [SV762: $i,SV419: $i,SV40: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV40 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ SV762 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ SV762 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2648,plain,
! [SV763: $i,SV420: $i,SV41: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV41 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV420 )
| ( c_Lim_OisUCont @ SV763 @ SV41 @ SV420 )
| ~ ( c_RealVector_Obounded__linear @ SV763 @ SV41 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2649,plain,
! [SV764: $i,SV421: $i,SV42: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV42 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV42 ) @ SV421 ) @ SV764 @ SV42 @ SV42 @ tc_nat ) @ SV42 )
| ~ ( c_SEQ_OZseq @ SV764 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2650,plain,
! [SV765: $i,SV422: $i,SV43: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV43 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV43 ) @ SV422 ) @ SV765 @ SV43 @ SV43 @ tc_nat ) @ SV43 )
| ~ ( c_SEQ_OZseq @ SV765 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2651,plain,
! [SV766: $i,SV423: $i,SV44: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV44 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SV766 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SV766 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2652,plain,
! [SV767: $i,SV424: $i,SV45: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ SV45 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV424 ) @ SV767 @ SV424 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV45 @ SV767 @ SV424 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2653,plain,
! [SV768: $i,SV425: $i,SV47: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV47 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV425 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV47 ) @ SV425 ) ) @ SV768 ) )
= SV768 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2654,plain,
! [SV1012: $i,SV769: $i,SV426: $i,SV48: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV48 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV48 )
| ~ ( class_RealVector_Ometric__space @ SV426 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2655,plain,
! [SV770: $i,SV427: $i,SV49: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV49 ) )
= $true )
| ( ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SV770 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SV770 ) @ SV49 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2656,plain,
! [SV428: $i,SV50: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV50 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV50 ) @ SV428 ) @ SV428 )
= SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2657,plain,
! [SV1013: $i,SV771: $i,SV429: $i,SV51: $i] :
( ( ! [SY2887: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV51 )
| ~ ( class_RealVector_Ometric__space @ SV429 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SY2887 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SV1013 @ SY2887 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2658,plain,
! [SV1014: $i,SV772: $i,SV430: $i,SV52: $i] :
( ( ! [SY2888: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV52 )
| ~ ( class_RealVector_Ometric__space @ SV430 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SY2888 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SV1014 @ SY2888 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2659,plain,
! [SV431: $i,SV53: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV53 )
= $false )
| ( ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV53 ) @ SV431 ) @ SV53 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2660,plain,
! [SV54: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV54 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV54 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2295]) ).
thf(2661,plain,
! [SV1015: $i,SV773: $i,SV432: $i,SV56: $i] :
( ( ! [SY2889: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV56 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SV773 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV1015 ) @ SY2889 @ SV773 @ SV56 )
| ~ ( c_Limits_Otendsto @ SV432 @ SV1015 @ SY2889 @ SV773 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2662,plain,
! [SV1016: $i,SV774: $i,SV433: $i,SV57: $i] :
( ( ! [SY2890: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV57 )
| ( c_Limits_Otendsto @ SV433 @ SV774 @ SV1016 @ SY2890 @ SV57 )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SY2890 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV774 ) @ SV1016 @ SY2890 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2663,plain,
! [SV1017: $i,SV775: $i,SV434: $i,SV58: $i] :
( ( ! [SY2891: $i,SY2892: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV58 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV434 )
| ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SY2891 @ SV434 @ SV58 @ SV775 ) @ SY2892 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SY2891 @ SY2892 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2664,plain,
! [SV435: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV59 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ SV435 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ SV435 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2665,plain,
! [SV436: $i,SV61: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV61 )
= $false )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV61 ) @ SV436 @ SV61 @ SV61 @ tc_nat ) @ SV61 )
| ~ ( c_Series_Osummable @ SV436 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2666,plain,
! [SV1018: $i,SV776: $i,SV437: $i,SV62: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV62 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ SV776 ) ) @ SV1018 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV776 ) @ SV1018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2667,plain,
! [SV1019: $i,SV777: $i,SV438: $i,SV63: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SV777 ) ) @ SV1019 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SV1019 ) ) @ SV777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2668,plain,
! [SV1020: $i,SV778: $i,SV439: $i,SV64: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV64 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ SV778 ) ) @ SV1020 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV778 ) @ SV1020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2669,plain,
! [SV1021: $i,SV779: $i,SV440: $i,SV65: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV779 ) @ SV1021 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ SV779 ) ) @ SV1021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2670,plain,
! [SV1022: $i,SV780: $i,SV441: $i,SV66: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ SV1022 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ SV1022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2671,plain,
! [SV1023: $i,SV781: $i,SV442: $i,SV67: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV781 ) @ SV1023 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ SV781 ) ) @ SV1023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2672,plain,
! [SV1024: $i,SV782: $i,SV443: $i,SV68: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV443 ) @ SV782 ) ) @ SV1024 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV443 ) @ SV1024 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV782 ) @ SV1024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2673,plain,
! [SV1025: $i,SV783: $i,SV444: $i,SV69: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV783 ) @ SV1025 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SV783 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SV1025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2674,plain,
! [SV1026: $i,SV784: $i,SV445: $i,SV70: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV70 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV784 ) @ SV1026 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SV784 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SV1026 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2675,plain,
! [SV1027: $i,SV785: $i,SV446: $i,SV71: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV71 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV446 ) @ SV785 ) ) @ SV1027 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV446 ) @ SV1027 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV785 ) @ SV1027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2676,plain,
! [SV1028: $i,SV786: $i,SV447: $i,SV72: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV72 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV447 ) @ SV786 ) ) @ SV1028 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV447 ) @ SV1028 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV786 ) @ SV1028 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2677,plain,
! [SV1029: $i,SV787: $i,SV448: $i,SV73: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV73 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV787 ) @ SV1029 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SV787 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SV1029 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2678,plain,
! [SV1030: $i,SV788: $i,SV449: $i,SV74: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV74 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV449 ) @ SV788 ) ) @ SV1030 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV449 ) @ SV1030 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV788 ) @ SV1030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2679,plain,
! [SV1031: $i,SV789: $i,SV450: $i,SV75: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV75 )
| ~ ( class_HOL_Ozero @ SV75 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2680,plain,
! [SV790: $i,SV451: $i,SV76: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV76 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ ( c_Series_Osuminf @ SV790 @ SV76 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ SV790 @ SV76 @ SV76 @ tc_nat ) @ SV76 ) )
| ~ ( c_Series_Osummable @ SV790 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2681,plain,
! [SV1032: $i,SV791: $i,SV452: $i,SV77: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV77 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV452 ) @ SV791 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV1032 ) @ SV791 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV452 ) @ SV1032 ) ) @ SV791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2682,plain,
! [SV453: $i,SV78: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV78 )
= $false )
| ( ( c_RealVector_Obounded__linear @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV78 ) @ SV453 @ SV78 @ SV78 @ SV78 ) @ SV78 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2683,plain,
! [SV792: $i,SV454: $i,SV79: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV79 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ SV454 ) ) @ SV792 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ SV454 ) @ SV792 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2684,plain,
! [SV793: $i,SV455: $i,SV80: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV80 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ SV455 ) ) @ SV793 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ SV455 ) @ SV793 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2685,plain,
! [SV794: $i,SV456: $i,SV81: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV81 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ SV794 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ SV794 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2321]) ).
thf(2686,plain,
! [SV795: $i,SV457: $i,SV82: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV82 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ SV795 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ SV795 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2687,plain,
! [SV458: $i,SV83: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV83 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SV458 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV83 ) @ SV458 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV83 ) @ SV458 ) @ SV458 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2688,plain,
! [SV796: $i,SV459: $i,SV84: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV84 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SV459 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SV796 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ SV459 ) @ SV796 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2689,plain,
! [SV1033: $i,SV797: $i,SV460: $i,SV85: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV85 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV85 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SV1033 @ SV797 @ SV85 )
| ~ ( c_Limits_OZfun @ SV460 @ SV1033 @ SV797 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2690,plain,
! [SV1034: $i,SV798: $i,SV461: $i,SV86: $i] :
( ( ! [SY2893: $i,SY2894: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV86 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SV1034 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SY2893 ) @ SY2894 @ SV1034 @ SV86 )
| ~ ( c_Limits_Otendsto @ SV798 @ SY2893 @ SY2894 @ SV1034 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2691,plain,
! [SV1035: $i,SV799: $i,SV462: $i,SV87: $i] :
( ( ! [SY2895: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV87 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SV799 @ SV87 @ SV87 @ SV1035 ) @ SY2895 @ SV1035 @ SV87 )
| ~ ( c_Limits_OZfun @ SV799 @ SY2895 @ SV1035 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2692,plain,
! [SV1036: $i,SV800: $i,SV463: $i,SV88: $i] :
( ( ! [SY2896: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV88 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SV800 @ SV88 @ SV88 @ SV1036 ) @ SY2896 @ SV1036 @ SV88 )
| ~ ( c_Limits_OZfun @ SV800 @ SY2896 @ SV1036 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2693,plain,
! [SV801: $i,SV464: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV89 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV464 ) @ SV801 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) ) )
| ( SV801
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
| ( SV464
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2694,plain,
! [SV802: $i,SV465: $i,SV90: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV465 ) @ SV802 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) ) )
| ( SV802
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2695,plain,
! [SV803: $i,SV466: $i,SV92: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV92 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ ( c_Series_Osuminf @ SV803 @ SV92 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ SV803 @ SV92 @ SV92 @ tc_nat ) @ SV92 ) )
| ~ ( c_Series_Osummable @ SV803 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2696,plain,
! [SV804: $i,SV467: $i,SV93: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV93 ) )
= $true )
| ( ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ SV804 @ SV93 @ SV93 @ tc_nat ) @ SV93 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ ( c_Series_Osuminf @ SV804 @ SV93 ) ) )
| ~ ( c_Series_Osummable @ SV804 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2697,plain,
! [SV1037: $i,SV805: $i,SV468: $i,SV95: $i] :
( ( ! [SY2897: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV95 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV805 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1037 ) @ SY2897 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV1037 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV805 ) @ SY2897 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2698,plain,
! [SV1038: $i,SV806: $i,SV469: $i,SV96: $i] :
( ( ! [SY2898: $i,SY2899: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV96 )
| ~ ( class_RealVector_Ometric__space @ SV469 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SY2898 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SY2899 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SV1038 @ SY2898 @ SY2899 @ SV469 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2699,plain,
! [SV1039: $i,SV807: $i,SV470: $i,SV97: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV97 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SV470 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SV807 @ ( hAPP @ c_Complex_ORe @ SV1039 ) @ SV97 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV470 @ SV807 @ SV1039 @ SV97 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2700,plain,
! [SV808: $i,SV471: $i,SV98: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV98 ) )
= $true )
| ( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV98 ) @ SV471 @ SV98 @ SV98 @ SV98 ) @ SV808 @ SV98 )
| ~ ( c_Deriv_Odifferentiable @ SV471 @ SV808 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2701,plain,
! [SV809: $i,SV472: $i,SV99: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV99 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV99 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ SV472 ) @ SV809 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV472 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV809 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2702,plain,
! [SV810: $i,SV473: $i,SV100: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV100 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ SV473 ) @ SV810 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV810 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV473 ) ) )
| ( SV810
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2703,plain,
! [SV1040: $i,SV811: $i,SV474: $i,SV101: $i] :
( ( ! [SY2900: $i] :
( ~ ( class_RealVector_Ometric__space @ SV101 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SY2900 @ SV474 @ SV101 )
| ( SV811 = SY2900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2704,plain,
! [SV1041: $i,SV812: $i,SV475: $i,SV102: $i] :
( ( ! [SY2901: $i] :
( ~ ( class_RealVector_Ometric__space @ SV102 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
| ( SV812 = SV1041 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SY2901 @ SV1041 @ SV475 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2705,plain,
! [SV476: $i,SV103: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV103 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ SV476 ) )
= SV476 )
| ( SV476
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2706,plain,
! [SV1042: $i,SV813: $i,SV477: $i,SV104: $i] :
( ( ! [SY2902: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV104 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ ( c_Finite__Set_Osetsum @ SV813 @ SV1042 @ SY2902 @ SV104 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ SV813 @ SV104 @ SV104 @ SY2902 ) @ SV1042 @ SY2902 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2707,plain,
! [SV1043: $i,SV814: $i,SV478: $i,SV105: $i] :
( ( ! [SY2903: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ ( c_Finite__Set_Osetsum @ SV814 @ SV1043 @ SY2903 @ SV105 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ SV814 @ SV105 @ SV105 @ SY2903 ) @ SV1043 @ SY2903 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2708,plain,
! [SV1044: $i,SV815: $i,SV480: $i,SV107: $i] :
( ( ! [SY2904: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
| ~ ( class_RealVector_Ometric__space @ SV480 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SY2904 ) @ SV480 @ SV107 )
| ( SY2904
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SY2904 @ SV480 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2709,plain,
! [SV1045: $i,SV816: $i,SV481: $i,SV108: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV108 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV481 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SV1045 @ SV108 @ SV481 )
| ~ ( c_Lim_OisCont @ SV816 @ SV1045 @ SV108 @ SV481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2710,plain,
! [SV482: $i,SV109: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV109 )
= $false )
| ( ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ SV482 @ SV109 @ SV109 @ tc_nat ) @ SV109 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ ( c_Series_Osuminf @ SV482 @ SV109 ) ) )
| ~ ( c_Series_Osummable @ SV482 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2711,plain,
! [SV1046: $i,SV817: $i,SV483: $i,SV110: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ SV817 ) ) @ SV1046 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ SV817 ) @ SV1046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2712,plain,
! [SV1047: $i,SV818: $i,SV484: $i,SV111: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ SV818 ) ) @ SV1047 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ SV818 ) @ SV1047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2713,plain,
! [SV1048: $i,SV819: $i,SV485: $i,SV112: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ SV1048 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ SV1048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2714,plain,
! [SV1049: $i,SV820: $i,SV486: $i,SV114: $i] :
( ( ! [SY2905: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV114 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV114 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SY2905 @ SV820 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SV1049 @ SY2905 @ SV820 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2715,plain,
! [SV1050: $i,SV821: $i,SV487: $i,SV116: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV116 )
| ~ ( class_RealVector_Ometric__space @ SV487 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1050 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SV1050 ) @ SV116 @ SV487 )
| ~ ( c_Lim_OisCont @ SV821 @ SV1050 @ SV116 @ SV487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2716,plain,
! [SV1051: $i,SV822: $i,SV488: $i,SV117: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV117 )
| ~ ( class_RealVector_Ometric__space @ SV488 )
| ( c_Lim_OisCont @ SV822 @ SV1051 @ SV117 @ SV488 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV1051 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SV1051 ) @ SV117 @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2717,plain,
! [SV823: $i,SV489: $i,SV118: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV118 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SV489 @ SV118 @ SV118 @ SV118 ) @ SV823 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SV823 ) @ SV489 ) @ SV118 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2718,plain,
! [SV1052: $i,SV824: $i,SV490: $i,SV119: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV119 )
| ~ ( class_RealVector_Ometric__space @ SV490 )
| ( c_Lim_OisCont @ SV824 @ SV1052 @ SV119 @ SV490 )
| ~ ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2719,plain,
! [SV1053: $i,SV825: $i,SV491: $i,SV120: $i] :
( ( ! [SY2906: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV120 )
| ~ ( class_RealVector_Ometric__space @ SV491 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SY2906 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SV1053 @ SY2906 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2720,plain,
! [SV1054: $i,SV826: $i,SV492: $i,SV121: $i] :
( ( ! [SY2907: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV121 )
| ~ ( class_RealVector_Ometric__space @ SV492 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SY2907 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SV1054 @ SY2907 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2721,plain,
! [SV1055: $i,SV827: $i,SV493: $i,SV122: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV122 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV827 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV1055 ) @ SV122 )
| ~ ( c_Series_Osums @ SV827 @ SV1055 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2722,plain,
! [SV828: $i,SV494: $i,SV124: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV124 ) )
= $true )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV124 ) @ SV494 ) @ SV828 @ SV124 @ SV124 @ tc_nat ) @ SV124 )
| ~ ( c_Series_Osummable @ SV828 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2723,plain,
! [SV829: $i,SV495: $i,SV125: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV125 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ SV829 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ SV829 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2724,plain,
! [SV830: $i,SV496: $i,SV126: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV126 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ SV830 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ SV830 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2725,plain,
! [SV1056: $i,SV831: $i,SV497: $i,SV127: $i] :
( ( ! [SY2908: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV127 )
| ~ ( class_RealVector_Ometric__space @ SV497 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SY2908 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SV831 @ SV1056 @ SY2908 @ SV497 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2726,plain,
! [SV1057: $i,SV832: $i,SV498: $i,SV129: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV129 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV498 )
| ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
| ~ ( c_SEQ_OZseq @ SV1057 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2727,plain,
! [SV1058: $i,SV833: $i,SV499: $i,SV130: $i] :
( ( ! [SY2909: $i,SY2910: $i,SY2911: $i] :
( ~ ( class_RealVector_Ometric__space @ SV130 )
| ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SY2909 @ SV130 @ SV499 @ SV833 ) @ SY2910 @ ( hAPP @ SV1058 @ SY2911 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SY2909 @ SY2910 @ SY2911 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SY2911 @ SV130 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2728,plain,
! [SV1059: $i,SV834: $i,SV500: $i,SV131: $i] :
( ( ! [SY2912: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV131 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV131 )
| ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SY2912 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SY2912 @ SV500 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2729,plain,
! [SV1060: $i,SV836: $i,SV502: $i,SV133: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV133 )
| ~ ( class_Int_Onumber__ring @ SV133 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2730,plain,
! [SV1061: $i,SV837: $i,SV503: $i,SV134: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV134 )
| ~ ( class_Int_Onumber__ring @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2731,plain,
! [SV1062: $i,SV838: $i,SV504: $i,SV135: $i] :
( ( ! [SY2913: $i,SY2914: $i,SY2915: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV135 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SY2913 @ SV135 @ SV504 @ SV838 ) @ SY2914 @ ( hAPP @ SV1062 @ SY2915 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SY2913 @ SY2914 @ SY2915 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2732,plain,
! [SV1063: $i,SV839: $i,SV505: $i,SV136: $i] :
( ( ! [SY2916: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV136 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SV839 @ SV136 @ SV136 @ SV1063 ) @ SY2916 @ SV1063 @ SV136 )
| ~ ( c_Limits_OZfun @ SV839 @ SY2916 @ SV1063 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2733,plain,
! [SV1064: $i,SV840: $i,SV506: $i,SV137: $i] :
( ( ! [SY2917: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV137 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SV840 @ SV137 @ SV137 @ SV1064 ) @ SY2917 @ SV1064 @ SV137 )
| ~ ( c_Limits_OZfun @ SV840 @ SY2917 @ SV1064 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2734,plain,
! [SV507: $i,SV138: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV138 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV138 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ SV507 ) )
= SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2735,plain,
! [SV841: $i,SV508: $i,SV139: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV139 ) )
= $true )
| ( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SV508 @ SV139 @ SV139 @ SV139 ) @ SV841 @ SV139 )
| ( ( hAPP @ SV508 @ SV841 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
| ~ ( c_Deriv_Odifferentiable @ SV508 @ SV841 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2736,plain,
! [SV1065: $i,SV842: $i,SV509: $i,SV140: $i] :
( ( ! [SY2918: $i,SY2919: $i,SY2920: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV140 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SY2918 ) @ ( hAPP @ SV842 @ SY2919 ) @ SY2920 @ SY2918 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SY2919 @ SY2920 @ SY2918 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2737,plain,
! [SV843: $i,SV510: $i,SV141: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV141 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SV510 ) @ SV843 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SV843 ) @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2738,plain,
! [SV844: $i,SV511: $i,SV143: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SV511 ) @ SV844 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SV844 ) @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2739,plain,
! [SV845: $i,SV512: $i,SV144: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV144 ) )
= $true )
| ( ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV144 ) @ SV512 @ SV144 @ SV144 @ SV144 ) @ SV845 @ SV144 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2740,plain,
! [SV1066: $i,SV846: $i,SV513: $i,SV145: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV145 )
| ~ ( class_RealVector_Ometric__space @ SV513 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV846 @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2741,plain,
! [SV1067: $i,SV847: $i,SV514: $i,SV146: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV146 )
| ~ ( class_RealVector_Ometric__space @ SV514 )
| ( c_Lim_OLIM @ SV847 @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2742,plain,
! [SV1068: $i,SV848: $i,SV515: $i,SV147: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ SV1068 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ SV1068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2743,plain,
! [SV1069: $i,SV849: $i,SV516: $i,SV148: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ SV849 ) ) @ SV1069 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV849 ) @ SV1069 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2744,plain,
! [SV1070: $i,SV850: $i,SV517: $i,SV149: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV149 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV850 ) @ SV1070 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ SV850 ) ) @ SV1070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2745,plain,
! [SV1071: $i,SV853: $i,SV520: $i,SV152: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ SV1071 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ SV1071 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2746,plain,
! [SV1072: $i,SV854: $i,SV521: $i,SV153: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ SV854 ) ) @ SV1072 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV854 ) @ SV1072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2747,plain,
! [SV1073: $i,SV855: $i,SV522: $i,SV154: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV154 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV855 ) @ SV1073 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ SV855 ) ) @ SV1073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2748,plain,
! [SV1074: $i,SV856: $i,SV523: $i,SV155: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV155 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SV856 ) ) @ SV1074 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SV1074 ) ) @ SV856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2749,plain,
! [SV1075: $i,SV857: $i,SV524: $i,SV156: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ SV1075 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ SV1075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2750,plain,
! [SV1076: $i,SV858: $i,SV525: $i,SV157: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV858 ) ) @ SV1076 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV858 ) @ SV1076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2751,plain,
! [SV859: $i,SV526: $i,SV158: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV158 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV158 ) @ SV526 ) @ SV859 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV158 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV158 ) @ SV526 ) ) @ SV859 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2752,plain,
! [SV1077: $i,SV860: $i,SV527: $i,SV159: $i] :
( ( ! [SY2921: $i,SY2922: $i] :
( ( hAPP @ ( c_COMBC @ SV159 @ SV527 @ SV860 @ SV1077 @ SY2921 ) @ SY2922 )
= ( hAPP @ ( hAPP @ SV159 @ SY2922 ) @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2753,plain,
! [SV1078: $i,SV861: $i,SV528: $i,SV160: $i] :
( ( ( hAPP @ ( c_COMBK @ SV160 @ SV528 @ SV861 ) @ SV1078 )
= SV160 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2754,plain,
! [SV1079: $i,SV862: $i,SV529: $i,SV161: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV161 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV529 )
| ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
| ~ ( c_Series_Osummable @ SV1079 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2755,plain,
! [SV1080: $i,SV863: $i,SV530: $i,SV162: $i] :
( ( ! [SY2923: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV1080 ) @ SY2923 @ SV863 @ SV162 )
| ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SV530 @ SV1080 @ SY2923 @ SV863 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2756,plain,
! [SV531: $i,SV163: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV163 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV163 ) @ SV531 ) @ ( c_HOL_Ozero__class_Ozero @ SV163 ) )
= ( c_HOL_Ozero__class_Ozero @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2757,plain,
! [SV532: $i,SV164: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV164 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV532 )
= ( c_HOL_Ozero__class_Ozero @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2758,plain,
! [SV533: $i,SV165: $i] :
( ( ( class_RealVector_Oreal__vector @ SV165 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV165 ) @ SV533 ) @ ( c_HOL_Ozero__class_Ozero @ SV165 ) )
= ( c_HOL_Ozero__class_Ozero @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2759,plain,
! [SV534: $i,SV166: $i] :
( ( ( class_RealVector_Oreal__vector @ SV166 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV166 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV534 )
= ( c_HOL_Ozero__class_Ozero @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2760,plain,
! [SV1081: $i,SV864: $i,SV535: $i,SV167: $i] :
( ( ! [SY2924: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV167 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV535 ) @ SV864 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV1081 ) @ SV864 ) ) @ SY2924 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ SV535 ) @ SV1081 ) ) @ SV864 ) ) @ SY2924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2761,plain,
! [SV536: $i,SV168: $i] :
( ( ( class_RealVector_Ometric__space @ SV168 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ SV536 @ ( c_SEQ_Olim @ SV536 @ SV168 ) @ SV168 )
| ~ ( c_SEQ_Oconvergent @ SV536 @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2762,plain,
! [SV537: $i,SV169: $i] :
( ( ( class_RealVector_Ometric__space @ SV169 )
= $false )
| ( ( ( c_SEQ_Oconvergent @ SV537 @ SV169 )
| ~ ( c_SEQ_OLIMSEQ @ SV537 @ ( c_SEQ_Olim @ SV537 @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2763,plain,
! [SV538: $i,SV170: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV170 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV170 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV170 ) @ SV538 ) ) @ SV538 )
= ( c_HOL_Ozero__class_Ozero @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2764,plain,
! [SV539: $i,SV171: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV171 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV171 ) @ SV539 ) ) @ SV539 )
= ( c_HOL_Ozero__class_Ozero @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2765,plain,
! [SV540: $i,SV172: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV172 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV172 ) @ SV540 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV172 ) @ SV540 ) )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2766,plain,
! [SV541: $i,SV173: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV173 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV173 ) @ SV541 ) ) @ SV541 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2767,plain,
! [SV1082: $i,SV865: $i,SV542: $i,SV174: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV174 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV542 )
| ( c_Lim_OisCont @ SV865 @ SV1082 @ SV174 @ SV542 )
| ~ ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2768,plain,
! [SV543: $i,SV175: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV175 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV175 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SV543 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SV543 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
| ~ ( c_Series_Osummable @ SV543 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2769,plain,
! [SV544: $i,SV176: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV176 )
= $false )
| ( ( ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ SV544 @ SV176 @ SV176 @ tc_nat ) @ SV176 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ ( c_SEQ_Olim @ SV544 @ SV176 ) ) )
| ~ ( c_SEQ_Oconvergent @ SV544 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2770,plain,
! [SV1083: $i,SV866: $i,SV545: $i,SV177: $i] :
( ( ! [SY2925: $i] :
( ~ ( class_RealVector_Oreal__vector @ SV177 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ ( c_Finite__Set_Osetsum @ SV866 @ SV1083 @ SY2925 @ SV177 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ SV866 @ SV177 @ SV177 @ SY2925 ) @ SV1083 @ SY2925 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2771,plain,
! [SV1084: $i,SV867: $i,SV546: $i,SV179: $i] :
( ( ! [SY2926: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV179 )
| ~ ( class_RealVector_Ometric__space @ SV546 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SY2926 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV867 @ SV1084 @ SY2926 @ SV546 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2772,plain,
! [SV547: $i,SV180: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV180 )
= $false )
| ( ( ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV180 ) @ SV547 @ SV180 @ SV180 @ tc_nat ) @ SV180 )
| ~ ( c_SEQ_Oconvergent @ SV547 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2773,plain,
! [SV548: $i,SV181: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV181 )
= $false )
| ( ( ( c_SEQ_Oconvergent @ SV548 @ SV181 )
| ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV181 ) @ SV548 @ SV181 @ SV181 @ tc_nat ) @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2774,plain,
! [SV549: $i,SV182: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ SV182 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 ) @ SV182 @ SV182 )
| ( SV549
= ( c_HOL_Ozero__class_Ozero @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2775,plain,
! [SV1085: $i,SV868: $i,SV550: $i,SV183: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV868 ) @ SV1085 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SV868 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SV1085 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2776,plain,
! [SV1086: $i,SV869: $i,SV551: $i,SV184: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ SV869 ) @ SV1086 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SV869 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SV1086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2777,plain,
! [SV1087: $i,SV870: $i,SV552: $i,SV185: $i] :
( ( ! [SY2927: $i,SY2928: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV185 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV552 )
| ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SY2927 ) @ SY2928 @ SY2927 @ SV185 )
| ~ ( c_Limits_OZfun @ SV1087 @ SY2928 @ SY2927 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2778,plain,
! [SV553: $i,SV186: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV186 )
= $false )
| ( ( c_Lim_OisUCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV186 ) @ SV553 @ SV186 @ SV186 @ SV186 ) @ SV186 @ SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2779,plain,
! [SV1088: $i,SV871: $i,SV554: $i,SV188: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV188 )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ SV554 @ SV188 @ SV188 @ SV871 ) @ SV1088 @ SV871 @ SV188 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ ( c_Finite__Set_Osetsum @ SV554 @ SV1088 @ SV871 @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2780,plain,
! [SV555: $i,SV189: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV189 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SV555 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2781,plain,
! [SV556: $i,SV190: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV190 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SV556 )
= SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2782,plain,
! [SV557: $i,SV191: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV191 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SV557 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SV557 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2783,plain,
! [SV558: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV192 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV192 )
| ( SV558
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV558 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2784,plain,
! [SV559: $i,SV193: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SV559 )
= SV559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2785,plain,
! [SV560: $i,SV194: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV194 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ ( c_HOL_Ozero__class_Ozero @ SV194 ) ) @ SV560 )
= SV560 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2786,plain,
! [SV561: $i,SV195: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV195 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV195 ) @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) )
= SV561 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2787,plain,
! [SV562: $i,SV196: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV196 ) @ ( c_HOL_Ozero__class_Ozero @ SV196 ) ) @ SV562 )
= SV562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2788,plain,
! [SV563: $i,SV197: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV197 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV197 ) @ SV563 ) )
= SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2789,plain,
! [SV564: $i,SV198: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV198 )
= $false )
| ( ( SV564
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV198 ) @ SV564 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2790,plain,
! [SV565: $i,SV199: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV199 )
= $false )
| ( ( SV565
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV199 ) @ SV565 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2791,plain,
! [SV566: $i,SV200: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV200 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV200 ) @ SV566 ) )
= SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2792,plain,
! [SV567: $i,SV201: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV201 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV201 ) @ SV567 ) )
= SV567 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2793,plain,
! [SV568: $i,SV202: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV202 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV202 )
| ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SV568 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
| ~ ( c_Series_Osummable @ SV568 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2794,plain,
! [SV1089: $i,SV872: $i,SV569: $i,SV203: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV203 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ SV1089 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ SV1089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(2795,plain,
! [SV1090: $i,SV873: $i,SV570: $i,SV204: $i] :
( ( ~ ( class_RealVector_Oreal__algebra @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ SV873 ) ) @ SV1090 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ SV873 ) @ SV1090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2796,plain,
! [SV1091: $i,SV874: $i,SV571: $i,SV205: $i] :
( ( ~ ( class_RealVector_Oreal__algebra @ SV205 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ SV1091 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ SV1091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2797,plain,
! [SV1092: $i,SV875: $i,SV572: $i,SV206: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV206 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SV1092 @ SV206 @ SV572 )
| ~ ( c_Lim_OisCont @ SV875 @ SV1092 @ SV206 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2798,plain,
! [SV1093: $i,SV876: $i,SV573: $i,SV207: $i] :
( ( ! [SY2929: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV207 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV573 )
| ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SY2929 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SY2929 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2799,plain,
! [SV1094: $i,SV877: $i,SV574: $i,SV208: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV208 )
| ~ ( class_RealVector_Ometric__space @ SV574 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
| ~ ( c_SEQ_OCauchy @ SV1094 @ SV208 )
| ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2800,plain,
! [SV1095: $i,SV878: $i,SV575: $i,SV209: $i] :
( ( ! [SY2930: $i] :
( ~ ( class_RealVector_Ometric__space @ SV209 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV575 )
| ( c_Lim_OLIM @ SV878 @ SV1095 @ SY2930 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SY2930 @ SV575 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(2801,plain,
! [SV1096: $i,SV879: $i,SV576: $i,SV210: $i] :
( ( ! [SY2931: $i] :
( ~ ( class_RealVector_Ometric__space @ SV210 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV576 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SY2931 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SV879 @ SV1096 @ SY2931 @ SV576 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2802,plain,
! [SV1097: $i,SV880: $i,SV577: $i,SV211: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV211 )
| ~ ( class_RealVector_Ometric__space @ SV577 )
| ( c_Lim_OLIM @ SV880 @ SV1097 @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV1097 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2803,plain,
! [SV1098: $i,SV881: $i,SV578: $i,SV212: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV212 )
| ~ ( class_RealVector_Ometric__space @ SV578 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV1098 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
| ~ ( c_Lim_OLIM @ SV881 @ SV1098 @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2804,plain,
! [SV882: $i,SV579: $i,SV213: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV213 ) )
= $true )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV213 ) @ SV579 ) @ SV882 @ SV213 @ SV213 @ tc_nat ) @ SV213 )
| ~ ( c_Series_Osummable @ SV882 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2805,plain,
! [SV883: $i,SV580: $i,SV214: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV214 ) )
= $true )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV214 ) @ SV580 ) @ SV883 @ SV214 @ SV214 @ tc_nat ) @ SV214 )
| ~ ( c_Series_Osummable @ SV883 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2806,plain,
! [SV1099: $i,SV884: $i,SV581: $i,SV215: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV215 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV884 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV1099 ) @ SV215 )
| ~ ( c_Series_Osums @ SV884 @ SV1099 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2807,plain,
! [SV1100: $i,SV885: $i,SV582: $i,SV216: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 )
| ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV885 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV1100 ) @ SV216 )
| ~ ( c_Series_Osums @ SV885 @ SV1100 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2808,plain,
! [SV886: $i,SV583: $i,SV217: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV217 ) )
= $true )
| ( ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 @ SV583 ) @ SV886 @ SV583 @ SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(2809,plain,
! [SV887: $i,SV584: $i,SV218: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV218 ) )
= $true )
| ( ( ( c_Series_Osummable @ SV584 @ SV218 )
| ~ ( c_Series_Osums @ SV584 @ SV887 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2810,plain,
! [SV888: $i,SV585: $i,SV219: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV219 ) )
= $true )
| ( ( ( c_Series_Osummable @ SV585 @ SV219 )
| ~ ( c_Series_Osums @ SV585 @ SV888 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2811,plain,
! [SV889: $i,SV586: $i,SV220: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV220 ) )
= $true )
| ( ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV220 ) @ SV586 ) @ SV889 @ SV220 @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2812,plain,
! [SV1101: $i,SV890: $i,SV587: $i,SV221: $i] :
( ( ! [SY2932: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV221 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SV890 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV1101 ) @ SY2932 @ SV890 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV587 @ SV1101 @ SY2932 @ SV890 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2813,plain,
! [SV891: $i,SV590: $i,SV224: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV224 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 @ SV590 ) @ SV891 @ SV590 @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2814,plain,
! [SV591: $i,SV225: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV225 )
= $false )
| ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV225 ) @ SV591 ) )
= ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV225 ) @ SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2815,plain,
! [SV1102: $i,SV892: $i,SV592: $i,SV226: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV226 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ SV1102 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ SV1102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2816,plain,
! [SV1103: $i,SV893: $i,SV593: $i,SV227: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV227 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ SV1103 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ SV1103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2817,plain,
! [SV1104: $i,SV894: $i,SV594: $i,SV228: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ SV1104 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ SV1104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2818,plain,
! [SV595: $i,SV229: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV229 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV229 )
| ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SV595 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
| ~ ( c_SEQ_OZseq @ SV595 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2819,plain,
! [SV1105: $i,SV895: $i,SV596: $i,SV230: $i] :
( ( ~ ( class_RealVector_Otopological__space @ SV230 )
| ( c_Limits_Otendsto @ ( c_COMBK @ SV596 @ SV230 @ SV895 ) @ SV596 @ SV1105 @ SV895 @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2820,plain,
! [SV896: $i,SV597: $i,SV231: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV231 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SV597 ) @ SV896 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SV896 ) @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2821,plain,
! [SV897: $i,SV599: $i,SV233: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SV599 ) @ SV897 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SV897 ) @ SV599 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2822,plain,
! [SV898: $i,SV600: $i,SV234: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV234 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV600 ) @ SV898 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV898 ) @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2823,plain,
! [SV1106: $i,SV899: $i,SV601: $i,SV236: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV236 )
| ~ ( class_RealVector_Ometric__space @ SV601 )
| ( c_Lim_OLIM @ ( c_COMBK @ SV899 @ SV236 @ SV601 ) @ SV1106 @ SV899 @ SV601 @ SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2824,plain,
! [SV1107: $i,SV900: $i,SV602: $i,SV237: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV237 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV237 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SV602 @ SV900 @ SV1107 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SV602 @ tc_RealDef_Oreal @ SV237 @ SV1107 ) @ SV900 @ SV1107 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2825,plain,
! [SV603: $i,SV238: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV238 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ SV603 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ SV603 ) ) )
| ( SV603
= ( c_HOL_Ozero__class_Ozero @ SV238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2826,plain,
! [SV604: $i,SV239: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV239 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) ) @ SV604 )
= ( c_HOL_Ozero__class_Ozero @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2827,plain,
! [SV605: $i,SV240: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV240 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV240 ) @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV240 ) )
= ( c_HOL_Ozero__class_Ozero @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2828,plain,
! [SV606: $i,SV241: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV241 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV241 ) @ ( c_HOL_Ozero__class_Ozero @ SV241 ) ) @ SV606 )
= ( c_HOL_Ozero__class_Ozero @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2829,plain,
! [SV607: $i,SV242: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV242 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV242 ) @ ( c_HOL_Ozero__class_Ozero @ SV242 ) ) @ SV607 )
= ( c_HOL_Ozero__class_Ozero @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2830,plain,
! [SV608: $i,SV243: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV243 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV243 ) @ SV608 ) @ ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2831,plain,
! [SV609: $i,SV244: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV244 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV244 ) @ SV609 ) @ ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2832,plain,
! [SV610: $i,SV245: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV245 ) @ ( c_HOL_Ozero__class_Ozero @ SV245 ) ) @ SV610 )
= ( c_HOL_Ozero__class_Ozero @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2833,plain,
! [SV611: $i,SV246: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV246 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) ) @ SV611 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2834,plain,
! [SV612: $i,SV247: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV247 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV247 ) @ SV612 ) @ ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= ( c_HOL_Ozero__class_Ozero @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2835,plain,
! [SV613: $i,SV248: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV248 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV248 ) @ ( c_HOL_Ozero__class_Ozero @ SV248 ) ) @ SV613 )
= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2836,plain,
! [SV614: $i,SV249: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV249 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV249 ) @ SV614 ) @ ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= ( c_HOL_Ozero__class_Ozero @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2837,plain,
! [SV901: $i,SV615: $i,SV250: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV250 ) )
= $true )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ SV615 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV901 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV250 @ tc_nat ) @ SV250 )
| ~ ( c_Series_Osummable @ SV615 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2485]) ).
thf(2838,plain,
! [SV1108: $i,SV902: $i,SV616: $i,SV251: $i] :
( ( ! [SY2933: $i,SY2934: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV251 )
| ~ ( class_RealVector_Ometric__space @ SV616 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SY2933 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SY2934 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SV1108 @ SY2933 @ SY2934 @ SV616 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2839,plain,
! [SV903: $i,SV617: $i,SV252: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV252 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV252 ) @ SV617 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ SV903 ) @ SV617 ) )
= SV903 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2840,plain,
! [SV904: $i,SV618: $i,SV253: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV253 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV253 ) @ SV618 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ SV618 ) @ SV904 ) )
= SV904 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2841,plain,
! [SV1109: $i,SV905: $i,SV619: $i,SV254: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ SV254 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV619 ) @ ( hAPP @ c_Complex_ORe @ SV905 ) @ SV1109 @ SV619 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV254 @ SV905 @ SV1109 @ SV619 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2842,plain,
! [SV1110: $i,SV906: $i,SV620: $i,SV255: $i] :
( ( ! [SY2935: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV255 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV620 )
| ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SY2935 ) @ SV620 )
| ~ ( c_Series_Osums @ SV1110 @ SY2935 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2843,plain,
! [SV621: $i,SV256: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV256 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ SV621 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
| ~ ( c_Series_Osummable @ SV621 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2844,plain,
! [SV907: $i,SV622: $i,SV257: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV257 ) )
= $true )
| ( ( ( SV622
= ( c_Series_Osuminf @ SV907 @ SV257 ) )
| ~ ( c_Series_Osums @ SV907 @ SV622 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2845,plain,
! [SV908: $i,SV623: $i,SV258: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV258 ) )
= $true )
| ( ( ( ( c_Series_Osuminf @ SV623 @ SV258 )
= SV908 )
| ~ ( c_Series_Osums @ SV623 @ SV908 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2846,plain,
! [SV624: $i,SV259: $i] :
( ( ( c_Series_Osums @ SV259 @ SV624 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ c_Complex_ORe @ SV259 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SV624 ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2847,plain,
! [SV625: $i,SV262: $i] :
( ( ( class_SEQ_Ocomplete__space @ SV262 )
= $false )
| ( ( ( c_SEQ_OCauchy @ SV625 @ SV262 )
| ~ ( c_SEQ_Oconvergent @ SV625 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2848,plain,
! [SV626: $i,SV263: $i] :
( ( ( class_SEQ_Ocomplete__space @ SV263 )
= $false )
| ( ( ( c_SEQ_Oconvergent @ SV626 @ SV263 )
| ~ ( c_SEQ_OCauchy @ SV626 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2849,plain,
! [SV627: $i,SV264: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV264 )
= $false )
| ( ( c_Lim_OisUCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV264 ) @ SV627 ) @ SV264 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2850,plain,
! [SV628: $i,SV265: $i] :
( ( ( class_RealVector_Ometric__space @ SV265 )
= $false )
| ( ( ( c_SEQ_OCauchy @ SV628 @ SV265 )
| ~ ( c_SEQ_Oconvergent @ SV628 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2851,plain,
! [SV909: $i,SV629: $i,SV267: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV267 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SV629 ) ) @ SV909 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ SV629 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SV909 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2852,plain,
! [SV910: $i,SV630: $i,SV268: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV268 ) )
= $true )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV630 @ SV268 @ SV268 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV910 ) @ SV268 )
| ~ ( c_Series_Osums @ SV630 @ SV910 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2502]) ).
thf(2853,plain,
! [SV1111: $i,SV911: $i,SV631: $i,SV271: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV271 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV631 )
| ( c_Lim_OLIM @ SV911 @ SV1111 @ ( hAPP @ SV911 @ SV1111 ) @ SV271 @ SV631 )
| ~ ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2854,plain,
! [SV912: $i,SV632: $i,SV272: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV272 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV272 ) @ SV632 ) @ SV912 @ SV272 @ SV272 @ tc_nat ) @ SV272 )
| ~ ( c_SEQ_OZseq @ SV912 @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2855,plain,
! [SV913: $i,SV633: $i,SV273: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV273 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV273 ) @ SV633 ) @ SV913 @ SV273 @ SV273 @ tc_nat ) @ SV273 )
| ~ ( c_SEQ_OZseq @ SV913 @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2856,plain,
! [SV634: $i,SV274: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV274 )
= $false )
| ( ( ( c_Series_Osums @ SV634 @ ( c_Series_Osuminf @ SV634 @ SV274 ) @ SV274 )
| ~ ( c_Series_Osummable @ SV634 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2857,plain,
! [SV635: $i,SV275: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV275 )
= $false )
| ( ( ~ ( c_Series_Osummable @ SV635 @ SV275 )
| ( c_Series_Osums @ SV635 @ ( c_Series_Osuminf @ SV635 @ SV275 ) @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2858,plain,
! [SV1112: $i,SV914: $i,SV636: $i,SV276: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV276 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV636 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
| ~ ( c_SEQ_OCauchy @ SV1112 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2859,plain,
! [SV1113: $i,SV915: $i,SV637: $i,SV277: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV277 )
| ~ ( class_RealVector_Ometric__space @ SV637 )
| ( c_Lim_OisCont @ SV915 @ SV1113 @ SV277 @ SV637 )
| ~ ( c_Lim_OLIM @ SV915 @ SV1113 @ ( hAPP @ SV915 @ SV1113 ) @ SV277 @ SV637 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2860,plain,
! [SV1114: $i,SV916: $i,SV638: $i,SV278: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV278 )
| ~ ( class_RealVector_Ometric__space @ SV638 )
| ( c_Lim_OLIM @ SV916 @ SV1114 @ ( hAPP @ SV916 @ SV1114 ) @ SV278 @ SV638 )
| ~ ( c_Lim_OisCont @ SV916 @ SV1114 @ SV278 @ SV638 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2861,plain,
! [SV917: $i,SV639: $i,SV279: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV279 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV639 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2862,plain,
! [SV918: $i,SV640: $i,SV280: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV280 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SV640 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SV918 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2863,plain,
! [SV1115: $i,SV919: $i,SV641: $i,SV281: $i] :
( ( ! [SY2936: $i,SY2937: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV281 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SY2936 ) @ SY2937 @ SV1115 @ SV281 )
| ~ ( c_Limits_Otendsto @ SV919 @ SY2936 @ SY2937 @ SV1115 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2864,plain,
! [SV920: $i,SV642: $i,SV282: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV282 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV282 ) @ SV642 ) @ SV920 @ SV282 @ SV282 @ tc_nat ) @ SV282 )
| ~ ( c_SEQ_OCauchy @ SV920 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2865,plain,
! [SV921: $i,SV644: $i,SV285: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV285 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV285 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SV921 ) @ SV285 )
| ~ ( c_Series_Osums @ SV644 @ SV921 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2866,plain,
! [SV1116: $i,SV922: $i,SV645: $i,SV286: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV286 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV645 )
| ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
| ~ ( c_Series_Osummable @ SV1116 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(2867,plain,
! [SV1117: $i,SV923: $i,SV646: $i,SV287: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV287 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV646 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SV1117 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SV923 @ SV1117 @ SV287 @ SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(2868,plain,
! [SV647: $i,SV288: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV288 )
= $false )
| ( ( c_RealVector_Obounded__linear @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV288 ) @ SV647 ) @ SV288 @ SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2869,plain,
! [SV924: $i,SV648: $i,SV289: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV289 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ SV648 ) @ SV924 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SV924 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SV648 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2870,plain,
! [SV925: $i,SV649: $i,SV290: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV290 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ SV649 ) @ SV925 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SV649 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SV925 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2871,plain,
! [SV650: $i,SV292: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV292 @ SV650 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_OIm @ SV292 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SV650 ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2872,plain,
! [SV1118: $i,SV926: $i,SV651: $i,SV293: $i] :
( ( ! [SY2938: $i,SY2939: $i] :
( ( c_Set_Oimage @ SV293 @ ( c_Set_Oimage @ SV651 @ SV926 @ SV1118 @ SY2938 ) @ SY2938 @ SY2939 )
= ( c_Set_Oimage @ ( c_COMBB @ SV293 @ SV651 @ SY2938 @ SY2939 @ SV1118 ) @ SV926 @ SV1118 @ SY2939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2873,plain,
! [SV927: $i,SV652: $i,SV294: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV294 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV652 @ SV294 @ SV294 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV927 ) @ SV294 )
| ~ ( c_SEQ_OLIMSEQ @ SV652 @ SV927 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2874,plain,
! [SV928: $i,SV653: $i,SV295: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV295 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ SV653 @ SV928 @ SV295 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV653 @ SV295 @ SV295 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV928 ) @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2875,plain,
! [SV929: $i,SV654: $i,SV297: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV297 ) )
= $true )
| ( ( ( c_SEQ_Oconvergent @ SV654 @ SV297 )
| ~ ( c_SEQ_OLIMSEQ @ SV654 @ SV929 @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2529]) ).
thf(2876,plain,
! [SV930: $i,SV655: $i,SV298: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV298 ) )
= $true )
| ( ( ( c_SEQ_Oconvergent @ SV655 @ SV298 )
| ~ ( c_SEQ_OLIMSEQ @ SV655 @ SV930 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2877,plain,
! [SV931: $i,SV656: $i,SV299: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV299 ) )
= $true )
| ( ( ( SV656 = SV931 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV656 @ SV299 @ tc_nat ) @ SV931 @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2878,plain,
! [SV1119: $i,SV932: $i,SV657: $i,SV300: $i] :
( ( ! [SY2940: $i,SY2941: $i,SY2942: $i] :
( ~ ( class_RealVector_Ometric__space @ SV300 )
| ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SY2940 @ SV300 @ SV657 @ SV932 ) @ SY2941 @ ( hAPP @ SV1119 @ SY2942 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SY2940 @ SY2941 @ SY2942 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SY2942 @ ( hAPP @ SV1119 @ SY2942 ) @ SV300 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(2879,plain,
! [SV658: $i,SV301: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV301 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ SV658 @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV301 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV301 ) @ SV658 @ SV301 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2880,plain,
! [SV659: $i,SV302: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV302 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV302 ) @ SV659 @ SV302 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV659 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2881,plain,
! [SV933: $i,SV660: $i,SV303: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV303 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV660 @ SV303 @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV933 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV660 @ SV933 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2882,plain,
! [SV1120: $i,SV934: $i,SV662: $i,SV305: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV305 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV662 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV934 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SV1120 @ SV305 )
| ~ ( c_SEQ_OLIMSEQ @ SV662 @ SV1120 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(2883,plain,
! [SV1121: $i,SV935: $i,SV663: $i,SV306: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV306 )
| ( c_SEQ_OLIMSEQ @ SV663 @ SV935 @ SV306 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV663 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1121 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SV935 @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(2884,plain,
! [SV936: $i,SV664: $i,SV307: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV307 ) )
= $true )
| ( ( ( ( c_SEQ_Olim @ SV664 @ SV307 )
= SV936 )
| ~ ( c_SEQ_OLIMSEQ @ SV664 @ SV936 @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2885,plain,
! [SV1122: $i,SV937: $i,SV665: $i,SV308: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ SV308 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV665 ) @ ( hAPP @ c_Complex_OIm @ SV937 ) @ SV1122 @ SV665 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV308 @ SV937 @ SV1122 @ SV665 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2886,plain,
! [SV666: $i,SV310: $i] :
( ( ( class_RealVector_Ometric__space @ SV310 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV666 @ SV310 @ tc_nat ) @ SV666 @ SV310 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2887,plain,
! [SV667: $i,SV311: $i] :
( ( ( class_RealVector_Ometric__space @ SV311 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV667 @ SV311 @ tc_nat ) @ SV667 @ SV311 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2888,plain,
! [SV1123: $i,SV938: $i,SV668: $i,SV312: $i] :
( ( ! [SY2943: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV312 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV668 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SY2943 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SY2943 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2889,plain,
! [SV1124: $i,SV939: $i,SV669: $i,SV313: $i] :
( ( ! [SY2944: $i,SY2945: $i] :
( ~ ( class_RealVector_Ometric__space @ SV313 )
| ~ ( class_RealVector_Ometric__space @ SV669 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SY2944 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SY2945 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SY2945 @ SV669 ) )
= SY2945 )
| ~ ( c_Lim_OLIM @ SV939 @ SY2945 @ SY2944 @ SV669 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2890,plain,
! [SV941: $i,SV671: $i,SV315: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV315 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV315 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SV941 ) @ SV315 )
| ~ ( c_SEQ_OLIMSEQ @ SV671 @ SV941 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2891,plain,
! [SV672: $i,SV316: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV316 @ SV672 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ c_Complex_ORe @ SV316 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_ORe @ SV672 ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2892,plain,
! [SV673: $i,SV318: $i] :
( ( ( c_Series_Osums @ SV318 @ SV673 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ c_Complex_OIm @ SV318 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ c_Complex_OIm @ SV673 ) @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2893,plain,
! [SV942: $i,SV674: $i,SV319: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ SV319 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV674 ) @ SV942 @ SV674 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV319 @ SV942 @ SV674 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2894,plain,
! [SV1125: $i,SV943: $i,SV675: $i,SV320: $i] :
( ( ! [SY2946: $i,SY2947: $i] :
( ~ ( class_RealVector_Ometric__space @ SV320 )
| ~ ( class_RealVector_Ometric__space @ SV675 )
| ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SY2946 @ SV943 @ SV675 @ SV320 ) @ SY2947 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SY2946 @ SY2947 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SY2946 @ SY2947 @ SV320 @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2895,plain,
! [SV1126: $i,SV944: $i,SV676: $i,SV321: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV321 )
| ( SV676 = SV944 )
| ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV944 @ SV321 )
| ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV676 @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2896,plain,
! [SV1127: $i,SV945: $i,SV677: $i,SV322: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV322 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV945 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV1127 ) @ SV322 )
| ~ ( c_SEQ_OLIMSEQ @ SV945 @ SV1127 @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2897,plain,
! [SV1128: $i,SV946: $i,SV678: $i,SV323: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV323 )
| ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SV1128 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV946 @ SV1128 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SV1128 ) @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2898,plain,
! [SV1129: $i,SV947: $i,SV679: $i,SV324: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV324 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV947 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV1129 ) @ SV324 )
| ~ ( c_SEQ_OLIMSEQ @ SV947 @ SV1129 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(2899,plain,
! [SV948: $i,SV680: $i,SV326: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV326 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ SV680 @ SV326 )
| ~ ( c_SEQ_OLIMSEQ @ SV680 @ SV948 @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2900,plain,
! [SV949: $i,SV681: $i,SV327: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV327 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV681 @ c_Suc @ tc_nat @ SV327 @ tc_nat ) @ SV949 @ SV327 )
| ~ ( c_SEQ_OLIMSEQ @ SV681 @ SV949 @ SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2901,plain,
! [SV950: $i,SV682: $i,SV328: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV328 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ SV682 @ SV950 @ SV328 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV682 @ c_Suc @ tc_nat @ SV328 @ tc_nat ) @ SV950 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2902,plain,
! [SV1130: $i,SV951: $i,SV683: $i,SV329: $i] :
( ( ! [SY2948: $i,SY2949: $i] :
( ( hAPP @ ( c_COMBB @ SV329 @ SV683 @ SV951 @ SV1130 @ SY2948 ) @ SY2949 )
= ( hAPP @ SV329 @ ( hAPP @ SV683 @ SY2949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(2903,plain,
! [SV952: $i,SV684: $i,SV330: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV330 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV684 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV952 ) @ SV330 )
| ( SV952
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ~ ( c_SEQ_OLIMSEQ @ SV684 @ SV952 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2904,plain,
! [SV1131: $i,SV953: $i,SV685: $i,SV331: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV331 )
| ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SV685 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SV953 @ ( hAPP @ c_Complex_OIm @ SV1131 ) @ SV331 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV685 @ SV953 @ SV1131 @ SV331 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(2905,plain,
! [SV334: $i,SV686: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV686 )
= $false )
| ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV334 @ SV686 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2906,plain,
! [SV1132: $i,SV954: $i,SV687: $i,SV335: $i] :
( ( ! [SY2950: $i,SY2951: $i] :
( ( hAPP @ ( c_COMBC @ SV335 @ SV687 @ SV954 @ SV1132 @ SY2950 ) @ SY2951 )
= ( hAPP @ ( hAPP @ SV335 @ SY2951 ) @ SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2907,plain,
! [SV1133: $i,SV955: $i,SV688: $i,SV336: $i] :
( ( ! [SY2952: $i,SY2953: $i] :
( ( hAPP @ ( c_COMBB @ SV336 @ SV688 @ SV955 @ SV1133 @ SY2952 ) @ SY2953 )
= ( hAPP @ SV336 @ ( hAPP @ SV688 @ SY2953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2908,plain,
! [SV956: $i,SV690: $i,SV338: $i] :
( ( ( SV338 = SV690 )
= $true )
| ( ( ~ ( c_fequal @ SV338 @ SV690 @ SV956 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2909,plain,
! [SV957: $i,SV691: $i,SV339: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV339 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV691 ) @ SV691 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV957 ) @ SV957 ) )
| ( SV691
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SV957 ) )
| ( SV691 = SV957 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2910,plain,
! [SV1134: $i,SV958: $i,SV692: $i,SV340: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV692 ) @ SV958 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1134 ) @ SV958 ) )
| ( SV692 = SV1134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2911,plain,
! [SV959: $i,SV693: $i,SV342: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV342 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SV693 ) @ SV959 )
!= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV693
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV959
= ( c_HOL_Ozero__class_Ozero @ SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2912,plain,
! [SV960: $i,SV694: $i,SV343: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SV960 ) )
= $true )
| ( ( SV694 = SV960 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2571]) ).
thf(2913,plain,
! [SV695: $i,SV344: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV344 )
= $false )
| ( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV344 ) @ SV695 )
!= ( c_HOL_Ozero__class_Ozero @ SV344 ) )
| ( SV695
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2914,plain,
! [SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ! [SY2954: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV345 )
| ~ ( class_Int_Onumber__ring @ SV345 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SY2954 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SY2954 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
| ( SV961 = SY2954 )
| ( SV696 = SV1135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2915,plain,
! [SV697: $i,SV346: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV346 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV346 ) @ SV697 ) @ SV697 )
!= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
| ( SV697
= ( c_HOL_Ozero__class_Ozero @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2916,plain,
! [SV962: $i,SV698: $i,SV347: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV347 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV962 ) )
| ( SV698 = SV962 )
| ( SV962
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2575]) ).
thf(2917,plain,
! [SV963: $i,SV699: $i,SV348: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV348 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ SV699 ) @ SV963 )
!= ( c_HOL_Ozero__class_Ozero @ SV348 ) )
| ( SV699
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV348 ) @ SV963 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2918,plain,
! [SV964: $i,SV700: $i,SV349: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV349 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV700 ) @ SV700 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV964 ) @ SV964 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
| ( SV700
= ( c_HOL_Ozero__class_Ozero @ SV349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2919,plain,
! [SV965: $i,SV701: $i,SV350: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SV701 ) @ SV965 )
!= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV965
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2578]) ).
thf(2920,plain,
! [SV1136: $i,SV966: $i,SV702: $i,SV351: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ SV351 @ SV702 )
!= ( c_Complex_Ocomplex_OComplex @ SV966 @ SV1136 ) )
| ( SV702 = SV1136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(2921,plain,
! [SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ! [SY2955: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV352 )
| ~ ( class_Int_Onumber__ring @ SV352 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SY2955 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SY2955 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
| ( SV967 = SY2955 )
| ( SV703 = SV1137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(2922,plain,
! [SV704: $i,SV353: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV353 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV353 ) @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ SV353 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2923,plain,
! [SV1138: $i,SV968: $i,SV705: $i,SV354: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV354 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV968 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV1138 ) )
| ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV968 = SV1138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(2924,plain,
! [SV969: $i,SV706: $i,SV355: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SV706 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SV969 ) )
= $true )
| ( ( SV706 = SV969 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2925,plain,
! [SV707: $i,SV356: $i] :
( ( ( ( hAPP @ c_Suc @ SV356 )
= ( hAPP @ c_Suc @ SV707 ) )
= $false )
| ( ( SV356 = SV707 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2926,plain,
! [SV970: $i,SV708: $i,SV357: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV357 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SV708 ) @ SV970 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV970
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV708
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2927,plain,
! [SV1139: $i,SV971: $i,SV709: $i,SV358: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV971 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV1139 ) )
| ( SV971 = SV1139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2928,plain,
! [SV972: $i,SV710: $i,SV359: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV359 ) @ SV710 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV972 ) @ SV710 ) )
= $true )
| ( ( SV359 = SV972 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2929,plain,
! [SV973: $i,SV711: $i,SV360: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV360 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV711 ) @ SV973 )
!= ( c_HOL_Ozero__class_Ozero @ SV360 ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV360 ) @ SV711 )
= SV973 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2930,plain,
! [SV974: $i,SV712: $i,SV361: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV361 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV361 )
| ( SV712
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2931,plain,
! [SV975: $i,SV713: $i,SV362: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV362 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SV713 ) @ SV975 )
!= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV975
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV362 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(2932,plain,
! [SV714: $i,SV363: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV363 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV363 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SV714 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( SV714
= ( c_HOL_Ozero__class_Ozero @ SV363 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2933,plain,
! [SV976: $i,SV715: $i,SV364: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV364 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV715 ) @ SV715 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV976 ) @ SV976 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
| ( SV976
= ( c_HOL_Ozero__class_Ozero @ SV364 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2934,plain,
! [SV977: $i,SV716: $i,SV365: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV365 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV716 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV977 ) )
| ( SV716 = SV977 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2935,plain,
! [SV1140: $i,SV978: $i,SV717: $i,SV366: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV366 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SV978 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV1140 ) @ SV978 ) )
| ( SV978
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SV717 = SV1140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(2936,plain,
! [SV718: $i,SV367: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV367 )
= $false )
| ( ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV367 ) @ SV718 )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV367 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2937,plain,
! [SV719: $i,SV368: $i] :
( ( ( class_OrderedGroup_Oordered__ab__group__add @ SV368 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV368 ) @ SV719 )
!= SV719 )
| ( SV719
= ( c_HOL_Ozero__class_Ozero @ SV368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2938,plain,
! [SV720: $i,SV369: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV369 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV369 ) @ SV720 )
!= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
| ( SV720
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2939,plain,
! [SV1141: $i,SV979: $i,SV721: $i,SV370: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ SV370 @ SV721 )
!= ( c_Complex_Ocomplex_OComplex @ SV979 @ SV1141 ) )
| ( SV370 = SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(2940,plain,
! [SV722: $i,SV371: $i] :
( ( ( ( hAPP @ c_Complex_OIm @ SV371 )
= ( hAPP @ c_Complex_OIm @ SV722 ) )
= $false )
| ( ( ( ( hAPP @ c_Complex_ORe @ SV371 )
!= ( hAPP @ c_Complex_ORe @ SV722 ) )
| ( SV371 = SV722 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2941,plain,
! [SV723: $i,SV372: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV372 )
= $false )
| ( ( ( ( c_HOL_Ozero__class_Ozero @ SV372 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV372 ) @ SV723 ) )
| ( ( c_HOL_Ozero__class_Ozero @ SV372 )
= SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2942,plain,
! [SV980: $i,SV724: $i,SV373: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV373 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV980 ) )
| ( SV724 = SV980 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2943,plain,
! [SV981: $i,SV725: $i,SV374: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV374 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV725 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV981 ) )
| ( SV725 = SV981 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2944,plain,
! [SV1142: $i,SV982: $i,SV726: $i,SV375: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV375 )
| ~ ( class_Int_Onumber__ring @ SV375 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV1142 ) )
| ( SV982 = SV1142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(2945,plain,
! [SV983: $i,SV727: $i,SV376: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV376 ) )
= $true )
| ( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV727 )
!= ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV983 ) )
| ( SV727 = SV983 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2946,plain,
! [SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ! [SY2956: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SY2956 ) ) )
| ( SV1143 = SY2956 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(2947,plain,
! [SV1144: $i,SV985: $i,SV729: $i,SV379: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV985 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV1144 ) )
| ( SV985 = SV1144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2948,plain,
! [SV730: $i,SV380: $i] :
( ( ( ( hAPP @ c_Suc @ SV380 )
= ( hAPP @ c_Suc @ SV730 ) )
= $false )
| ( ( SV380 = SV730 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2949,plain,
! [SV1145: $i,SV986: $i,SV731: $i,SV381: $i] :
( ( ! [SY2957: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV381 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1145 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SY2957 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SV1145 )
= SY2957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(2950,plain,
! [SV1146: $i,SV987: $i,SV732: $i,SV382: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV382 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV987 ) @ SV1146 ) )
!= SV987 )
| ( SV732
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SV1146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(2951,plain,
! [SV1147: $i,SV988: $i,SV733: $i,SV383: $i,SV2: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV2 )
| ~ ( class_RealVector_Ometric__space @ SV383 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SV733 @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(2952,plain,
! [SV1148: $i,SV989: $i,SV734: $i,SV384: $i,SV3: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV3 )
| ~ ( class_RealVector_Ometric__space @ SV384 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SV734 @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2953,plain,
! [SV1149: $i,SV990: $i,SV735: $i,SV385: $i,SV4: $i] :
( ( ! [SY2958: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV4 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SV990 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV1149 ) @ SV990 ) @ SY2958 @ SV735 @ SV4 )
| ~ ( c_Limits_Otendsto @ SV385 @ SV1149 @ SY2958 @ SV735 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(2954,plain,
! [SV1150: $i,SV991: $i,SV736: $i,SV386: $i,SV5: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV5 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SV736 ) @ SV991 @ SV736 @ SV5 @ SV5 ) @ SV1150 @ SV736 @ SV5 )
| ~ ( c_Limits_OZfun @ SV386 @ SV1150 @ SV736 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(2955,plain,
! [SV1151: $i,SV992: $i,SV737: $i,SV387: $i,SV6: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV6 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SV737 ) @ SV992 @ SV737 @ SV6 @ SV6 ) @ SV1151 @ SV737 @ SV6 )
| ~ ( c_Limits_OZfun @ SV387 @ SV1151 @ SV737 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(2956,plain,
! [SV1152: $i,SV993: $i,SV738: $i,SV388: $i,SV7: $i] :
( ( ! [SY2959: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV7 )
| ~ ( class_RealVector_Ometric__space @ SV388 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SY2959 ) @ SV993 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SV1152 @ SY2959 @ SV388 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(2957,plain,
! [SV1153: $i,SV994: $i,SV739: $i,SV389: $i,SV8: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV8 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ ( c_Finite__Set_Osetsum @ SV389 @ SV739 @ SV994 @ SV8 ) ) @ SV1153 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ SV389 @ SV8 @ ( tc_fun @ SV8 @ SV8 ) @ SV994 ) @ SV1153 @ SV994 @ SV8 @ SV8 ) @ SV739 @ SV994 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(2958,plain,
! [SV1154: $i,SV995: $i,SV740: $i,SV390: $i,SV9: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV9 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ ( c_Finite__Set_Osetsum @ SV390 @ SV740 @ SV995 @ SV9 ) ) @ SV1154 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ SV390 @ SV9 @ ( tc_fun @ SV9 @ SV9 ) @ SV995 ) @ SV1154 @ SV995 @ SV9 @ SV9 ) @ SV740 @ SV995 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2959,plain,
! [SV1155: $i,SV996: $i,SV741: $i,SV391: $i,SV10: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV10 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ ( c_Finite__Set_Osetsum @ SV391 @ SV741 @ SV996 @ tc_RealDef_Oreal ) ) @ SV1155 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ SV391 @ tc_RealDef_Oreal @ ( tc_fun @ SV10 @ SV10 ) @ SV996 ) @ SV1155 @ SV996 @ SV10 @ SV10 ) @ SV741 @ SV996 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(2960,plain,
! [SV1156: $i,SV997: $i,SV742: $i,SV392: $i,SV11: $i] :
( ( ! [SY2960: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV11 )
| ~ ( class_RealVector_Ometric__space @ SV392 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SY2960 ) @ SV997 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SV1156 @ SY2960 @ SV392 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2961,plain,
! [SV1157: $i,SV998: $i,SV743: $i,SV393: $i,SV12: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV12 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SV743 ) @ SV998 @ SV743 @ SV12 @ SV12 ) @ SV1157 @ SV743 @ SV12 )
| ~ ( c_Limits_OZfun @ SV393 @ SV1157 @ SV743 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(2962,plain,
! [SV1158: $i,SV999: $i,SV744: $i,SV394: $i,SV13: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV13 )
| ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SV744 ) @ SV999 @ SV744 @ SV13 @ SV13 ) @ SV1158 @ SV744 @ SV13 )
| ~ ( c_Limits_OZfun @ SV394 @ SV1158 @ SV744 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(2963,plain,
! [SV1159: $i,SV1000: $i,SV745: $i,SV395: $i,SV14: $i] :
( ( ! [SY2961: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV14 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SV1000 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV1159 ) @ SV1000 ) @ SY2961 @ SV745 @ SV14 )
| ~ ( c_Limits_Otendsto @ SV395 @ SV1159 @ SY2961 @ SV745 @ tc_RealDef_Oreal ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(2964,plain,
! [SV396: $i,SV15: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV15 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SV396 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
| ~ ( c_SEQ_OCauchy @ SV396 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2965,plain,
! [SV398: $i,SV17: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV17 ) @ SV398 @ SV17 @ SV17 @ tc_nat ) @ SV17 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV398 @ SV17 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2966,plain,
! [SV1160: $i,SV1001: $i,SV746: $i,SV399: $i,SV18: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ SV1160 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ SV1160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(2967,plain,
! [SV1161: $i,SV1002: $i,SV747: $i,SV400: $i,SV19: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ SV747 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SV1161 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV747 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SV1161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(2968,plain,
! [SV1162: $i,SV1003: $i,SV748: $i,SV401: $i,SV20: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV748 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV1003 ) @ SV1162 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV1003 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV748 ) @ SV1162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(2969,plain,
! [SV21: $i,SV402: $i] :
( ( ( c_Series_Osummable @ SV402 @ SV21 )
= $true )
| ( ( ~ ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV21 ) @ SV402 @ SV21 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_SEQ_Obanach @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2629]) ).
thf(2970,plain,
! [SV23: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV23 )
= $false )
| ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV23 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2971,plain,
! [SV749: $i,SV403: $i,SV24: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV24 )
= $false )
| ( ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV24 ) @ SV403 ) @ SV749 ) @ SV24 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2972,plain,
! [SV1004: $i,SV750: $i,SV404: $i,SV25: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV25 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
| ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2973,plain,
! [SV751: $i,SV405: $i,SV26: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV26 )
= $false )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBK @ SV405 @ SV26 @ SV26 ) @ SV751 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2974,plain,
! [SV27: $i,SV406: $i] :
( ( ( c_SEQ_OZseq @ SV406 @ SV27 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV27 ) @ SV406 @ SV27 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2975,plain,
! [SV407: $i,SV28: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV28 ) @ SV407 @ SV28 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV407 @ SV28 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2976,plain,
! [SV752: $i,SV408: $i,SV29: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV29 )
= $false )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV29 ) @ SV408 ) @ SV752 @ SV29 @ SV29 @ tc_nat ) @ SV29 )
| ~ ( c_SEQ_OCauchy @ SV752 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2977,plain,
! [SV753: $i,SV409: $i,SV30: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV30 )
= $false )
| ( ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV30 ) @ SV409 ) @ SV753 @ SV30 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2978,plain,
! [SV1163: $i,SV1005: $i,SV754: $i,SV410: $i,SV31: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV31 )
| ~ ( class_RealVector_Ometric__space @ SV410 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SV754 @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(2979,plain,
! [SV1164: $i,SV1006: $i,SV755: $i,SV411: $i,SV32: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV32 )
| ~ ( class_RealVector_Ometric__space @ SV411 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SV755 @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(2980,plain,
! [SV33: $i,SV412: $i] :
( ( ( SV412
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ ( c_COMBK @ SV412 @ SV33 @ tc_nat ) @ SV33 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2981,plain,
! [SV1165: $i,SV1007: $i,SV756: $i,SV413: $i,SV34: $i] :
( ( ! [SY2962: $i] :
( ~ ( class_RealVector_Ometric__space @ SV34 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
| ( SV756 = SV1007 )
| ~ ( c_Lim_OLIM @ SV1165 @ SY2962 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SV1165 @ SY2962 @ SV756 @ SV413 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2982,plain,
! [SV1008: $i,SV757: $i,SV414: $i,SV35: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV35 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SV414 @ SV35 @ tc_RealDef_Oreal @ SV757 ) @ SV1008 @ SV757 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV414 @ SV1008 @ SV757 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2983,plain,
! [SV1009: $i,SV758: $i,SV415: $i,SV36: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV36 ) )
= $true )
| ( ( ( c_Limits_OZfun @ SV415 @ SV758 @ SV1009 @ SV36 )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SV415 @ SV36 @ tc_RealDef_Oreal @ SV1009 ) @ SV758 @ SV1009 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2984,plain,
! [SV1010: $i,SV759: $i,SV416: $i,SV37: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV37 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV416 )
| ( c_Lim_OisCont @ ( c_COMBK @ SV759 @ SV416 @ SV37 ) @ SV1010 @ SV37 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2985,plain,
! [SV1011: $i,SV760: $i,SV417: $i,SV38: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV38 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SV417 @ SV38 @ SV38 @ SV760 ) @ SV1011 @ SV760 @ SV38 )
| ~ ( c_Limits_OZfun @ SV417 @ SV1011 @ SV760 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2986,plain,
! [SV761: $i,SV418: $i,SV39: $i] :
( ( ( class_Ring__and__Field_Oring @ SV39 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ SV418 ) @ SV761 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV39 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV39 ) @ SV418 ) ) @ SV761 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2987,plain,
! [SV762: $i,SV419: $i,SV40: $i] :
( ( ( class_Ring__and__Field_Oring @ SV40 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ SV762 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV40 ) @ SV419 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV40 ) @ SV762 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2988,plain,
! [SV763: $i,SV420: $i,SV41: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV41 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV420 )
| ( c_Lim_OisUCont @ SV763 @ SV41 @ SV420 )
| ~ ( c_RealVector_Obounded__linear @ SV763 @ SV41 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2989,plain,
! [SV764: $i,SV421: $i,SV42: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV42 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV42 ) @ SV421 ) @ SV764 @ SV42 @ SV42 @ tc_nat ) @ SV42 )
| ~ ( c_SEQ_OZseq @ SV764 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2990,plain,
! [SV765: $i,SV422: $i,SV43: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV43 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV43 ) @ SV422 ) @ SV765 @ SV43 @ SV43 @ tc_nat ) @ SV43 )
| ~ ( c_SEQ_OZseq @ SV765 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2991,plain,
! [SV766: $i,SV423: $i,SV44: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV44 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SV766 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV44 ) @ SV423 ) @ SV766 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2992,plain,
! [SV424: $i,SV767: $i,SV45: $i] :
( ( ( c_Limits_OZfun @ SV45 @ SV767 @ SV424 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_ORe @ SV45 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV424 ) @ SV767 @ SV424 @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2993,plain,
! [SV768: $i,SV425: $i,SV47: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV47 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV425 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV47 ) @ SV425 ) ) @ SV768 ) )
= SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2994,plain,
! [SV1012: $i,SV769: $i,SV426: $i,SV48: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV48 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV48 )
| ~ ( class_RealVector_Ometric__space @ SV426 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2995,plain,
! [SV770: $i,SV427: $i,SV49: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV49 )
= $false )
| ( ( c_Lim_OLIM @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SV770 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV49 ) @ SV427 ) @ SV770 ) @ SV49 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2996,plain,
! [SV1166: $i,SV1013: $i,SV771: $i,SV429: $i,SV51: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV51 )
| ~ ( class_RealVector_Ometric__space @ SV429 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SV1013 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(2997,plain,
! [SV1167: $i,SV1014: $i,SV772: $i,SV430: $i,SV52: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV52 )
| ~ ( class_RealVector_Ometric__space @ SV430 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SV1014 @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(2998,plain,
! [SV54: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV54 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV54 ) @ ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2999,plain,
! [SV1168: $i,SV1015: $i,SV773: $i,SV432: $i,SV56: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV56 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SV773 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV1015 ) @ SV1168 @ SV773 @ SV56 )
| ~ ( c_Limits_Otendsto @ SV432 @ SV1015 @ SV1168 @ SV773 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3000,plain,
! [SV1169: $i,SV1016: $i,SV774: $i,SV433: $i,SV57: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV57 )
| ( c_Limits_Otendsto @ SV433 @ SV774 @ SV1016 @ SV1169 @ SV57 )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SV1169 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV774 ) @ SV1016 @ SV1169 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3001,plain,
! [SV1170: $i,SV1017: $i,SV775: $i,SV434: $i,SV58: $i] :
( ( ! [SY2963: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV58 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV434 )
| ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SY2963 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SY2963 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3002,plain,
! [SV435: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ SV435 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ SV435 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2664]) ).
thf(3003,plain,
! [SV436: $i,SV61: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV61 ) @ SV436 @ SV61 @ SV61 @ tc_nat ) @ SV61 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV436 @ SV61 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2665]) ).
thf(3004,plain,
! [SV1018: $i,SV776: $i,SV437: $i,SV62: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV62 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ SV776 ) ) @ SV1018 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV776 ) @ SV1018 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(3005,plain,
! [SV1019: $i,SV777: $i,SV438: $i,SV63: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SV777 ) ) @ SV1019 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SV1019 ) ) @ SV777 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(3006,plain,
! [SV1020: $i,SV778: $i,SV439: $i,SV64: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV64 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ SV778 ) ) @ SV1020 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV778 ) @ SV1020 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(3007,plain,
! [SV1021: $i,SV779: $i,SV440: $i,SV65: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV779 ) @ SV1021 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ SV779 ) ) @ SV1021 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(3008,plain,
! [SV1022: $i,SV780: $i,SV441: $i,SV66: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ SV1022 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ SV1022 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(3009,plain,
! [SV1023: $i,SV781: $i,SV442: $i,SV67: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV781 ) @ SV1023 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ SV781 ) ) @ SV1023 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(3010,plain,
! [SV1024: $i,SV782: $i,SV443: $i,SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV443 ) @ SV782 ) ) @ SV1024 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV443 ) @ SV1024 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV782 ) @ SV1024 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2672]) ).
thf(3011,plain,
! [SV1025: $i,SV783: $i,SV444: $i,SV69: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV69 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV783 ) @ SV1025 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SV783 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SV1025 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(3012,plain,
! [SV1026: $i,SV784: $i,SV445: $i,SV70: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV70 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV784 ) @ SV1026 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SV784 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SV1026 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(3013,plain,
! [SV1027: $i,SV785: $i,SV446: $i,SV71: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV71 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV446 ) @ SV785 ) ) @ SV1027 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV446 ) @ SV1027 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV785 ) @ SV1027 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(3014,plain,
! [SV1028: $i,SV786: $i,SV447: $i,SV72: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV72 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV447 ) @ SV786 ) ) @ SV1028 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV447 ) @ SV1028 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV786 ) @ SV1028 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(3015,plain,
! [SV1029: $i,SV787: $i,SV448: $i,SV73: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV73 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV787 ) @ SV1029 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SV787 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SV1029 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(3016,plain,
! [SV1030: $i,SV788: $i,SV449: $i,SV74: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV74 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV449 ) @ SV788 ) ) @ SV1030 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV449 ) @ SV1030 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV788 ) @ SV1030 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(3017,plain,
! [SV1031: $i,SV789: $i,SV450: $i,SV75: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV75 ) )
= $true )
| ( ( ~ ( class_HOL_Ozero @ SV75 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(3018,plain,
! [SV790: $i,SV451: $i,SV76: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV76 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ ( c_Series_Osuminf @ SV790 @ SV76 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ SV790 @ SV76 @ SV76 @ tc_nat ) @ SV76 ) )
| ~ ( c_Series_Osummable @ SV790 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(3019,plain,
! [SV1032: $i,SV791: $i,SV452: $i,SV77: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV77 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV452 ) @ SV791 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV1032 ) @ SV791 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV452 ) @ SV1032 ) ) @ SV791 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(3020,plain,
! [SV792: $i,SV454: $i,SV79: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV79 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ SV454 ) ) @ SV792 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV79 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV79 ) @ SV454 ) @ SV792 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(3021,plain,
! [SV793: $i,SV455: $i,SV80: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV80 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ SV455 ) ) @ SV793 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV80 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV80 ) @ SV455 ) @ SV793 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(3022,plain,
! [SV794: $i,SV456: $i,SV81: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV81 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ SV794 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV81 ) @ SV456 ) @ SV794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(3023,plain,
! [SV795: $i,SV457: $i,SV82: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV82 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ SV795 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV82 ) @ SV457 ) @ SV795 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(3024,plain,
! [SV796: $i,SV459: $i,SV84: $i] :
( ( ( class_Ring__and__Field_Oring @ SV84 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SV459 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV84 ) @ SV796 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV84 ) @ SV459 ) @ SV796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(3025,plain,
! [SV1033: $i,SV797: $i,SV460: $i,SV85: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV85 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV85 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SV1033 @ SV797 @ SV85 )
| ~ ( c_Limits_OZfun @ SV460 @ SV1033 @ SV797 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2689]) ).
thf(3026,plain,
! [SV1171: $i,SV1034: $i,SV798: $i,SV461: $i,SV86: $i] :
( ( ! [SY2964: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV86 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SV1034 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV1171 ) @ SY2964 @ SV1034 @ SV86 )
| ~ ( c_Limits_Otendsto @ SV798 @ SV1171 @ SY2964 @ SV1034 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3027,plain,
! [SV1172: $i,SV1035: $i,SV799: $i,SV462: $i,SV87: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV87 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SV799 @ SV87 @ SV87 @ SV1035 ) @ SV1172 @ SV1035 @ SV87 )
| ~ ( c_Limits_OZfun @ SV799 @ SV1172 @ SV1035 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3028,plain,
! [SV1173: $i,SV1036: $i,SV800: $i,SV463: $i,SV88: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV88 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SV800 @ SV88 @ SV88 @ SV1036 ) @ SV1173 @ SV1036 @ SV88 )
| ~ ( c_Limits_OZfun @ SV800 @ SV1173 @ SV1036 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3029,plain,
! [SV801: $i,SV464: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV89 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV464 ) @ SV801 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) ) )
| ( SV801
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
| ( SV464
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(3030,plain,
! [SV802: $i,SV465: $i,SV90: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV90 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV465 ) @ SV802 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) ) )
| ( SV802
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(3031,plain,
! [SV803: $i,SV466: $i,SV92: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV92 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ ( c_Series_Osuminf @ SV803 @ SV92 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ SV803 @ SV92 @ SV92 @ tc_nat ) @ SV92 ) )
| ~ ( c_Series_Osummable @ SV803 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(3032,plain,
! [SV804: $i,SV467: $i,SV93: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV93 )
= $false )
| ( ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ SV804 @ SV93 @ SV93 @ tc_nat ) @ SV93 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ ( c_Series_Osuminf @ SV804 @ SV93 ) ) )
| ~ ( c_Series_Osummable @ SV804 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(3033,plain,
! [SV1174: $i,SV1037: $i,SV805: $i,SV468: $i,SV95: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV95 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV805 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1037 ) @ SV1174 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV1037 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV805 ) @ SV1174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3034,plain,
! [SV1175: $i,SV1038: $i,SV806: $i,SV469: $i,SV96: $i] :
( ( ! [SY2965: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV96 )
| ~ ( class_RealVector_Ometric__space @ SV469 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SY2965 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SV1038 @ SV1175 @ SY2965 @ SV469 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3035,plain,
! [SV1039: $i,SV807: $i,SV470: $i,SV97: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV97 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SV470 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SV807 @ ( hAPP @ c_Complex_ORe @ SV1039 ) @ SV97 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV470 @ SV807 @ SV1039 @ SV97 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2699]) ).
thf(3036,plain,
! [SV808: $i,SV471: $i,SV98: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV98 )
= $false )
| ( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV98 ) @ SV471 @ SV98 @ SV98 @ SV98 ) @ SV808 @ SV98 )
| ~ ( c_Deriv_Odifferentiable @ SV471 @ SV808 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(3037,plain,
! [SV809: $i,SV472: $i,SV99: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV99 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV99 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ SV472 ) @ SV809 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV472 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV809 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(3038,plain,
! [SV810: $i,SV473: $i,SV100: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV100 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ SV473 ) @ SV810 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV810 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV473 ) ) )
| ( SV810
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(3039,plain,
! [SV1176: $i,SV1040: $i,SV811: $i,SV474: $i,SV101: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV101 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SV1176 @ SV474 @ SV101 )
| ( SV811 = SV1176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3040,plain,
! [SV1177: $i,SV1041: $i,SV812: $i,SV475: $i,SV102: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV102 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
| ( SV812 = SV1041 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SV1177 @ SV1041 @ SV475 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3041,plain,
! [SV476: $i,SV103: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV103 ) @ SV476 ) )
= SV476 )
= $true )
| ( ( SV476
= ( c_HOL_Ozero__class_Ozero @ SV103 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(3042,plain,
! [SV1178: $i,SV1042: $i,SV813: $i,SV477: $i,SV104: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV104 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ ( c_Finite__Set_Osetsum @ SV813 @ SV1042 @ SV1178 @ SV104 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ SV813 @ SV104 @ SV104 @ SV1178 ) @ SV1042 @ SV1178 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3043,plain,
! [SV1179: $i,SV1043: $i,SV814: $i,SV478: $i,SV105: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ ( c_Finite__Set_Osetsum @ SV814 @ SV1043 @ SV1179 @ SV105 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ SV814 @ SV105 @ SV105 @ SV1179 ) @ SV1043 @ SV1179 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3044,plain,
! [SV1180: $i,SV1044: $i,SV815: $i,SV480: $i,SV107: $i] :
( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
| ~ ( class_RealVector_Ometric__space @ SV480 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
| ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3045,plain,
! [SV1045: $i,SV816: $i,SV481: $i,SV108: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV108 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV481 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SV1045 @ SV108 @ SV481 )
| ~ ( c_Lim_OisCont @ SV816 @ SV1045 @ SV108 @ SV481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(3046,plain,
! [SV482: $i,SV109: $i] :
( ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ SV482 @ SV109 @ SV109 @ tc_nat ) @ SV109 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ ( c_Series_Osuminf @ SV482 @ SV109 ) ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV482 @ SV109 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2710]) ).
thf(3047,plain,
! [SV1046: $i,SV817: $i,SV483: $i,SV110: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV110 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ SV817 ) ) @ SV1046 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ SV817 ) @ SV1046 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(3048,plain,
! [SV1047: $i,SV818: $i,SV484: $i,SV111: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV111 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ SV818 ) ) @ SV1047 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ SV818 ) @ SV1047 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(3049,plain,
! [SV1048: $i,SV819: $i,SV485: $i,SV112: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV112 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ SV1048 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ SV1048 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(3050,plain,
! [SV1181: $i,SV1049: $i,SV820: $i,SV486: $i,SV114: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV114 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV114 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SV1181 @ SV820 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SV1049 @ SV1181 @ SV820 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3051,plain,
! [SV1050: $i,SV821: $i,SV487: $i,SV116: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV116 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV487 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1050 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SV1050 ) @ SV116 @ SV487 )
| ~ ( c_Lim_OisCont @ SV821 @ SV1050 @ SV116 @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(3052,plain,
! [SV1051: $i,SV822: $i,SV488: $i,SV117: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV117 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV488 )
| ( c_Lim_OisCont @ SV822 @ SV1051 @ SV117 @ SV488 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV1051 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SV1051 ) @ SV117 @ SV488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(3053,plain,
! [SV823: $i,SV489: $i,SV118: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV118 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SV489 @ SV118 @ SV118 @ SV118 ) @ SV823 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV118 ) @ SV823 ) @ SV489 ) @ SV118 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(3054,plain,
! [SV1052: $i,SV824: $i,SV490: $i,SV119: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV119 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV490 )
| ( c_Lim_OisCont @ SV824 @ SV1052 @ SV119 @ SV490 )
| ~ ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(3055,plain,
! [SV1182: $i,SV1053: $i,SV825: $i,SV491: $i,SV120: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV120 )
| ~ ( class_RealVector_Ometric__space @ SV491 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SV1053 @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3056,plain,
! [SV1183: $i,SV1054: $i,SV826: $i,SV492: $i,SV121: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV121 )
| ~ ( class_RealVector_Ometric__space @ SV492 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SV1054 @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3057,plain,
! [SV1055: $i,SV827: $i,SV493: $i,SV122: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV122 ) )
= $true )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV827 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV1055 ) @ SV122 )
| ~ ( c_Series_Osums @ SV827 @ SV1055 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(3058,plain,
! [SV828: $i,SV494: $i,SV124: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV124 )
= $false )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV124 ) @ SV494 ) @ SV828 @ SV124 @ SV124 @ tc_nat ) @ SV124 )
| ~ ( c_Series_Osummable @ SV828 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(3059,plain,
! [SV829: $i,SV495: $i,SV125: $i] :
( ( ( class_RealVector_Oreal__vector @ SV125 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ SV829 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV125 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV125 ) @ SV495 ) @ SV829 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(3060,plain,
! [SV830: $i,SV496: $i,SV126: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV126 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ SV830 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV126 ) @ SV496 ) @ SV830 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(3061,plain,
! [SV1184: $i,SV1056: $i,SV831: $i,SV497: $i,SV127: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV127 )
| ~ ( class_RealVector_Ometric__space @ SV497 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV1184 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SV831 @ SV1056 @ SV1184 @ SV497 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3062,plain,
! [SV1057: $i,SV832: $i,SV498: $i,SV129: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV129 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV498 )
| ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
| ~ ( c_SEQ_OZseq @ SV1057 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(3063,plain,
! [SV1185: $i,SV1058: $i,SV833: $i,SV499: $i,SV130: $i] :
( ( ! [SY2966: $i,SY2967: $i] :
( ~ ( class_RealVector_Ometric__space @ SV130 )
| ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SY2966 @ ( hAPP @ SV1058 @ SY2967 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SY2966 @ SY2967 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SY2967 @ SV130 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3064,plain,
! [SV1186: $i,SV1059: $i,SV834: $i,SV500: $i,SV131: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV131 )
| ~ ( class_RealVector_Oreal__algebra__1 @ SV131 )
| ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3065,plain,
! [SV1060: $i,SV836: $i,SV502: $i,SV133: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV133 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV133 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(3066,plain,
! [SV1061: $i,SV837: $i,SV503: $i,SV134: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV134 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(3067,plain,
! [SV1187: $i,SV1062: $i,SV838: $i,SV504: $i,SV135: $i] :
( ( ! [SY2968: $i,SY2969: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV135 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SY2968 @ ( hAPP @ SV1062 @ SY2969 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SY2968 @ SY2969 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3068,plain,
! [SV1188: $i,SV1063: $i,SV839: $i,SV505: $i,SV136: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV136 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SV839 @ SV136 @ SV136 @ SV1063 ) @ SV1188 @ SV1063 @ SV136 )
| ~ ( c_Limits_OZfun @ SV839 @ SV1188 @ SV1063 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3069,plain,
! [SV1189: $i,SV1064: $i,SV840: $i,SV506: $i,SV137: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV137 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SV840 @ SV137 @ SV137 @ SV1064 ) @ SV1189 @ SV1064 @ SV137 )
| ~ ( c_Limits_OZfun @ SV840 @ SV1189 @ SV1064 @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3070,plain,
! [SV507: $i,SV138: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV138 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ SV507 ) )
= SV507 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(3071,plain,
! [SV841: $i,SV508: $i,SV139: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV139 )
= $false )
| ( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SV508 @ SV139 @ SV139 @ SV139 ) @ SV841 @ SV139 )
| ( ( hAPP @ SV508 @ SV841 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
| ~ ( c_Deriv_Odifferentiable @ SV508 @ SV841 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(3072,plain,
! [SV1190: $i,SV1065: $i,SV842: $i,SV509: $i,SV140: $i] :
( ( ! [SY2970: $i,SY2971: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV140 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SY2970 ) @ SY2971 @ SV1190 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SY2970 @ SY2971 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3073,plain,
! [SV843: $i,SV510: $i,SV141: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV141 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SV510 ) @ SV843 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV141 ) @ SV843 ) @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(3074,plain,
! [SV844: $i,SV511: $i,SV143: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SV511 ) @ SV844 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV143 ) @ SV844 ) @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(3075,plain,
! [SV845: $i,SV512: $i,SV144: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV144 )
= $false )
| ( ( c_Lim_OisCont @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ SV144 ) @ SV512 @ SV144 @ SV144 @ SV144 ) @ SV845 @ SV144 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(3076,plain,
! [SV1066: $i,SV846: $i,SV513: $i,SV145: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV145 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV513 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV846 @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(3077,plain,
! [SV1067: $i,SV847: $i,SV514: $i,SV146: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV146 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV514 )
| ( c_Lim_OLIM @ SV847 @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(3078,plain,
! [SV1068: $i,SV848: $i,SV515: $i,SV147: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ SV1068 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ SV1068 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(3079,plain,
! [SV1069: $i,SV849: $i,SV516: $i,SV148: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ SV849 ) ) @ SV1069 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV849 ) @ SV1069 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(3080,plain,
! [SV1070: $i,SV850: $i,SV517: $i,SV149: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV149 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV850 ) @ SV1070 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ SV850 ) ) @ SV1070 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2744]) ).
thf(3081,plain,
! [SV1071: $i,SV853: $i,SV520: $i,SV152: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV152 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ SV1071 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ SV1071 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2745]) ).
thf(3082,plain,
! [SV1072: $i,SV854: $i,SV521: $i,SV153: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV153 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ SV854 ) ) @ SV1072 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV854 ) @ SV1072 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2746]) ).
thf(3083,plain,
! [SV1073: $i,SV855: $i,SV522: $i,SV154: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV154 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV855 ) @ SV1073 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ SV855 ) ) @ SV1073 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(3084,plain,
! [SV1074: $i,SV856: $i,SV523: $i,SV155: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV155 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SV856 ) ) @ SV1074 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SV1074 ) ) @ SV856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(3085,plain,
! [SV1075: $i,SV857: $i,SV524: $i,SV156: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV156 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ SV1075 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ SV1075 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2749]) ).
thf(3086,plain,
! [SV1076: $i,SV858: $i,SV525: $i,SV157: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV858 ) ) @ SV1076 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV858 ) @ SV1076 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(3087,plain,
! [SV859: $i,SV526: $i,SV158: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV158 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV158 ) @ SV526 ) @ SV859 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV158 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV158 ) @ SV526 ) ) @ SV859 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(3088,plain,
! [SV1191: $i,SV1077: $i,SV860: $i,SV527: $i,SV159: $i] :
( ( ! [SY2972: $i] :
( ( hAPP @ ( c_COMBC @ SV159 @ SV527 @ SV860 @ SV1077 @ SV1191 ) @ SY2972 )
= ( hAPP @ ( hAPP @ SV159 @ SY2972 ) @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3089,plain,
! [SV1079: $i,SV862: $i,SV529: $i,SV161: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV161 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV529 )
| ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
| ~ ( c_Series_Osummable @ SV1079 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(3090,plain,
! [SV1192: $i,SV1080: $i,SV863: $i,SV530: $i,SV162: $i] :
( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV1080 ) @ SV1192 @ SV863 @ SV162 )
| ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SV530 @ SV1080 @ SV1192 @ SV863 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3091,plain,
! [SV1193: $i,SV1081: $i,SV864: $i,SV535: $i,SV167: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV167 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV535 ) @ SV864 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV1081 ) @ SV864 ) ) @ SV1193 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ SV535 ) @ SV1081 ) ) @ SV864 ) ) @ SV1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3092,plain,
! [SV168: $i,SV536: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV536 @ ( c_SEQ_Olim @ SV536 @ SV168 ) @ SV168 )
= $true )
| ( ( ~ ( c_SEQ_Oconvergent @ SV536 @ SV168 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(3093,plain,
! [SV169: $i,SV537: $i] :
( ( ( c_SEQ_Oconvergent @ SV537 @ SV169 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV537 @ ( c_SEQ_Olim @ SV537 @ SV169 ) @ SV169 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(3094,plain,
! [SV1082: $i,SV865: $i,SV542: $i,SV174: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV174 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV542 )
| ( c_Lim_OisCont @ SV865 @ SV1082 @ SV174 @ SV542 )
| ~ ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2767]) ).
thf(3095,plain,
! [SV543: $i,SV175: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV175 ) )
= $true )
| ( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SV543 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SV543 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
| ~ ( c_Series_Osummable @ SV543 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2768]) ).
thf(3096,plain,
! [SV544: $i,SV176: $i] :
( ( ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ SV544 @ SV176 @ SV176 @ tc_nat ) @ SV176 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ ( c_SEQ_Olim @ SV544 @ SV176 ) ) )
= $true )
| ( ( ~ ( c_SEQ_Oconvergent @ SV544 @ SV176 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(3097,plain,
! [SV1194: $i,SV1083: $i,SV866: $i,SV545: $i,SV177: $i] :
( ( ~ ( class_RealVector_Oreal__vector @ SV177 )
| ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ ( c_Finite__Set_Osetsum @ SV866 @ SV1083 @ SV1194 @ SV177 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ SV866 @ SV177 @ SV177 @ SV1194 ) @ SV1083 @ SV1194 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3098,plain,
! [SV1195: $i,SV1084: $i,SV867: $i,SV546: $i,SV179: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV179 )
| ~ ( class_RealVector_Ometric__space @ SV546 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV1195 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV867 @ SV1084 @ SV1195 @ SV546 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3099,plain,
! [SV547: $i,SV180: $i] :
( ( ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV180 ) @ SV547 @ SV180 @ SV180 @ tc_nat ) @ SV180 )
= $true )
| ( ( ~ ( c_SEQ_Oconvergent @ SV547 @ SV180 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(3100,plain,
! [SV181: $i,SV548: $i] :
( ( ( c_SEQ_Oconvergent @ SV548 @ SV181 )
= $true )
| ( ( ~ ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV181 ) @ SV548 @ SV181 @ SV181 @ tc_nat ) @ SV181 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3101,plain,
! [SV549: $i,SV182: $i] :
( ( ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV182 ) @ SV549 ) @ SV182 @ SV182 )
= $true )
| ( ( SV549
= ( c_HOL_Ozero__class_Ozero @ SV182 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(3102,plain,
! [SV1085: $i,SV868: $i,SV550: $i,SV183: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV183 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV868 ) @ SV1085 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SV868 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SV1085 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(3103,plain,
! [SV1086: $i,SV869: $i,SV551: $i,SV184: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV184 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ SV869 ) @ SV1086 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SV869 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SV1086 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(3104,plain,
! [SV1196: $i,SV1087: $i,SV870: $i,SV552: $i,SV185: $i] :
( ( ! [SY2973: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV185 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV552 )
| ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SY2973 @ SV1196 @ SV185 )
| ~ ( c_Limits_OZfun @ SV1087 @ SY2973 @ SV1196 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3105,plain,
! [SV1088: $i,SV871: $i,SV554: $i,SV188: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV188 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ SV554 @ SV188 @ SV188 @ SV871 ) @ SV1088 @ SV871 @ SV188 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ ( c_Finite__Set_Osetsum @ SV554 @ SV1088 @ SV871 @ SV188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(3106,plain,
! [SV558: $i,SV192: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV192 ) )
= $true )
| ( ( SV558
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV558 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3107,plain,
! [SV568: $i,SV202: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV202 ) )
= $true )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SV568 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
| ~ ( c_Series_Osummable @ SV568 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(3108,plain,
! [SV1089: $i,SV872: $i,SV569: $i,SV203: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV203 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ SV1089 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ SV1089 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(3109,plain,
! [SV1090: $i,SV873: $i,SV570: $i,SV204: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra @ SV204 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ SV873 ) ) @ SV1090 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ SV873 ) @ SV1090 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(3110,plain,
! [SV1091: $i,SV874: $i,SV571: $i,SV205: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra @ SV205 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ SV1091 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ SV1091 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(3111,plain,
! [SV1092: $i,SV875: $i,SV572: $i,SV206: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV206 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SV1092 @ SV206 @ SV572 )
| ~ ( c_Lim_OisCont @ SV875 @ SV1092 @ SV206 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(3112,plain,
! [SV1197: $i,SV1093: $i,SV876: $i,SV573: $i,SV207: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV207 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV573 )
| ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SV1197 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SV1197 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3113,plain,
! [SV1094: $i,SV877: $i,SV574: $i,SV208: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV208 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV574 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
| ~ ( c_SEQ_OCauchy @ SV1094 @ SV208 )
| ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(3114,plain,
! [SV1198: $i,SV1095: $i,SV878: $i,SV575: $i,SV209: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV209 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV575 )
| ( c_Lim_OLIM @ SV878 @ SV1095 @ SV1198 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV1198 @ SV575 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3115,plain,
! [SV1199: $i,SV1096: $i,SV879: $i,SV576: $i,SV210: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV210 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV576 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SV1199 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SV879 @ SV1096 @ SV1199 @ SV576 @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3116,plain,
! [SV1097: $i,SV880: $i,SV577: $i,SV211: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV211 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV577 )
| ( c_Lim_OLIM @ SV880 @ SV1097 @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV1097 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(3117,plain,
! [SV1098: $i,SV881: $i,SV578: $i,SV212: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV212 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV578 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV1098 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
| ~ ( c_Lim_OLIM @ SV881 @ SV1098 @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(3118,plain,
! [SV882: $i,SV579: $i,SV213: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV213 )
= $false )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV213 ) @ SV579 ) @ SV882 @ SV213 @ SV213 @ tc_nat ) @ SV213 )
| ~ ( c_Series_Osummable @ SV882 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(3119,plain,
! [SV883: $i,SV580: $i,SV214: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV214 )
= $false )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV214 ) @ SV580 ) @ SV883 @ SV214 @ SV214 @ tc_nat ) @ SV214 )
| ~ ( c_Series_Osummable @ SV883 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(3120,plain,
! [SV1099: $i,SV884: $i,SV581: $i,SV215: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV215 ) )
= $true )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV884 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV1099 ) @ SV215 )
| ~ ( c_Series_Osums @ SV884 @ SV1099 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(3121,plain,
! [SV1100: $i,SV885: $i,SV582: $i,SV216: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV216 ) )
= $true )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV885 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV1100 ) @ SV216 )
| ~ ( c_Series_Osums @ SV885 @ SV1100 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(3122,plain,
! [SV886: $i,SV583: $i,SV217: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV217 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 @ SV583 ) @ SV886 @ SV583 @ SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(3123,plain,
! [SV887: $i,SV584: $i,SV218: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV218 )
= $false )
| ( ( ( c_Series_Osummable @ SV584 @ SV218 )
| ~ ( c_Series_Osums @ SV584 @ SV887 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3124,plain,
! [SV888: $i,SV585: $i,SV219: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV219 )
= $false )
| ( ( ( c_Series_Osummable @ SV585 @ SV219 )
| ~ ( c_Series_Osums @ SV585 @ SV888 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(3125,plain,
! [SV889: $i,SV586: $i,SV220: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV220 )
= $false )
| ( ( c_Lim_OisCont @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV220 ) @ SV586 ) @ SV889 @ SV220 @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3126,plain,
! [SV1200: $i,SV1101: $i,SV890: $i,SV587: $i,SV221: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV221 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SV890 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV1101 ) @ SV1200 @ SV890 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV587 @ SV1101 @ SV1200 @ SV890 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3127,plain,
! [SV891: $i,SV590: $i,SV224: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV224 )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 @ SV590 ) @ SV891 @ SV590 @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(3128,plain,
! [SV1102: $i,SV892: $i,SV592: $i,SV226: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV226 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ SV1102 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ SV1102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(3129,plain,
! [SV1103: $i,SV893: $i,SV593: $i,SV227: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV227 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ SV1103 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ SV1103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(3130,plain,
! [SV1104: $i,SV894: $i,SV594: $i,SV228: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV228 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ SV1104 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ SV1104 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(3131,plain,
! [SV595: $i,SV229: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV229 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SV595 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
| ~ ( c_SEQ_OZseq @ SV595 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(3132,plain,
! [SV1105: $i,SV895: $i,SV596: $i,SV230: $i] :
( ( ( ~ ( class_RealVector_Otopological__space @ SV230 ) )
= $true )
| ( ( c_Limits_Otendsto @ ( c_COMBK @ SV596 @ SV230 @ SV895 ) @ SV596 @ SV1105 @ SV895 @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2819]) ).
thf(3133,plain,
! [SV896: $i,SV597: $i,SV231: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV231 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SV597 ) @ SV896 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV231 ) @ SV896 ) @ SV597 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3134,plain,
! [SV897: $i,SV599: $i,SV233: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SV599 ) @ SV897 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV233 ) @ SV897 ) @ SV599 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(3135,plain,
! [SV898: $i,SV600: $i,SV234: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV234 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV600 ) @ SV898 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV898 ) @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(3136,plain,
! [SV1106: $i,SV899: $i,SV601: $i,SV236: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV236 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV601 )
| ( c_Lim_OLIM @ ( c_COMBK @ SV899 @ SV236 @ SV601 ) @ SV1106 @ SV899 @ SV601 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(3137,plain,
! [SV1107: $i,SV900: $i,SV602: $i,SV237: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV237 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV237 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SV602 @ SV900 @ SV1107 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SV602 @ tc_RealDef_Oreal @ SV237 @ SV1107 ) @ SV900 @ SV1107 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3138,plain,
! [SV603: $i,SV238: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ SV603 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV238 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV238 ) @ SV603 ) ) )
= $true )
| ( ( SV603
= ( c_HOL_Ozero__class_Ozero @ SV238 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(3139,plain,
! [SV901: $i,SV615: $i,SV250: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV250 )
= $false )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ SV615 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV901 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV250 @ tc_nat ) @ SV250 )
| ~ ( c_Series_Osummable @ SV615 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(3140,plain,
! [SV1201: $i,SV1108: $i,SV902: $i,SV616: $i,SV251: $i] :
( ( ! [SY2974: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV251 )
| ~ ( class_RealVector_Ometric__space @ SV616 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SY2974 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SV1108 @ SV1201 @ SY2974 @ SV616 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3141,plain,
! [SV903: $i,SV617: $i,SV252: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV252 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV252 ) @ SV617 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV252 ) @ SV903 ) @ SV617 ) )
= SV903 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(3142,plain,
! [SV904: $i,SV618: $i,SV253: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV253 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV253 ) @ SV618 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV253 ) @ SV618 ) @ SV904 ) )
= SV904 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(3143,plain,
! [SV1109: $i,SV905: $i,SV619: $i,SV254: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ SV254 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV619 ) @ ( hAPP @ c_Complex_ORe @ SV905 ) @ SV1109 @ SV619 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV254 @ SV905 @ SV1109 @ SV619 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2841]) ).
thf(3144,plain,
! [SV1202: $i,SV1110: $i,SV906: $i,SV620: $i,SV255: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV255 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV620 )
| ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
| ~ ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3145,plain,
! [SV256: $i,SV621: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV621 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV621 @ SV256 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3146,plain,
! [SV907: $i,SV622: $i,SV257: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV257 )
= $false )
| ( ( ( SV622
= ( c_Series_Osuminf @ SV907 @ SV257 ) )
| ~ ( c_Series_Osums @ SV907 @ SV622 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(3147,plain,
! [SV908: $i,SV623: $i,SV258: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV258 )
= $false )
| ( ( ( ( c_Series_Osuminf @ SV623 @ SV258 )
= SV908 )
| ~ ( c_Series_Osums @ SV623 @ SV908 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(3148,plain,
! [SV262: $i,SV625: $i] :
( ( ( c_SEQ_OCauchy @ SV625 @ SV262 )
= $true )
| ( ( ~ ( c_SEQ_Oconvergent @ SV625 @ SV262 ) )
= $true )
| ( ( class_SEQ_Ocomplete__space @ SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(3149,plain,
! [SV263: $i,SV626: $i] :
( ( ( c_SEQ_Oconvergent @ SV626 @ SV263 )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV626 @ SV263 ) )
= $true )
| ( ( class_SEQ_Ocomplete__space @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(3150,plain,
! [SV265: $i,SV628: $i] :
( ( ( c_SEQ_OCauchy @ SV628 @ SV265 )
= $true )
| ( ( ~ ( c_SEQ_Oconvergent @ SV628 @ SV265 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2850]) ).
thf(3151,plain,
! [SV909: $i,SV629: $i,SV267: $i] :
( ( ( class_Ring__and__Field_Oring @ SV267 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SV629 ) ) @ SV909 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV267 ) @ SV629 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV267 ) @ SV909 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(3152,plain,
! [SV910: $i,SV630: $i,SV268: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV268 )
= $false )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV630 @ SV268 @ SV268 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV910 ) @ SV268 )
| ~ ( c_Series_Osums @ SV630 @ SV910 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(3153,plain,
! [SV1111: $i,SV911: $i,SV631: $i,SV271: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV271 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV631 )
| ( c_Lim_OLIM @ SV911 @ SV1111 @ ( hAPP @ SV911 @ SV1111 ) @ SV271 @ SV631 )
| ~ ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(3154,plain,
! [SV912: $i,SV632: $i,SV272: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV272 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV272 ) @ SV632 ) @ SV912 @ SV272 @ SV272 @ tc_nat ) @ SV272 )
| ~ ( c_SEQ_OZseq @ SV912 @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(3155,plain,
! [SV913: $i,SV633: $i,SV273: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV273 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV273 ) @ SV633 ) @ SV913 @ SV273 @ SV273 @ tc_nat ) @ SV273 )
| ~ ( c_SEQ_OZseq @ SV913 @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(3156,plain,
! [SV274: $i,SV634: $i] :
( ( ( c_Series_Osums @ SV634 @ ( c_Series_Osuminf @ SV634 @ SV274 ) @ SV274 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV634 @ SV274 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2856]) ).
thf(3157,plain,
! [SV275: $i,SV635: $i] :
( ( ( ~ ( c_Series_Osummable @ SV635 @ SV275 ) )
= $true )
| ( ( c_Series_Osums @ SV635 @ ( c_Series_Osuminf @ SV635 @ SV275 ) @ SV275 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV275 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3158,plain,
! [SV1112: $i,SV914: $i,SV636: $i,SV276: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV276 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV636 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
| ~ ( c_SEQ_OCauchy @ SV1112 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(3159,plain,
! [SV1113: $i,SV915: $i,SV637: $i,SV277: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV277 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV637 )
| ( c_Lim_OisCont @ SV915 @ SV1113 @ SV277 @ SV637 )
| ~ ( c_Lim_OLIM @ SV915 @ SV1113 @ ( hAPP @ SV915 @ SV1113 ) @ SV277 @ SV637 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2859]) ).
thf(3160,plain,
! [SV1114: $i,SV916: $i,SV638: $i,SV278: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV278 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV638 )
| ( c_Lim_OLIM @ SV916 @ SV1114 @ ( hAPP @ SV916 @ SV1114 ) @ SV278 @ SV638 )
| ~ ( c_Lim_OisCont @ SV916 @ SV1114 @ SV278 @ SV638 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(3161,plain,
! [SV917: $i,SV639: $i,SV279: $i] :
( ( ( class_RealVector_Oreal__vector @ SV279 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV639 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV279 ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ SV917 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(3162,plain,
! [SV918: $i,SV640: $i,SV280: $i] :
( ( ( class_RealVector_Oreal__vector @ SV280 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SV640 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV280 ) @ SV918 ) @ ( c_HOL_Ozero__class_Ozero @ SV280 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(3163,plain,
! [SV1203: $i,SV1115: $i,SV919: $i,SV641: $i,SV281: $i] :
( ( ! [SY2975: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV281 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV1203 ) @ SY2975 @ SV1115 @ SV281 )
| ~ ( c_Limits_Otendsto @ SV919 @ SV1203 @ SY2975 @ SV1115 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3164,plain,
! [SV920: $i,SV642: $i,SV282: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV282 )
= $false )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV282 ) @ SV642 ) @ SV920 @ SV282 @ SV282 @ tc_nat ) @ SV282 )
| ~ ( c_SEQ_OCauchy @ SV920 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(3165,plain,
! [SV921: $i,SV644: $i,SV285: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV285 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV285 )
| ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SV921 ) @ SV285 )
| ~ ( c_Series_Osums @ SV644 @ SV921 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(3166,plain,
! [SV1116: $i,SV922: $i,SV645: $i,SV286: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV286 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV645 )
| ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
| ~ ( c_Series_Osummable @ SV1116 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(3167,plain,
! [SV1117: $i,SV923: $i,SV646: $i,SV287: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV287 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV646 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SV1117 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SV923 @ SV1117 @ SV287 @ SV646 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(3168,plain,
! [SV924: $i,SV648: $i,SV289: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV289 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ SV648 ) @ SV924 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV289 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SV924 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV289 ) @ SV648 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(3169,plain,
! [SV925: $i,SV649: $i,SV290: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV290 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ SV649 ) @ SV925 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV290 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SV649 ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV290 ) @ SV925 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(3170,plain,
! [SV1204: $i,SV1118: $i,SV926: $i,SV651: $i,SV293: $i] :
( ( ! [SY2976: $i] :
( ( c_Set_Oimage @ SV293 @ ( c_Set_Oimage @ SV651 @ SV926 @ SV1118 @ SV1204 ) @ SV1204 @ SY2976 )
= ( c_Set_Oimage @ ( c_COMBB @ SV293 @ SV651 @ SV1204 @ SY2976 @ SV1118 ) @ SV926 @ SV1118 @ SY2976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3171,plain,
! [SV927: $i,SV652: $i,SV294: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV294 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV652 @ SV294 @ SV294 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV927 ) @ SV294 )
| ~ ( c_SEQ_OLIMSEQ @ SV652 @ SV927 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(3172,plain,
! [SV928: $i,SV653: $i,SV295: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV295 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ SV653 @ SV928 @ SV295 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV653 @ SV295 @ SV295 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV928 ) @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3173,plain,
! [SV929: $i,SV654: $i,SV297: $i] :
( ( ( class_RealVector_Ometric__space @ SV297 )
= $false )
| ( ( ( c_SEQ_Oconvergent @ SV654 @ SV297 )
| ~ ( c_SEQ_OLIMSEQ @ SV654 @ SV929 @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(3174,plain,
! [SV930: $i,SV655: $i,SV298: $i] :
( ( ( class_RealVector_Ometric__space @ SV298 )
= $false )
| ( ( ( c_SEQ_Oconvergent @ SV655 @ SV298 )
| ~ ( c_SEQ_OLIMSEQ @ SV655 @ SV930 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(3175,plain,
! [SV931: $i,SV656: $i,SV299: $i] :
( ( ( class_RealVector_Ometric__space @ SV299 )
= $false )
| ( ( ( SV656 = SV931 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV656 @ SV299 @ tc_nat ) @ SV931 @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(3176,plain,
! [SV1205: $i,SV1119: $i,SV932: $i,SV657: $i,SV300: $i] :
( ( ! [SY2977: $i,SY2978: $i] :
( ~ ( class_RealVector_Ometric__space @ SV300 )
| ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SY2977 @ ( hAPP @ SV1119 @ SY2978 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SY2977 @ SY2978 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SY2978 @ ( hAPP @ SV1119 @ SY2978 ) @ SV300 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3177,plain,
! [SV301: $i,SV658: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV658 @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV301 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV301 ) @ SV658 @ SV301 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2879]) ).
thf(3178,plain,
! [SV659: $i,SV302: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV302 ) @ SV659 @ SV302 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV659 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3179,plain,
! [SV933: $i,SV660: $i,SV303: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV303 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV660 @ SV303 @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV933 ) @ tc_RealDef_Oreal )
| ~ ( c_SEQ_OLIMSEQ @ SV660 @ SV933 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2881]) ).
thf(3180,plain,
! [SV1120: $i,SV934: $i,SV662: $i,SV305: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV305 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV662 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV934 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SV1120 @ SV305 )
| ~ ( c_SEQ_OLIMSEQ @ SV662 @ SV1120 @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(3181,plain,
! [SV1121: $i,SV935: $i,SV663: $i,SV306: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV306 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ SV663 @ SV935 @ SV306 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV663 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1121 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SV935 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(3182,plain,
! [SV936: $i,SV664: $i,SV307: $i] :
( ( ( class_RealVector_Ometric__space @ SV307 )
= $false )
| ( ( ( ( c_SEQ_Olim @ SV664 @ SV307 )
= SV936 )
| ~ ( c_SEQ_OLIMSEQ @ SV664 @ SV936 @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(3183,plain,
! [SV1122: $i,SV937: $i,SV665: $i,SV308: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ SV308 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV665 ) @ ( hAPP @ c_Complex_OIm @ SV937 ) @ SV1122 @ SV665 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV308 @ SV937 @ SV1122 @ SV665 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2885]) ).
thf(3184,plain,
! [SV1206: $i,SV1123: $i,SV938: $i,SV668: $i,SV312: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV312 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV668 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3185,plain,
! [SV1207: $i,SV1124: $i,SV939: $i,SV669: $i,SV313: $i] :
( ( ! [SY2979: $i] :
( ~ ( class_RealVector_Ometric__space @ SV313 )
| ~ ( class_RealVector_Ometric__space @ SV669 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SY2979 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SY2979 @ SV669 ) )
= SY2979 )
| ~ ( c_Lim_OLIM @ SV939 @ SY2979 @ SV1207 @ SV669 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3186,plain,
! [SV941: $i,SV671: $i,SV315: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV315 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV315 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SV941 ) @ SV315 )
| ~ ( c_SEQ_OLIMSEQ @ SV671 @ SV941 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(3187,plain,
! [SV674: $i,SV942: $i,SV319: $i] :
( ( ( c_Limits_OZfun @ SV319 @ SV942 @ SV674 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ c_Complex_OIm @ SV319 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV674 ) @ SV942 @ SV674 @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(3188,plain,
! [SV1208: $i,SV1125: $i,SV943: $i,SV675: $i,SV320: $i] :
( ( ! [SY2980: $i] :
( ~ ( class_RealVector_Ometric__space @ SV320 )
| ~ ( class_RealVector_Ometric__space @ SV675 )
| ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SY2980 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SY2980 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SY2980 @ SV320 @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3189,plain,
! [SV1126: $i,SV944: $i,SV676: $i,SV321: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV321 ) )
= $true )
| ( ( ( SV676 = SV944 )
| ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV944 @ SV321 )
| ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV676 @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(3190,plain,
! [SV1127: $i,SV945: $i,SV677: $i,SV322: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV322 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV945 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV1127 ) @ SV322 )
| ~ ( c_SEQ_OLIMSEQ @ SV945 @ SV1127 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3191,plain,
! [SV1128: $i,SV946: $i,SV678: $i,SV323: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV323 ) )
= $true )
| ( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SV1128 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV946 @ SV1128 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SV1128 ) @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(3192,plain,
! [SV1129: $i,SV947: $i,SV679: $i,SV324: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV324 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV947 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV1129 ) @ SV324 )
| ~ ( c_SEQ_OLIMSEQ @ SV947 @ SV1129 @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2898]) ).
thf(3193,plain,
! [SV948: $i,SV680: $i,SV326: $i] :
( ( ( class_RealVector_Ometric__space @ SV326 )
= $false )
| ( ( ( c_SEQ_OCauchy @ SV680 @ SV326 )
| ~ ( c_SEQ_OLIMSEQ @ SV680 @ SV948 @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2899]) ).
thf(3194,plain,
! [SV949: $i,SV681: $i,SV327: $i] :
( ( ( class_RealVector_Ometric__space @ SV327 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV681 @ c_Suc @ tc_nat @ SV327 @ tc_nat ) @ SV949 @ SV327 )
| ~ ( c_SEQ_OLIMSEQ @ SV681 @ SV949 @ SV327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(3195,plain,
! [SV950: $i,SV682: $i,SV328: $i] :
( ( ( class_RealVector_Ometric__space @ SV328 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ SV682 @ SV950 @ SV328 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV682 @ c_Suc @ tc_nat @ SV328 @ tc_nat ) @ SV950 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(3196,plain,
! [SV1209: $i,SV1130: $i,SV951: $i,SV683: $i,SV329: $i] :
( ( ! [SY2981: $i] :
( ( hAPP @ ( c_COMBB @ SV329 @ SV683 @ SV951 @ SV1130 @ SV1209 ) @ SY2981 )
= ( hAPP @ SV329 @ ( hAPP @ SV683 @ SY2981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3197,plain,
! [SV952: $i,SV684: $i,SV330: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ SV330 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV684 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV952 ) @ SV330 )
| ( SV952
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ~ ( c_SEQ_OLIMSEQ @ SV684 @ SV952 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(3198,plain,
! [SV1131: $i,SV953: $i,SV685: $i,SV331: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV331 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SV685 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SV953 @ ( hAPP @ c_Complex_OIm @ SV1131 ) @ SV331 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV685 @ SV953 @ SV1131 @ SV331 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(3199,plain,
! [SV1210: $i,SV1132: $i,SV954: $i,SV687: $i,SV335: $i] :
( ( ! [SY2982: $i] :
( ( hAPP @ ( c_COMBC @ SV335 @ SV687 @ SV954 @ SV1132 @ SV1210 ) @ SY2982 )
= ( hAPP @ ( hAPP @ SV335 @ SY2982 ) @ SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3200,plain,
! [SV1211: $i,SV1133: $i,SV955: $i,SV688: $i,SV336: $i] :
( ( ! [SY2983: $i] :
( ( hAPP @ ( c_COMBB @ SV336 @ SV688 @ SV955 @ SV1133 @ SV1211 ) @ SY2983 )
= ( hAPP @ SV336 @ ( hAPP @ SV688 @ SY2983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3201,plain,
! [SV956: $i,SV690: $i,SV338: $i] :
( ( ( c_fequal @ SV338 @ SV690 @ SV956 )
= $false )
| ( ( SV338 = SV690 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(3202,plain,
! [SV957: $i,SV691: $i,SV339: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV691 ) @ SV691 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV957 ) @ SV957 ) )
| ( SV691
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SV957 ) )
| ( SV691 = SV957 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(3203,plain,
! [SV1134: $i,SV958: $i,SV692: $i,SV340: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV692 ) @ SV958 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1134 ) @ SV958 ) )
| ( SV692 = SV1134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3204,plain,
! [SV959: $i,SV693: $i,SV342: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV342 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SV693 ) @ SV959 )
!= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV693
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV959
= ( c_HOL_Ozero__class_Ozero @ SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(3205,plain,
! [SV960: $i,SV694: $i,SV343: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV343 ) @ SV960 ) )
= $false )
| ( ( SV694 = SV960 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(3206,plain,
! [SV695: $i,SV344: $i] :
( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV344 ) @ SV695 )
!= ( c_HOL_Ozero__class_Ozero @ SV344 ) )
= $true )
| ( ( SV695
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3207,plain,
! [SV1212: $i,SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV345 )
| ~ ( class_Int_Onumber__ring @ SV345 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
| ( SV961 = SV1212 )
| ( SV696 = SV1135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3208,plain,
! [SV697: $i,SV346: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV346 ) @ SV697 ) @ SV697 )
!= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
= $true )
| ( ( SV697
= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(3209,plain,
! [SV962: $i,SV698: $i,SV347: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV347 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV962 ) )
| ( SV698 = SV962 )
| ( SV962
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(3210,plain,
! [SV963: $i,SV699: $i,SV348: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV348 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ SV699 ) @ SV963 )
!= ( c_HOL_Ozero__class_Ozero @ SV348 ) )
| ( SV699
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV348 ) @ SV963 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(3211,plain,
! [SV964: $i,SV700: $i,SV349: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV349 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV700 ) @ SV700 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV964 ) @ SV964 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
| ( SV700
= ( c_HOL_Ozero__class_Ozero @ SV349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(3212,plain,
! [SV965: $i,SV701: $i,SV350: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SV701 ) @ SV965 )
!= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV965
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3213,plain,
! [SV1136: $i,SV966: $i,SV702: $i,SV351: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ SV351 @ SV702 )
!= ( c_Complex_Ocomplex_OComplex @ SV966 @ SV1136 ) )
= $true )
| ( ( SV702 = SV1136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(3214,plain,
! [SV1213: $i,SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV352 )
| ~ ( class_Int_Onumber__ring @ SV352 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
| ( SV967 = SV1213 )
| ( SV703 = SV1137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3215,plain,
! [SV704: $i,SV353: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV353 ) @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
= $true )
| ( ( SV704
= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3216,plain,
! [SV1138: $i,SV968: $i,SV705: $i,SV354: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV354 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV968 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV1138 ) )
| ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV968 = SV1138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(3217,plain,
! [SV969: $i,SV706: $i,SV355: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SV706 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV355 ) @ SV969 ) )
= $false )
| ( ( SV706 = SV969 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3218,plain,
! [SV970: $i,SV708: $i,SV357: $i] :
( ( ( class_RealVector_Oreal__vector @ SV357 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SV708 ) @ SV970 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV970
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV708
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3219,plain,
! [SV1139: $i,SV971: $i,SV709: $i,SV358: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV971 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV1139 ) )
| ( SV971 = SV1139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2927]) ).
thf(3220,plain,
! [SV972: $i,SV710: $i,SV359: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV359 ) @ SV710 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV972 ) @ SV710 ) )
= $false )
| ( ( SV359 = SV972 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3221,plain,
! [SV973: $i,SV711: $i,SV360: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV360 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV711 ) @ SV973 )
!= ( c_HOL_Ozero__class_Ozero @ SV360 ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV360 ) @ SV711 )
= SV973 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3222,plain,
! [SV974: $i,SV712: $i,SV361: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV361 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV361 )
| ( SV712
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3223,plain,
! [SV975: $i,SV713: $i,SV362: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV362 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SV713 ) @ SV975 )
!= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV975
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV362 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2931]) ).
thf(3224,plain,
! [SV714: $i,SV363: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV363 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SV714 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( SV714
= ( c_HOL_Ozero__class_Ozero @ SV363 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3225,plain,
! [SV976: $i,SV715: $i,SV364: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV364 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV715 ) @ SV715 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV976 ) @ SV976 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
| ( SV976
= ( c_HOL_Ozero__class_Ozero @ SV364 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(3226,plain,
! [SV977: $i,SV716: $i,SV365: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV365 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV716 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV977 ) )
| ( SV716 = SV977 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(3227,plain,
! [SV1140: $i,SV978: $i,SV717: $i,SV366: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV366 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SV978 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV1140 ) @ SV978 ) )
| ( SV978
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SV717 = SV1140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3228,plain,
! [SV718: $i,SV367: $i] :
( ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV367 ) @ SV718 )
!= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $true )
| ( ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(3229,plain,
! [SV719: $i,SV368: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV368 ) @ SV719 )
!= SV719 )
= $true )
| ( ( SV719
= ( c_HOL_Ozero__class_Ozero @ SV368 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__ab__group__add @ SV368 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3230,plain,
! [SV720: $i,SV369: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV369 ) @ SV720 )
!= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
= $true )
| ( ( SV720
= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3231,plain,
! [SV1141: $i,SV979: $i,SV721: $i,SV370: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ SV370 @ SV721 )
!= ( c_Complex_Ocomplex_OComplex @ SV979 @ SV1141 ) )
= $true )
| ( ( SV370 = SV979 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3232,plain,
! [SV722: $i,SV371: $i] :
( ( ( ( hAPP @ c_Complex_ORe @ SV371 )
!= ( hAPP @ c_Complex_ORe @ SV722 ) )
= $true )
| ( ( SV371 = SV722 )
= $true )
| ( ( ( hAPP @ c_Complex_OIm @ SV371 )
= ( hAPP @ c_Complex_OIm @ SV722 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3233,plain,
! [SV723: $i,SV372: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV372 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV372 ) @ SV723 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV372 )
= SV723 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV372 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(3234,plain,
! [SV980: $i,SV724: $i,SV373: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV373 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV980 ) )
| ( SV724 = SV980 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(3235,plain,
! [SV981: $i,SV725: $i,SV374: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV374 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV725 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV981 ) )
| ( SV725 = SV981 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3236,plain,
! [SV1142: $i,SV982: $i,SV726: $i,SV375: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV375 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV375 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV1142 ) )
| ( SV982 = SV1142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2944]) ).
thf(3237,plain,
! [SV983: $i,SV727: $i,SV376: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV376 )
= $false )
| ( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV727 )
!= ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV983 ) )
| ( SV727 = SV983 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3238,plain,
! [SV1214: $i,SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV377 )
| ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
| ( SV1143 = SV1214 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3239,plain,
! [SV1144: $i,SV985: $i,SV729: $i,SV379: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV985 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV1144 ) )
| ( SV985 = SV1144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3240,plain,
! [SV1215: $i,SV1145: $i,SV986: $i,SV731: $i,SV381: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV381 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1145 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1215 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SV1145 )
= SV1215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3241,plain,
! [SV1146: $i,SV987: $i,SV732: $i,SV382: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV382 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV987 ) @ SV1146 ) )
!= SV987 )
| ( SV732
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SV1146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3242,plain,
! [SV1147: $i,SV988: $i,SV733: $i,SV383: $i,SV2: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV2 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV383 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SV733 @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2951]) ).
thf(3243,plain,
! [SV1148: $i,SV989: $i,SV734: $i,SV384: $i,SV3: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV3 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV384 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SV734 @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2952]) ).
thf(3244,plain,
! [SV1216: $i,SV1149: $i,SV990: $i,SV735: $i,SV385: $i,SV4: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV4 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SV990 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV1149 ) @ SV990 ) @ SV1216 @ SV735 @ SV4 )
| ~ ( c_Limits_Otendsto @ SV385 @ SV1149 @ SV1216 @ SV735 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3245,plain,
! [SV1150: $i,SV991: $i,SV736: $i,SV386: $i,SV5: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV5 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SV736 ) @ SV991 @ SV736 @ SV5 @ SV5 ) @ SV1150 @ SV736 @ SV5 )
| ~ ( c_Limits_OZfun @ SV386 @ SV1150 @ SV736 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2954]) ).
thf(3246,plain,
! [SV1151: $i,SV992: $i,SV737: $i,SV387: $i,SV6: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV6 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SV737 ) @ SV992 @ SV737 @ SV6 @ SV6 ) @ SV1151 @ SV737 @ SV6 )
| ~ ( c_Limits_OZfun @ SV387 @ SV1151 @ SV737 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2955]) ).
thf(3247,plain,
! [SV1217: $i,SV1152: $i,SV993: $i,SV738: $i,SV388: $i,SV7: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV7 )
| ~ ( class_RealVector_Ometric__space @ SV388 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV1217 ) @ SV993 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SV1152 @ SV1217 @ SV388 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3248,plain,
! [SV1153: $i,SV994: $i,SV739: $i,SV389: $i,SV8: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV8 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ ( c_Finite__Set_Osetsum @ SV389 @ SV739 @ SV994 @ SV8 ) ) @ SV1153 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ SV389 @ SV8 @ ( tc_fun @ SV8 @ SV8 ) @ SV994 ) @ SV1153 @ SV994 @ SV8 @ SV8 ) @ SV739 @ SV994 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(3249,plain,
! [SV1154: $i,SV995: $i,SV740: $i,SV390: $i,SV9: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV9 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ ( c_Finite__Set_Osetsum @ SV390 @ SV740 @ SV995 @ SV9 ) ) @ SV1154 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ SV390 @ SV9 @ ( tc_fun @ SV9 @ SV9 ) @ SV995 ) @ SV1154 @ SV995 @ SV9 @ SV9 ) @ SV740 @ SV995 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2958]) ).
thf(3250,plain,
! [SV1155: $i,SV996: $i,SV741: $i,SV391: $i,SV10: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV10 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ ( c_Finite__Set_Osetsum @ SV391 @ SV741 @ SV996 @ tc_RealDef_Oreal ) ) @ SV1155 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ SV391 @ tc_RealDef_Oreal @ ( tc_fun @ SV10 @ SV10 ) @ SV996 ) @ SV1155 @ SV996 @ SV10 @ SV10 ) @ SV741 @ SV996 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3251,plain,
! [SV1218: $i,SV1156: $i,SV997: $i,SV742: $i,SV392: $i,SV11: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV11 )
| ~ ( class_RealVector_Ometric__space @ SV392 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV1218 ) @ SV997 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SV1156 @ SV1218 @ SV392 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3252,plain,
! [SV1157: $i,SV998: $i,SV743: $i,SV393: $i,SV12: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV12 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SV743 ) @ SV998 @ SV743 @ SV12 @ SV12 ) @ SV1157 @ SV743 @ SV12 )
| ~ ( c_Limits_OZfun @ SV393 @ SV1157 @ SV743 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2961]) ).
thf(3253,plain,
! [SV1158: $i,SV999: $i,SV744: $i,SV394: $i,SV13: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV13 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SV744 ) @ SV999 @ SV744 @ SV13 @ SV13 ) @ SV1158 @ SV744 @ SV13 )
| ~ ( c_Limits_OZfun @ SV394 @ SV1158 @ SV744 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(3254,plain,
! [SV1219: $i,SV1159: $i,SV1000: $i,SV745: $i,SV395: $i,SV14: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV14 )
| ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SV1000 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV1159 ) @ SV1000 ) @ SV1219 @ SV745 @ SV14 )
| ~ ( c_Limits_Otendsto @ SV395 @ SV1159 @ SV1219 @ SV745 @ tc_RealDef_Oreal ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3255,plain,
! [SV396: $i,SV15: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV15 )
= $false )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SV396 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
| ~ ( c_SEQ_OCauchy @ SV396 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3256,plain,
! [SV17: $i,SV398: $i] :
( ( ( c_SEQ_OZseq @ SV398 @ SV17 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV17 ) @ SV398 @ SV17 @ SV17 @ tc_nat ) @ SV17 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3257,plain,
! [SV1160: $i,SV1001: $i,SV746: $i,SV399: $i,SV18: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ SV1160 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ SV1160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3258,plain,
! [SV1161: $i,SV1002: $i,SV747: $i,SV400: $i,SV19: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ SV747 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SV1161 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV747 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SV1161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3259,plain,
! [SV1162: $i,SV1003: $i,SV748: $i,SV401: $i,SV20: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV748 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV1003 ) @ SV1162 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV1003 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV748 ) @ SV1162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3260,plain,
! [SV402: $i,SV21: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV21 ) @ SV402 @ SV21 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $false )
| ( ( c_Series_Osummable @ SV402 @ SV21 )
= $true )
| ( ( class_SEQ_Obanach @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3261,plain,
! [SV1004: $i,SV750: $i,SV404: $i,SV25: $i] :
( ( ( class_RealVector_Ometric__space @ SV25 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
| ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3262,plain,
! [SV406: $i,SV27: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV27 ) @ SV406 @ SV27 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $false )
| ( ( c_SEQ_OZseq @ SV406 @ SV27 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3263,plain,
! [SV28: $i,SV407: $i] :
( ( ( c_SEQ_OZseq @ SV407 @ SV28 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV28 ) @ SV407 @ SV28 @ tc_RealDef_Oreal @ tc_nat ) @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3264,plain,
! [SV752: $i,SV408: $i,SV29: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV29 ) @ SV408 ) @ SV752 @ SV29 @ SV29 @ tc_nat ) @ SV29 )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV752 @ SV29 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3265,plain,
! [SV1163: $i,SV1005: $i,SV754: $i,SV410: $i,SV31: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV31 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV410 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SV754 @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3266,plain,
! [SV1164: $i,SV1006: $i,SV755: $i,SV411: $i,SV32: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV32 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV411 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SV755 @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3267,plain,
! [SV33: $i,SV412: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBK @ SV412 @ SV33 @ tc_nat ) @ SV33 )
= $false )
| ( ( SV412
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3268,plain,
! [SV1220: $i,SV1165: $i,SV1007: $i,SV756: $i,SV413: $i,SV34: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV34 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
| ( SV756 = SV1007 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3269,plain,
! [SV1008: $i,SV757: $i,SV414: $i,SV35: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV35 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SV414 @ SV35 @ tc_RealDef_Oreal @ SV757 ) @ SV1008 @ SV757 @ tc_RealDef_Oreal )
| ~ ( c_Limits_OZfun @ SV414 @ SV1008 @ SV757 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3270,plain,
! [SV1009: $i,SV758: $i,SV415: $i,SV36: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV36 )
= $false )
| ( ( ( c_Limits_OZfun @ SV415 @ SV758 @ SV1009 @ SV36 )
| ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SV415 @ SV36 @ tc_RealDef_Oreal @ SV1009 ) @ SV758 @ SV1009 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3271,plain,
! [SV1010: $i,SV759: $i,SV416: $i,SV37: $i] :
( ( ( class_RealVector_Ometric__space @ SV37 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV416 )
| ( c_Lim_OisCont @ ( c_COMBK @ SV759 @ SV416 @ SV37 ) @ SV1010 @ SV37 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3272,plain,
! [SV1011: $i,SV760: $i,SV417: $i,SV38: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV38 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SV417 @ SV38 @ SV38 @ SV760 ) @ SV1011 @ SV760 @ SV38 )
| ~ ( c_Limits_OZfun @ SV417 @ SV1011 @ SV760 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3273,plain,
! [SV41: $i,SV763: $i,SV420: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV420 ) )
= $true )
| ( ( ( c_Lim_OisUCont @ SV763 @ SV41 @ SV420 )
| ~ ( c_RealVector_Obounded__linear @ SV763 @ SV41 @ SV420 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2988]) ).
thf(3274,plain,
! [SV764: $i,SV421: $i,SV42: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV42 ) @ SV421 ) @ SV764 @ SV42 @ SV42 @ tc_nat ) @ SV42 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV764 @ SV42 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2989]) ).
thf(3275,plain,
! [SV765: $i,SV422: $i,SV43: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV43 ) @ SV422 ) @ SV765 @ SV43 @ SV43 @ tc_nat ) @ SV43 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV765 @ SV43 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2990]) ).
thf(3276,plain,
! [SV1012: $i,SV769: $i,SV426: $i,SV48: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV48 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV48 )
| ~ ( class_RealVector_Ometric__space @ SV426 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3277,plain,
! [SV1166: $i,SV1013: $i,SV771: $i,SV429: $i,SV51: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV51 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV429 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SV1013 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3278,plain,
! [SV1167: $i,SV1014: $i,SV772: $i,SV430: $i,SV52: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV52 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV430 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SV1014 @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3279,plain,
! [SV1168: $i,SV1015: $i,SV773: $i,SV432: $i,SV56: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV56 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SV773 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV1015 ) @ SV1168 @ SV773 @ SV56 )
| ~ ( c_Limits_Otendsto @ SV432 @ SV1015 @ SV1168 @ SV773 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3280,plain,
! [SV1169: $i,SV1016: $i,SV774: $i,SV433: $i,SV57: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV57 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ SV433 @ SV774 @ SV1016 @ SV1169 @ SV57 )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SV1169 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV774 ) @ SV1016 @ SV1169 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3281,plain,
! [SV1221: $i,SV1170: $i,SV1017: $i,SV775: $i,SV434: $i,SV58: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV58 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV434 )
| ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3282,plain,
! [SV435: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ SV435 ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV59 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV59 ) @ SV435 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3283,plain,
! [SV61: $i,SV436: $i] :
( ( ( c_Series_Osummable @ SV436 @ SV61 )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV61 ) @ SV436 @ SV61 @ SV61 @ tc_nat ) @ SV61 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3284,plain,
! [SV1018: $i,SV776: $i,SV437: $i,SV62: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV62 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ SV776 ) ) @ SV1018 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV437 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV62 ) @ SV776 ) @ SV1018 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3285,plain,
! [SV1019: $i,SV777: $i,SV438: $i,SV63: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SV777 ) ) @ SV1019 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV63 ) @ SV438 ) @ SV1019 ) ) @ SV777 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3005]) ).
thf(3286,plain,
! [SV1020: $i,SV778: $i,SV439: $i,SV64: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV64 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ SV778 ) ) @ SV1020 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV439 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV64 ) @ SV778 ) @ SV1020 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3287,plain,
! [SV1021: $i,SV779: $i,SV440: $i,SV65: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV779 ) @ SV1021 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV65 ) @ SV440 ) @ SV779 ) ) @ SV1021 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3288,plain,
! [SV1022: $i,SV780: $i,SV441: $i,SV66: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV66 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ SV1022 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV780 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV66 ) @ SV441 ) @ SV1022 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3289,plain,
! [SV1023: $i,SV781: $i,SV442: $i,SV67: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV781 ) @ SV1023 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV67 ) @ SV442 ) @ SV781 ) ) @ SV1023 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3290,plain,
! [SV1024: $i,SV782: $i,SV443: $i,SV68: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV443 ) @ SV782 ) ) @ SV1024 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV443 ) @ SV1024 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV68 ) @ SV782 ) @ SV1024 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3291,plain,
! [SV1025: $i,SV783: $i,SV444: $i,SV69: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV69 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV783 ) @ SV1025 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SV783 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV69 ) @ SV444 ) @ SV1025 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3292,plain,
! [SV1026: $i,SV784: $i,SV445: $i,SV70: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV70 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV784 ) @ SV1026 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SV784 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV70 ) @ SV445 ) @ SV1026 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3293,plain,
! [SV1027: $i,SV785: $i,SV446: $i,SV71: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV71 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV446 ) @ SV785 ) ) @ SV1027 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV446 ) @ SV1027 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV71 ) @ SV785 ) @ SV1027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3294,plain,
! [SV1028: $i,SV786: $i,SV447: $i,SV72: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV72 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV447 ) @ SV786 ) ) @ SV1028 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV447 ) @ SV1028 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV72 ) @ SV786 ) @ SV1028 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3295,plain,
! [SV1029: $i,SV787: $i,SV448: $i,SV73: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV73 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV787 ) @ SV1029 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SV787 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV73 ) @ SV448 ) @ SV1029 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3296,plain,
! [SV1030: $i,SV788: $i,SV449: $i,SV74: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV74 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV449 ) @ SV788 ) ) @ SV1030 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV449 ) @ SV1030 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV74 ) @ SV788 ) @ SV1030 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3297,plain,
! [SV1031: $i,SV789: $i,SV450: $i,SV75: $i] :
( ( ( class_RealVector_Ometric__space @ SV75 )
= $false )
| ( ( ~ ( class_HOL_Ozero @ SV75 )
| ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3298,plain,
! [SV790: $i,SV451: $i,SV76: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ ( c_Series_Osuminf @ SV790 @ SV76 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ SV790 @ SV76 @ SV76 @ tc_nat ) @ SV76 ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV790 @ SV76 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3299,plain,
! [SV1032: $i,SV791: $i,SV452: $i,SV77: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV77 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV452 ) @ SV791 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ SV1032 ) @ SV791 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV452 ) @ SV1032 ) ) @ SV791 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3300,plain,
! [SV1033: $i,SV797: $i,SV460: $i,SV85: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV85 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV85 )
| ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SV1033 @ SV797 @ SV85 )
| ~ ( c_Limits_OZfun @ SV460 @ SV1033 @ SV797 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3301,plain,
! [SV1222: $i,SV1171: $i,SV1034: $i,SV798: $i,SV461: $i,SV86: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV86 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SV1034 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV1171 ) @ SV1222 @ SV1034 @ SV86 )
| ~ ( c_Limits_Otendsto @ SV798 @ SV1171 @ SV1222 @ SV1034 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3302,plain,
! [SV1172: $i,SV1035: $i,SV799: $i,SV462: $i,SV87: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV87 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SV799 @ SV87 @ SV87 @ SV1035 ) @ SV1172 @ SV1035 @ SV87 )
| ~ ( c_Limits_OZfun @ SV799 @ SV1172 @ SV1035 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3303,plain,
! [SV1173: $i,SV1036: $i,SV800: $i,SV463: $i,SV88: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV88 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SV800 @ SV88 @ SV88 @ SV1036 ) @ SV1173 @ SV1036 @ SV88 )
| ~ ( c_Limits_OZfun @ SV800 @ SV1173 @ SV1036 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3304,plain,
! [SV801: $i,SV464: $i,SV89: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV464 ) @ SV801 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) ) )
= $true )
| ( ( ( SV801
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
| ( SV464
= ( c_HOL_Ozero__class_Ozero @ SV89 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3305,plain,
! [SV802: $i,SV465: $i,SV90: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV465 ) @ SV802 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) ) )
= $true )
| ( ( ( SV802
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3030]) ).
thf(3306,plain,
! [SV803: $i,SV466: $i,SV92: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ ( c_Series_Osuminf @ SV803 @ SV92 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ SV803 @ SV92 @ SV92 @ tc_nat ) @ SV92 ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV803 @ SV92 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3307,plain,
! [SV804: $i,SV467: $i,SV93: $i] :
( ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ SV804 @ SV93 @ SV93 @ tc_nat ) @ SV93 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ ( c_Series_Osuminf @ SV804 @ SV93 ) ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV804 @ SV93 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3032]) ).
thf(3308,plain,
! [SV1174: $i,SV1037: $i,SV805: $i,SV468: $i,SV95: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV95 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV805 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1037 ) @ SV1174 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV1037 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV805 ) @ SV1174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3033]) ).
thf(3309,plain,
! [SV1223: $i,SV1175: $i,SV1038: $i,SV806: $i,SV469: $i,SV96: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV96 )
| ~ ( class_RealVector_Ometric__space @ SV469 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1223 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SV1038 @ SV1175 @ SV1223 @ SV469 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3310,plain,
! [SV1039: $i,SV807: $i,SV470: $i,SV97: $i] :
( ( ( class_RealVector_Ometric__space @ SV97 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SV470 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SV807 @ ( hAPP @ c_Complex_ORe @ SV1039 ) @ SV97 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV470 @ SV807 @ SV1039 @ SV97 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3311,plain,
! [SV808: $i,SV471: $i,SV98: $i] :
( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV98 ) @ SV471 @ SV98 @ SV98 @ SV98 ) @ SV808 @ SV98 )
= $true )
| ( ( ~ ( c_Deriv_Odifferentiable @ SV471 @ SV808 @ SV98 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3312,plain,
! [SV809: $i,SV472: $i,SV99: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV99 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ SV472 ) @ SV809 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV472 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV809 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3313,plain,
! [SV810: $i,SV473: $i,SV100: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ SV473 ) @ SV810 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV810 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV473 ) ) )
= $true )
| ( ( ( SV810
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV100 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3038]) ).
thf(3314,plain,
! [SV1176: $i,SV1040: $i,SV811: $i,SV474: $i,SV101: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV101 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SV1176 @ SV474 @ SV101 )
| ( SV811 = SV1176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3039]) ).
thf(3315,plain,
! [SV1177: $i,SV1041: $i,SV812: $i,SV475: $i,SV102: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV102 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
| ( SV812 = SV1041 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SV1177 @ SV1041 @ SV475 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3316,plain,
! [SV1178: $i,SV1042: $i,SV813: $i,SV477: $i,SV104: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV104 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ ( c_Finite__Set_Osetsum @ SV813 @ SV1042 @ SV1178 @ SV104 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ SV813 @ SV104 @ SV104 @ SV1178 ) @ SV1042 @ SV1178 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3317,plain,
! [SV1179: $i,SV1043: $i,SV814: $i,SV478: $i,SV105: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV105 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ ( c_Finite__Set_Osetsum @ SV814 @ SV1043 @ SV1179 @ SV105 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ SV814 @ SV105 @ SV105 @ SV1179 ) @ SV1043 @ SV1179 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3318,plain,
! [SV1180: $i,SV1044: $i,SV815: $i,SV480: $i,SV107: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV107 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV480 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
| ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3319,plain,
! [SV1045: $i,SV816: $i,SV481: $i,SV108: $i] :
( ( ( class_RealVector_Ometric__space @ SV108 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV481 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SV1045 @ SV108 @ SV481 )
| ~ ( c_Lim_OisCont @ SV816 @ SV1045 @ SV108 @ SV481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3320,plain,
! [SV109: $i,SV482: $i] :
( ( ( c_Series_Osummable @ SV482 @ SV109 )
= $false )
| ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ SV482 @ SV109 @ SV109 @ tc_nat ) @ SV109 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV109 ) @ ( c_Series_Osuminf @ SV482 @ SV109 ) ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3321,plain,
! [SV1046: $i,SV817: $i,SV483: $i,SV110: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV110 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ SV817 ) ) @ SV1046 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV110 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV110 ) @ SV817 ) @ SV1046 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3322,plain,
! [SV1047: $i,SV818: $i,SV484: $i,SV111: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV111 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ SV818 ) ) @ SV1047 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV111 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV111 ) @ SV818 ) @ SV1047 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3323,plain,
! [SV1048: $i,SV819: $i,SV485: $i,SV112: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV112 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ SV1048 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV112 ) @ SV819 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV112 ) @ SV485 ) @ SV1048 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3324,plain,
! [SV1181: $i,SV1049: $i,SV820: $i,SV486: $i,SV114: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV114 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV114 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SV1181 @ SV820 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SV1049 @ SV1181 @ SV820 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3050]) ).
thf(3325,plain,
! [SV1050: $i,SV821: $i,SV487: $i,SV116: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV116 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV487 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1050 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SV1050 ) @ SV116 @ SV487 )
| ~ ( c_Lim_OisCont @ SV821 @ SV1050 @ SV116 @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3326,plain,
! [SV1051: $i,SV822: $i,SV488: $i,SV117: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV117 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV488 )
| ( c_Lim_OisCont @ SV822 @ SV1051 @ SV117 @ SV488 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV1051 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SV1051 ) @ SV117 @ SV488 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3327,plain,
! [SV1052: $i,SV824: $i,SV490: $i,SV119: $i] :
( ( ( class_RealVector_Ometric__space @ SV119 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV490 )
| ( c_Lim_OisCont @ SV824 @ SV1052 @ SV119 @ SV490 )
| ~ ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3328,plain,
! [SV1182: $i,SV1053: $i,SV825: $i,SV491: $i,SV120: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV120 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV491 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SV1053 @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3055]) ).
thf(3329,plain,
! [SV1183: $i,SV1054: $i,SV826: $i,SV492: $i,SV121: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV121 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV492 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SV1054 @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3330,plain,
! [SV1055: $i,SV827: $i,SV493: $i,SV122: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV122 )
= $false )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV827 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV1055 ) @ SV122 )
| ~ ( c_Series_Osums @ SV827 @ SV1055 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3331,plain,
! [SV828: $i,SV494: $i,SV124: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV124 ) @ SV494 ) @ SV828 @ SV124 @ SV124 @ tc_nat ) @ SV124 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV828 @ SV124 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3058]) ).
thf(3332,plain,
! [SV1184: $i,SV1056: $i,SV831: $i,SV497: $i,SV127: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV127 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV497 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV1184 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SV831 @ SV1056 @ SV1184 @ SV497 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3333,plain,
! [SV1057: $i,SV832: $i,SV498: $i,SV129: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV129 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV498 )
| ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
| ~ ( c_SEQ_OZseq @ SV1057 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3334,plain,
! [SV1224: $i,SV1185: $i,SV1058: $i,SV833: $i,SV499: $i,SV130: $i] :
( ( ! [SY2984: $i] :
( ~ ( class_RealVector_Ometric__space @ SV130 )
| ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SY2984 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SY2984 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SY2984 @ SV130 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3335,plain,
! [SV1186: $i,SV1059: $i,SV834: $i,SV500: $i,SV131: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV131 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV131 )
| ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3064]) ).
thf(3336,plain,
! [SV1060: $i,SV836: $i,SV502: $i,SV133: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV133 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV133 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3337,plain,
! [SV1061: $i,SV837: $i,SV503: $i,SV134: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV134 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV134 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3338,plain,
! [SV1225: $i,SV1187: $i,SV1062: $i,SV838: $i,SV504: $i,SV135: $i] :
( ( ! [SY2985: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV135 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SY2985 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SY2985 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3339,plain,
! [SV1188: $i,SV1063: $i,SV839: $i,SV505: $i,SV136: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV136 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SV839 @ SV136 @ SV136 @ SV1063 ) @ SV1188 @ SV1063 @ SV136 )
| ~ ( c_Limits_OZfun @ SV839 @ SV1188 @ SV1063 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3340,plain,
! [SV1189: $i,SV1064: $i,SV840: $i,SV506: $i,SV137: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV137 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SV840 @ SV137 @ SV137 @ SV1064 ) @ SV1189 @ SV1064 @ SV137 )
| ~ ( c_Limits_OZfun @ SV840 @ SV1189 @ SV1064 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3341,plain,
! [SV507: $i,SV138: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV138 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV138 ) @ SV507 ) )
= SV507 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3342,plain,
! [SV841: $i,SV508: $i,SV139: $i] :
( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SV508 @ SV139 @ SV139 @ SV139 ) @ SV841 @ SV139 )
= $true )
| ( ( ( ( hAPP @ SV508 @ SV841 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
| ~ ( c_Deriv_Odifferentiable @ SV508 @ SV841 @ SV139 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3343,plain,
! [SV1226: $i,SV1190: $i,SV1065: $i,SV842: $i,SV509: $i,SV140: $i] :
( ( ! [SY2986: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV140 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SY2986 @ SV1190 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SY2986 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3344,plain,
! [SV1066: $i,SV846: $i,SV513: $i,SV145: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV145 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV513 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV846 @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3345,plain,
! [SV1067: $i,SV847: $i,SV514: $i,SV146: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV146 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV514 )
| ( c_Lim_OLIM @ SV847 @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3346,plain,
! [SV1068: $i,SV848: $i,SV515: $i,SV147: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ SV1068 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV848 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV515 ) @ SV1068 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3078]) ).
thf(3347,plain,
! [SV1069: $i,SV849: $i,SV516: $i,SV148: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ SV849 ) ) @ SV1069 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV849 ) @ SV1069 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3348,plain,
! [SV1070: $i,SV850: $i,SV517: $i,SV149: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV149 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV850 ) @ SV1070 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV517 ) @ SV850 ) ) @ SV1070 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3080]) ).
thf(3349,plain,
! [SV1071: $i,SV853: $i,SV520: $i,SV152: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV152 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ SV1071 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV853 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV520 ) @ SV1071 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3350,plain,
! [SV1072: $i,SV854: $i,SV521: $i,SV153: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV153 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ SV854 ) ) @ SV1072 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV521 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV854 ) @ SV1072 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3082]) ).
thf(3351,plain,
! [SV1073: $i,SV855: $i,SV522: $i,SV154: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV154 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV855 ) @ SV1073 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV154 ) @ SV522 ) @ SV855 ) ) @ SV1073 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3352,plain,
! [SV1074: $i,SV856: $i,SV523: $i,SV155: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV155 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SV856 ) ) @ SV1074 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV155 ) @ SV523 ) @ SV1074 ) ) @ SV856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3353,plain,
! [SV1075: $i,SV857: $i,SV524: $i,SV156: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV156 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ SV1075 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV524 ) @ SV1075 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3354,plain,
! [SV1076: $i,SV858: $i,SV525: $i,SV157: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ SV858 ) ) @ SV1076 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV525 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV858 ) @ SV1076 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3355,plain,
! [SV1227: $i,SV1191: $i,SV1077: $i,SV860: $i,SV527: $i,SV159: $i] :
( ( ( hAPP @ ( c_COMBC @ SV159 @ SV527 @ SV860 @ SV1077 @ SV1191 ) @ SV1227 )
= ( hAPP @ ( hAPP @ SV159 @ SV1227 ) @ SV527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3356,plain,
! [SV1079: $i,SV862: $i,SV529: $i,SV161: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV161 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV529 )
| ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
| ~ ( c_Series_Osummable @ SV1079 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3357,plain,
! [SV1192: $i,SV1080: $i,SV863: $i,SV530: $i,SV162: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV162 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV1080 ) @ SV1192 @ SV863 @ SV162 )
| ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SV530 @ SV1080 @ SV1192 @ SV863 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3358,plain,
! [SV1193: $i,SV1081: $i,SV864: $i,SV535: $i,SV167: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV167 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV535 ) @ SV864 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV1081 ) @ SV864 ) ) @ SV1193 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ SV535 ) @ SV1081 ) ) @ SV864 ) ) @ SV1193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3359,plain,
! [SV168: $i,SV536: $i] :
( ( ( c_SEQ_Oconvergent @ SV536 @ SV168 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV536 @ ( c_SEQ_Olim @ SV536 @ SV168 ) @ SV168 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3092]) ).
thf(3360,plain,
! [SV169: $i,SV537: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV537 @ ( c_SEQ_Olim @ SV537 @ SV169 ) @ SV169 )
= $false )
| ( ( c_SEQ_Oconvergent @ SV537 @ SV169 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3361,plain,
! [SV1082: $i,SV865: $i,SV542: $i,SV174: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV174 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV542 )
| ( c_Lim_OisCont @ SV865 @ SV1082 @ SV174 @ SV542 )
| ~ ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3362,plain,
! [SV543: $i,SV175: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV175 )
= $false )
| ( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SV543 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SV543 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
| ~ ( c_Series_Osummable @ SV543 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3363,plain,
! [SV176: $i,SV544: $i] :
( ( ( c_SEQ_Oconvergent @ SV544 @ SV176 )
= $false )
| ( ( ( c_SEQ_Olim @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ SV544 @ SV176 @ SV176 @ tc_nat ) @ SV176 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV176 ) @ ( c_SEQ_Olim @ SV544 @ SV176 ) ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3364,plain,
! [SV1194: $i,SV1083: $i,SV866: $i,SV545: $i,SV177: $i] :
( ( ( ~ ( class_RealVector_Oreal__vector @ SV177 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ ( c_Finite__Set_Osetsum @ SV866 @ SV1083 @ SV1194 @ SV177 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ SV866 @ SV177 @ SV177 @ SV1194 ) @ SV1083 @ SV1194 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3365,plain,
! [SV1195: $i,SV1084: $i,SV867: $i,SV546: $i,SV179: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV179 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV546 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV1195 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV867 @ SV1084 @ SV1195 @ SV546 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3366,plain,
! [SV180: $i,SV547: $i] :
( ( ( c_SEQ_Oconvergent @ SV547 @ SV180 )
= $false )
| ( ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV180 ) @ SV547 @ SV180 @ SV180 @ tc_nat ) @ SV180 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3367,plain,
! [SV548: $i,SV181: $i] :
( ( ( c_SEQ_Oconvergent @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV181 ) @ SV548 @ SV181 @ SV181 @ tc_nat ) @ SV181 )
= $false )
| ( ( c_SEQ_Oconvergent @ SV548 @ SV181 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3368,plain,
! [SV1085: $i,SV868: $i,SV550: $i,SV183: $i] :
( ( ( class_RealVector_Oreal__vector @ SV183 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ SV868 ) @ SV1085 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SV868 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV183 ) @ SV550 ) @ SV1085 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3369,plain,
! [SV1086: $i,SV869: $i,SV551: $i,SV184: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV184 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ SV869 ) @ SV1086 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SV869 ) ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV184 ) @ SV551 ) @ SV1086 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3370,plain,
! [SV1228: $i,SV1196: $i,SV1087: $i,SV870: $i,SV552: $i,SV185: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV185 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV552 )
| ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
| ~ ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3371,plain,
! [SV1088: $i,SV871: $i,SV554: $i,SV188: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV188 )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ SV554 @ SV188 @ SV188 @ SV871 ) @ SV1088 @ SV871 @ SV188 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV188 ) @ ( c_Finite__Set_Osetsum @ SV554 @ SV1088 @ SV871 @ SV188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3372,plain,
! [SV558: $i,SV192: $i] :
( ( ( class_Int_Onumber__ring @ SV192 )
= $false )
| ( ( SV558
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV558 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3373,plain,
! [SV568: $i,SV202: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV202 )
= $false )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SV568 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
| ~ ( c_Series_Osummable @ SV568 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3374,plain,
! [SV1089: $i,SV872: $i,SV569: $i,SV203: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV203 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ SV1089 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV203 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV203 ) @ SV569 ) @ SV1089 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3108]) ).
thf(3375,plain,
! [SV1090: $i,SV873: $i,SV570: $i,SV204: $i] :
( ( ( class_RealVector_Oreal__algebra @ SV204 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ SV873 ) ) @ SV1090 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV204 ) @ SV570 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV204 ) @ SV873 ) @ SV1090 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3376,plain,
! [SV1091: $i,SV874: $i,SV571: $i,SV205: $i] :
( ( ( class_RealVector_Oreal__algebra @ SV205 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ SV1091 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV205 ) @ SV874 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV205 ) @ SV571 ) @ SV1091 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3377,plain,
! [SV1092: $i,SV875: $i,SV572: $i,SV206: $i] :
( ( ( class_RealVector_Ometric__space @ SV206 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SV1092 @ SV206 @ SV572 )
| ~ ( c_Lim_OisCont @ SV875 @ SV1092 @ SV206 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3378,plain,
! [SV1197: $i,SV1093: $i,SV876: $i,SV573: $i,SV207: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV207 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV573 )
| ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SV1197 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SV1197 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3379,plain,
! [SV1094: $i,SV877: $i,SV574: $i,SV208: $i] :
( ( ( class_RealVector_Ometric__space @ SV208 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV574 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
| ~ ( c_SEQ_OCauchy @ SV1094 @ SV208 )
| ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3380,plain,
! [SV1198: $i,SV1095: $i,SV878: $i,SV575: $i,SV209: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV209 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV575 )
| ( c_Lim_OLIM @ SV878 @ SV1095 @ SV1198 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV1198 @ SV575 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3381,plain,
! [SV1199: $i,SV1096: $i,SV879: $i,SV576: $i,SV210: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV210 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV576 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SV1199 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SV879 @ SV1096 @ SV1199 @ SV576 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3382,plain,
! [SV1097: $i,SV880: $i,SV577: $i,SV211: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV211 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV577 )
| ( c_Lim_OLIM @ SV880 @ SV1097 @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV1097 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3383,plain,
! [SV1098: $i,SV881: $i,SV578: $i,SV212: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV212 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV578 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV1098 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
| ~ ( c_Lim_OLIM @ SV881 @ SV1098 @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3384,plain,
! [SV882: $i,SV579: $i,SV213: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV213 ) @ SV579 ) @ SV882 @ SV213 @ SV213 @ tc_nat ) @ SV213 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV882 @ SV213 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3118]) ).
thf(3385,plain,
! [SV883: $i,SV580: $i,SV214: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV214 ) @ SV580 ) @ SV883 @ SV214 @ SV214 @ tc_nat ) @ SV214 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV883 @ SV214 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3386,plain,
! [SV1099: $i,SV884: $i,SV581: $i,SV215: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV215 )
= $false )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV884 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV1099 ) @ SV215 )
| ~ ( c_Series_Osums @ SV884 @ SV1099 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3387,plain,
! [SV1100: $i,SV885: $i,SV582: $i,SV216: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV216 )
= $false )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV885 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV1100 ) @ SV216 )
| ~ ( c_Series_Osums @ SV885 @ SV1100 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3388,plain,
! [SV887: $i,SV218: $i,SV584: $i] :
( ( ( c_Series_Osummable @ SV584 @ SV218 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV584 @ SV887 @ SV218 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3389,plain,
! [SV888: $i,SV219: $i,SV585: $i] :
( ( ( c_Series_Osummable @ SV585 @ SV219 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV585 @ SV888 @ SV219 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3390,plain,
! [SV1200: $i,SV1101: $i,SV890: $i,SV587: $i,SV221: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV221 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SV890 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV1101 ) @ SV1200 @ SV890 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV587 @ SV1101 @ SV1200 @ SV890 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3126]) ).
thf(3391,plain,
! [SV1102: $i,SV892: $i,SV592: $i,SV226: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV226 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ SV1102 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV892 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV226 ) @ SV592 ) @ SV1102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3392,plain,
! [SV1103: $i,SV893: $i,SV593: $i,SV227: $i] :
( ( ( class_RealVector_Oreal__vector @ SV227 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ SV1103 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV227 ) @ SV593 ) @ SV1103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3393,plain,
! [SV1104: $i,SV894: $i,SV594: $i,SV228: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV228 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ SV1104 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV228 ) @ SV594 ) @ SV1104 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3394,plain,
! [SV595: $i,SV229: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV229 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SV595 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
| ~ ( c_SEQ_OZseq @ SV595 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3395,plain,
! [SV1105: $i,SV895: $i,SV596: $i,SV230: $i] :
( ( ( class_RealVector_Otopological__space @ SV230 )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBK @ SV596 @ SV230 @ SV895 ) @ SV596 @ SV1105 @ SV895 @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3396,plain,
! [SV1106: $i,SV899: $i,SV601: $i,SV236: $i] :
( ( ( class_RealVector_Ometric__space @ SV236 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV601 )
| ( c_Lim_OLIM @ ( c_COMBK @ SV899 @ SV236 @ SV601 ) @ SV1106 @ SV899 @ SV601 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3397,plain,
! [SV1107: $i,SV900: $i,SV602: $i,SV237: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV237 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV237 )
| ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SV602 @ SV900 @ SV1107 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SV602 @ tc_RealDef_Oreal @ SV237 @ SV1107 ) @ SV900 @ SV1107 @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3398,plain,
! [SV250: $i,SV901: $i,SV615: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ SV615 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV901 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV250 @ tc_nat ) @ SV250 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV615 @ SV250 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3399,plain,
! [SV1229: $i,SV1201: $i,SV1108: $i,SV902: $i,SV616: $i,SV251: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV251 )
| ~ ( class_RealVector_Ometric__space @ SV616 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1229 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SV1108 @ SV1201 @ SV1229 @ SV616 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3400,plain,
! [SV619: $i,SV1109: $i,SV905: $i,SV254: $i] :
( ( ( c_Limits_Otendsto @ SV254 @ SV905 @ SV1109 @ SV619 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_ORe @ SV254 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV619 ) @ ( hAPP @ c_Complex_ORe @ SV905 ) @ SV1109 @ SV619 @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3401,plain,
! [SV1202: $i,SV1110: $i,SV906: $i,SV620: $i,SV255: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV255 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV620 )
| ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
| ~ ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3402,plain,
! [SV256: $i,SV621: $i] :
( ( ( c_Series_Osummable @ SV621 @ SV256 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV621 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3403,plain,
! [SV257: $i,SV907: $i,SV622: $i] :
( ( ( SV622
= ( c_Series_Osuminf @ SV907 @ SV257 ) )
= $true )
| ( ( ~ ( c_Series_Osums @ SV907 @ SV622 @ SV257 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3404,plain,
! [SV908: $i,SV258: $i,SV623: $i] :
( ( ( ( c_Series_Osuminf @ SV623 @ SV258 )
= SV908 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV623 @ SV908 @ SV258 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3405,plain,
! [SV262: $i,SV625: $i] :
( ( ( c_SEQ_Oconvergent @ SV625 @ SV262 )
= $false )
| ( ( c_SEQ_OCauchy @ SV625 @ SV262 )
= $true )
| ( ( class_SEQ_Ocomplete__space @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3406,plain,
! [SV263: $i,SV626: $i] :
( ( ( c_SEQ_OCauchy @ SV626 @ SV263 )
= $false )
| ( ( c_SEQ_Oconvergent @ SV626 @ SV263 )
= $true )
| ( ( class_SEQ_Ocomplete__space @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3407,plain,
! [SV265: $i,SV628: $i] :
( ( ( c_SEQ_Oconvergent @ SV628 @ SV265 )
= $false )
| ( ( c_SEQ_OCauchy @ SV628 @ SV265 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3408,plain,
! [SV910: $i,SV630: $i,SV268: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV630 @ SV268 @ SV268 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV910 ) @ SV268 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV630 @ SV910 @ SV268 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3409,plain,
! [SV1111: $i,SV911: $i,SV631: $i,SV271: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV271 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV631 )
| ( c_Lim_OLIM @ SV911 @ SV1111 @ ( hAPP @ SV911 @ SV1111 ) @ SV271 @ SV631 )
| ~ ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3410,plain,
! [SV912: $i,SV632: $i,SV272: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV272 ) @ SV632 ) @ SV912 @ SV272 @ SV272 @ tc_nat ) @ SV272 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV912 @ SV272 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3411,plain,
! [SV913: $i,SV633: $i,SV273: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV273 ) @ SV633 ) @ SV913 @ SV273 @ SV273 @ tc_nat ) @ SV273 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV913 @ SV273 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3412,plain,
! [SV274: $i,SV634: $i] :
( ( ( c_Series_Osummable @ SV634 @ SV274 )
= $false )
| ( ( c_Series_Osums @ SV634 @ ( c_Series_Osuminf @ SV634 @ SV274 ) @ SV274 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3156]) ).
thf(3413,plain,
! [SV275: $i,SV635: $i] :
( ( ( c_Series_Osummable @ SV635 @ SV275 )
= $false )
| ( ( c_Series_Osums @ SV635 @ ( c_Series_Osuminf @ SV635 @ SV275 ) @ SV275 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3414,plain,
! [SV1112: $i,SV914: $i,SV636: $i,SV276: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV276 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV636 )
| ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
| ~ ( c_SEQ_OCauchy @ SV1112 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3415,plain,
! [SV1113: $i,SV915: $i,SV637: $i,SV277: $i] :
( ( ( class_RealVector_Ometric__space @ SV277 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV637 )
| ( c_Lim_OisCont @ SV915 @ SV1113 @ SV277 @ SV637 )
| ~ ( c_Lim_OLIM @ SV915 @ SV1113 @ ( hAPP @ SV915 @ SV1113 ) @ SV277 @ SV637 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3159]) ).
thf(3416,plain,
! [SV1114: $i,SV916: $i,SV638: $i,SV278: $i] :
( ( ( class_RealVector_Ometric__space @ SV278 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV638 )
| ( c_Lim_OLIM @ SV916 @ SV1114 @ ( hAPP @ SV916 @ SV1114 ) @ SV278 @ SV638 )
| ~ ( c_Lim_OisCont @ SV916 @ SV1114 @ SV278 @ SV638 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3417,plain,
! [SV1230: $i,SV1203: $i,SV1115: $i,SV919: $i,SV641: $i,SV281: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV281 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV1203 ) @ SV1230 @ SV1115 @ SV281 )
| ~ ( c_Limits_Otendsto @ SV919 @ SV1203 @ SV1230 @ SV1115 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3418,plain,
! [SV920: $i,SV642: $i,SV282: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV282 ) @ SV642 ) @ SV920 @ SV282 @ SV282 @ tc_nat ) @ SV282 )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV920 @ SV282 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3419,plain,
! [SV921: $i,SV644: $i,SV285: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV285 ) )
= $true )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SV921 ) @ SV285 )
| ~ ( c_Series_Osums @ SV644 @ SV921 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3420,plain,
! [SV1116: $i,SV922: $i,SV645: $i,SV286: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV286 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV645 )
| ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
| ~ ( c_Series_Osummable @ SV1116 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3421,plain,
! [SV1117: $i,SV923: $i,SV646: $i,SV287: $i] :
( ( ( class_RealVector_Ometric__space @ SV287 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV646 )
| ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SV1117 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SV923 @ SV1117 @ SV287 @ SV646 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3422,plain,
! [SV1231: $i,SV1204: $i,SV1118: $i,SV926: $i,SV651: $i,SV293: $i] :
( ( ( c_Set_Oimage @ SV293 @ ( c_Set_Oimage @ SV651 @ SV926 @ SV1118 @ SV1204 ) @ SV1204 @ SV1231 )
= ( c_Set_Oimage @ ( c_COMBB @ SV293 @ SV651 @ SV1204 @ SV1231 @ SV1118 ) @ SV926 @ SV1118 @ SV1231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3423,plain,
! [SV927: $i,SV652: $i,SV294: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV652 @ SV294 @ SV294 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV927 ) @ SV294 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV652 @ SV927 @ SV294 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3424,plain,
! [SV295: $i,SV928: $i,SV653: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV653 @ SV928 @ SV295 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV653 @ SV295 @ SV295 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV928 ) @ SV295 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3425,plain,
! [SV929: $i,SV297: $i,SV654: $i] :
( ( ( c_SEQ_Oconvergent @ SV654 @ SV297 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV654 @ SV929 @ SV297 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3426,plain,
! [SV930: $i,SV298: $i,SV655: $i] :
( ( ( c_SEQ_Oconvergent @ SV655 @ SV298 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV655 @ SV930 @ SV298 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3427,plain,
! [SV299: $i,SV931: $i,SV656: $i] :
( ( ( SV656 = SV931 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV656 @ SV299 @ tc_nat ) @ SV931 @ SV299 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3428,plain,
! [SV1232: $i,SV1205: $i,SV1119: $i,SV932: $i,SV657: $i,SV300: $i] :
( ( ! [SY2987: $i] :
( ~ ( class_RealVector_Ometric__space @ SV300 )
| ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SY2987 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SY2987 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SY2987 @ ( hAPP @ SV1119 @ SY2987 ) @ SV300 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3429,plain,
! [SV658: $i,SV301: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV301 ) @ SV658 @ SV301 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV658 @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV301 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3430,plain,
! [SV302: $i,SV659: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV659 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV302 ) @ SV659 @ SV302 @ tc_RealDef_Oreal @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3431,plain,
! [SV933: $i,SV660: $i,SV303: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV660 @ SV303 @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV933 ) @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV660 @ SV933 @ SV303 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3432,plain,
! [SV1120: $i,SV934: $i,SV662: $i,SV305: $i] :
( ( ( class_RealVector_Ometric__space @ SV305 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV662 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV934 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SV1120 @ SV305 )
| ~ ( c_SEQ_OLIMSEQ @ SV662 @ SV1120 @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3433,plain,
! [SV1121: $i,SV935: $i,SV663: $i,SV306: $i] :
( ( ( class_RealVector_Ometric__space @ SV306 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ SV663 @ SV935 @ SV306 )
| ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV663 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1121 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SV935 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3434,plain,
! [SV936: $i,SV307: $i,SV664: $i] :
( ( ( ( c_SEQ_Olim @ SV664 @ SV307 )
= SV936 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV664 @ SV936 @ SV307 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3182]) ).
thf(3435,plain,
! [SV665: $i,SV1122: $i,SV937: $i,SV308: $i] :
( ( ( c_Limits_Otendsto @ SV308 @ SV937 @ SV1122 @ SV665 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ c_Complex_OIm @ SV308 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV665 ) @ ( hAPP @ c_Complex_OIm @ SV937 ) @ SV1122 @ SV665 @ tc_RealDef_Oreal )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3436,plain,
! [SV1206: $i,SV1123: $i,SV938: $i,SV668: $i,SV312: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV312 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV668 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3437,plain,
! [SV1233: $i,SV1207: $i,SV1124: $i,SV939: $i,SV669: $i,SV313: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV313 )
| ~ ( class_RealVector_Ometric__space @ SV669 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3438,plain,
! [SV941: $i,SV671: $i,SV315: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV315 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SV941 ) @ SV315 )
| ~ ( c_SEQ_OLIMSEQ @ SV671 @ SV941 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3439,plain,
! [SV1234: $i,SV1208: $i,SV1125: $i,SV943: $i,SV675: $i,SV320: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV320 )
| ~ ( class_RealVector_Ometric__space @ SV675 )
| ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3440,plain,
! [SV1126: $i,SV944: $i,SV676: $i,SV321: $i] :
( ( ( class_RealVector_Ometric__space @ SV321 )
= $false )
| ( ( ( SV676 = SV944 )
| ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV944 @ SV321 )
| ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV676 @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3189]) ).
thf(3441,plain,
! [SV1127: $i,SV945: $i,SV677: $i,SV322: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV322 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV945 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV1127 ) @ SV322 )
| ~ ( c_SEQ_OLIMSEQ @ SV945 @ SV1127 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3442,plain,
! [SV1128: $i,SV946: $i,SV678: $i,SV323: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV323 )
= $false )
| ( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SV1128 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV946 @ SV1128 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SV1128 ) @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3443,plain,
! [SV1129: $i,SV947: $i,SV679: $i,SV324: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV324 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV947 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV1129 ) @ SV324 )
| ~ ( c_SEQ_OLIMSEQ @ SV947 @ SV1129 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3444,plain,
! [SV948: $i,SV326: $i,SV680: $i] :
( ( ( c_SEQ_OCauchy @ SV680 @ SV326 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV680 @ SV948 @ SV326 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3445,plain,
! [SV949: $i,SV327: $i,SV681: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV681 @ c_Suc @ tc_nat @ SV327 @ tc_nat ) @ SV949 @ SV327 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV681 @ SV949 @ SV327 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3446,plain,
! [SV328: $i,SV950: $i,SV682: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV682 @ SV950 @ SV328 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV682 @ c_Suc @ tc_nat @ SV328 @ tc_nat ) @ SV950 @ SV328 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3447,plain,
! [SV1235: $i,SV1209: $i,SV1130: $i,SV951: $i,SV683: $i,SV329: $i] :
( ( ( hAPP @ ( c_COMBB @ SV329 @ SV683 @ SV951 @ SV1130 @ SV1209 ) @ SV1235 )
= ( hAPP @ SV329 @ ( hAPP @ SV683 @ SV1235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3448,plain,
! [SV952: $i,SV684: $i,SV330: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV684 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV952 ) @ SV330 )
= $true )
| ( ( ( SV952
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ~ ( c_SEQ_OLIMSEQ @ SV684 @ SV952 @ SV330 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3449,plain,
! [SV1131: $i,SV953: $i,SV685: $i,SV331: $i] :
( ( ( class_RealVector_Ometric__space @ SV331 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SV685 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SV953 @ ( hAPP @ c_Complex_OIm @ SV1131 ) @ SV331 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV685 @ SV953 @ SV1131 @ SV331 @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3450,plain,
! [SV1236: $i,SV1210: $i,SV1132: $i,SV954: $i,SV687: $i,SV335: $i] :
( ( ( hAPP @ ( c_COMBC @ SV335 @ SV687 @ SV954 @ SV1132 @ SV1210 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV335 @ SV1236 ) @ SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3451,plain,
! [SV1237: $i,SV1211: $i,SV1133: $i,SV955: $i,SV688: $i,SV336: $i] :
( ( ( hAPP @ ( c_COMBB @ SV336 @ SV688 @ SV955 @ SV1133 @ SV1211 ) @ SV1237 )
= ( hAPP @ SV336 @ ( hAPP @ SV688 @ SV1237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3452,plain,
! [SV957: $i,SV691: $i,SV339: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV691 ) @ SV691 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV957 ) @ SV957 ) )
= $true )
| ( ( ( SV691
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SV957 ) )
| ( SV691 = SV957 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3453,plain,
! [SV1134: $i,SV958: $i,SV692: $i,SV340: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV692 ) @ SV958 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1134 ) @ SV958 ) )
| ( SV692 = SV1134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3454,plain,
! [SV959: $i,SV693: $i,SV342: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SV693 ) @ SV959 )
!= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
= $true )
| ( ( ( SV693
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV959
= ( c_HOL_Ozero__class_Ozero @ SV342 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV342 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3455,plain,
! [SV695: $i,SV344: $i] :
( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV344 ) @ SV695 )
= ( c_HOL_Ozero__class_Ozero @ SV344 ) )
= $false )
| ( ( SV695
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3456,plain,
! [SV1212: $i,SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV345 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV345 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
| ( SV961 = SV1212 )
| ( SV696 = SV1135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3457,plain,
! [SV697: $i,SV346: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV346 ) @ SV697 ) @ SV697 )
= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
= $false )
| ( ( SV697
= ( c_HOL_Ozero__class_Ozero @ SV346 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3458,plain,
! [SV962: $i,SV698: $i,SV347: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV962 ) )
= $true )
| ( ( ( SV698 = SV962 )
| ( SV962
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3459,plain,
! [SV963: $i,SV699: $i,SV348: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ SV699 ) @ SV963 )
!= ( c_HOL_Ozero__class_Ozero @ SV348 ) )
= $true )
| ( ( SV699
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV348 ) @ SV963 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3460,plain,
! [SV964: $i,SV700: $i,SV349: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV700 ) @ SV700 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV964 ) @ SV964 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
= $true )
| ( ( SV700
= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV349 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3461,plain,
! [SV965: $i,SV701: $i,SV350: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SV701 ) @ SV965 )
!= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
= $true )
| ( ( ( SV965
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ SV350 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3212]) ).
thf(3462,plain,
! [SV1136: $i,SV966: $i,SV702: $i,SV351: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ SV351 @ SV702 )
= ( c_Complex_Ocomplex_OComplex @ SV966 @ SV1136 ) )
= $false )
| ( ( SV702 = SV1136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3463,plain,
! [SV1213: $i,SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV352 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV352 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
| ( SV967 = SV1213 )
| ( SV703 = SV1137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3464,plain,
! [SV704: $i,SV353: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV353 ) @ SV704 )
= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
= $false )
| ( ( SV704
= ( c_HOL_Ozero__class_Ozero @ SV353 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3465,plain,
! [SV1138: $i,SV968: $i,SV705: $i,SV354: $i] :
( ( ( class_RealVector_Oreal__vector @ SV354 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV968 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV1138 ) )
| ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV968 = SV1138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3216]) ).
thf(3466,plain,
! [SV970: $i,SV708: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SV708 ) @ SV970 )
!= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $true )
| ( ( ( SV970
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV708
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true )
| ( ( class_RealVector_Oreal__vector @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3218]) ).
thf(3467,plain,
! [SV1139: $i,SV971: $i,SV709: $i,SV358: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV971 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV1139 ) )
| ( SV971 = SV1139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3468,plain,
! [SV973: $i,SV711: $i,SV360: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV711 ) @ SV973 )
!= ( c_HOL_Ozero__class_Ozero @ SV360 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV360 ) @ SV711 )
= SV973 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV360 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3221]) ).
thf(3469,plain,
! [SV974: $i,SV712: $i,SV361: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV361 ) )
= $true )
| ( ( ( SV712
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3470,plain,
! [SV975: $i,SV713: $i,SV362: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SV713 ) @ SV975 )
!= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
= $true )
| ( ( ( SV975
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV362 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3471,plain,
! [SV714: $i,SV363: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV363 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SV714 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
| ( SV714
= ( c_HOL_Ozero__class_Ozero @ SV363 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3472,plain,
! [SV976: $i,SV715: $i,SV364: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV715 ) @ SV715 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV976 ) @ SV976 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
= $true )
| ( ( SV976
= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3473,plain,
! [SV977: $i,SV716: $i,SV365: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV716 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV977 ) )
= $true )
| ( ( SV716 = SV977 )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3474,plain,
! [SV1140: $i,SV978: $i,SV717: $i,SV366: $i] :
( ( ( class_RealVector_Oreal__vector @ SV366 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SV978 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV1140 ) @ SV978 ) )
| ( SV978
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SV717 = SV1140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3475,plain,
! [SV718: $i,SV367: $i] :
( ( ( ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV367 ) @ SV718 )
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $false )
| ( ( SV718
= ( c_HOL_Ozero__class_Ozero @ SV367 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3476,plain,
! [SV719: $i,SV368: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV368 ) @ SV719 )
= SV719 )
= $false )
| ( ( SV719
= ( c_HOL_Ozero__class_Ozero @ SV368 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__ab__group__add @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3229]) ).
thf(3477,plain,
! [SV720: $i,SV369: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV369 ) @ SV720 )
= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
= $false )
| ( ( SV720
= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3478,plain,
! [SV1141: $i,SV979: $i,SV721: $i,SV370: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ SV370 @ SV721 )
= ( c_Complex_Ocomplex_OComplex @ SV979 @ SV1141 ) )
= $false )
| ( ( SV370 = SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3479,plain,
! [SV722: $i,SV371: $i] :
( ( ( ( hAPP @ c_Complex_ORe @ SV371 )
= ( hAPP @ c_Complex_ORe @ SV722 ) )
= $false )
| ( ( SV371 = SV722 )
= $true )
| ( ( ( hAPP @ c_Complex_OIm @ SV371 )
= ( hAPP @ c_Complex_OIm @ SV722 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3232]) ).
thf(3480,plain,
! [SV723: $i,SV372: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV372 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV372 ) @ SV723 ) )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV372 )
= SV723 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3481,plain,
! [SV980: $i,SV724: $i,SV373: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 ) )
= $true )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV980 ) )
| ( SV724 = SV980 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV373 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3234]) ).
thf(3482,plain,
! [SV981: $i,SV725: $i,SV374: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV725 )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV981 ) )
= $true )
| ( ( SV725 = SV981 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV374 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3235]) ).
thf(3483,plain,
! [SV1142: $i,SV982: $i,SV726: $i,SV375: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV375 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV375 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV1142 ) )
| ( SV982 = SV1142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3484,plain,
! [SV983: $i,SV727: $i,SV376: $i] :
( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV727 )
!= ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV983 ) )
= $true )
| ( ( SV727 = SV983 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3237]) ).
thf(3485,plain,
! [SV1214: $i,SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV377 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
| ( SV1143 = SV1214 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3486,plain,
! [SV1144: $i,SV985: $i,SV729: $i,SV379: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV985 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV1144 ) )
| ( SV985 = SV1144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3487,plain,
! [SV1215: $i,SV1145: $i,SV986: $i,SV731: $i,SV381: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV381 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1145 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1215 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SV1145 )
= SV1215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3240]) ).
thf(3488,plain,
! [SV1146: $i,SV987: $i,SV732: $i,SV382: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV382 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV987 ) @ SV1146 ) )
!= SV987 )
| ( SV732
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SV1146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3489,plain,
! [SV1147: $i,SV988: $i,SV733: $i,SV383: $i,SV2: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV2 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV383 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SV733 @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3490,plain,
! [SV1148: $i,SV989: $i,SV734: $i,SV384: $i,SV3: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV3 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV384 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SV734 @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3491,plain,
! [SV1216: $i,SV1149: $i,SV990: $i,SV735: $i,SV385: $i,SV4: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV4 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SV990 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV1149 ) @ SV990 ) @ SV1216 @ SV735 @ SV4 )
| ~ ( c_Limits_Otendsto @ SV385 @ SV1149 @ SV1216 @ SV735 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3244]) ).
thf(3492,plain,
! [SV1150: $i,SV991: $i,SV736: $i,SV386: $i,SV5: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV5 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SV736 ) @ SV991 @ SV736 @ SV5 @ SV5 ) @ SV1150 @ SV736 @ SV5 )
| ~ ( c_Limits_OZfun @ SV386 @ SV1150 @ SV736 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3493,plain,
! [SV1151: $i,SV992: $i,SV737: $i,SV387: $i,SV6: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV6 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SV737 ) @ SV992 @ SV737 @ SV6 @ SV6 ) @ SV1151 @ SV737 @ SV6 )
| ~ ( c_Limits_OZfun @ SV387 @ SV1151 @ SV737 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3494,plain,
! [SV1217: $i,SV1152: $i,SV993: $i,SV738: $i,SV388: $i,SV7: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV7 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV388 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV1217 ) @ SV993 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SV1152 @ SV1217 @ SV388 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3495,plain,
! [SV1153: $i,SV994: $i,SV739: $i,SV389: $i,SV8: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV8 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ ( c_Finite__Set_Osetsum @ SV389 @ SV739 @ SV994 @ SV8 ) ) @ SV1153 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV8 ) @ SV389 @ SV8 @ ( tc_fun @ SV8 @ SV8 ) @ SV994 ) @ SV1153 @ SV994 @ SV8 @ SV8 ) @ SV739 @ SV994 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3496,plain,
! [SV1154: $i,SV995: $i,SV740: $i,SV390: $i,SV9: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV9 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ ( c_Finite__Set_Osetsum @ SV390 @ SV740 @ SV995 @ SV9 ) ) @ SV1154 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV9 ) @ SV390 @ SV9 @ ( tc_fun @ SV9 @ SV9 ) @ SV995 ) @ SV1154 @ SV995 @ SV9 @ SV9 ) @ SV740 @ SV995 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3497,plain,
! [SV1155: $i,SV996: $i,SV741: $i,SV391: $i,SV10: $i] :
( ( ( class_RealVector_Oreal__vector @ SV10 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ ( c_Finite__Set_Osetsum @ SV391 @ SV741 @ SV996 @ tc_RealDef_Oreal ) ) @ SV1155 )
= ( c_Finite__Set_Osetsum @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV10 ) @ SV391 @ tc_RealDef_Oreal @ ( tc_fun @ SV10 @ SV10 ) @ SV996 ) @ SV1155 @ SV996 @ SV10 @ SV10 ) @ SV741 @ SV996 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3498,plain,
! [SV1218: $i,SV1156: $i,SV997: $i,SV742: $i,SV392: $i,SV11: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV11 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV392 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV1218 ) @ SV997 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SV1156 @ SV1218 @ SV392 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3499,plain,
! [SV1157: $i,SV998: $i,SV743: $i,SV393: $i,SV12: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV12 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SV743 ) @ SV998 @ SV743 @ SV12 @ SV12 ) @ SV1157 @ SV743 @ SV12 )
| ~ ( c_Limits_OZfun @ SV393 @ SV1157 @ SV743 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3500,plain,
! [SV1158: $i,SV999: $i,SV744: $i,SV394: $i,SV13: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV13 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SV744 ) @ SV999 @ SV744 @ SV13 @ SV13 ) @ SV1158 @ SV744 @ SV13 )
| ~ ( c_Limits_OZfun @ SV394 @ SV1158 @ SV744 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3501,plain,
! [SV1219: $i,SV1159: $i,SV1000: $i,SV745: $i,SV395: $i,SV14: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV14 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SV1000 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV1159 ) @ SV1000 ) @ SV1219 @ SV745 @ SV14 )
| ~ ( c_Limits_Otendsto @ SV395 @ SV1159 @ SV1219 @ SV745 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3254]) ).
thf(3502,plain,
! [SV396: $i,SV15: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SV396 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV396 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV15 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3255]) ).
thf(3503,plain,
! [SV1160: $i,SV1001: $i,SV746: $i,SV399: $i,SV18: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV18 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ SV1160 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV18 ) @ SV399 ) @ SV746 ) ) @ SV1160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3504,plain,
! [SV1161: $i,SV1002: $i,SV747: $i,SV400: $i,SV19: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV19 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ SV747 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SV1161 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV400 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV747 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV19 ) @ SV1002 ) @ SV1161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3505,plain,
! [SV1162: $i,SV1003: $i,SV748: $i,SV401: $i,SV20: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV20 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV748 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV1003 ) @ SV1162 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV401 ) @ SV1003 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV20 ) @ SV748 ) @ SV1162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3506,plain,
! [SV1004: $i,SV25: $i,SV750: $i,SV404: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV404 ) )
= $true )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
| ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3507,plain,
! [SV408: $i,SV29: $i,SV752: $i] :
( ( ( c_SEQ_OCauchy @ SV752 @ SV29 )
= $false )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV29 ) @ SV408 ) @ SV752 @ SV29 @ SV29 @ tc_nat ) @ SV29 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3508,plain,
! [SV1163: $i,SV1005: $i,SV754: $i,SV410: $i,SV31: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV31 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV410 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SV754 @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3509,plain,
! [SV1164: $i,SV1006: $i,SV755: $i,SV411: $i,SV32: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV32 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV411 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SV755 @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3510,plain,
! [SV1220: $i,SV1165: $i,SV1007: $i,SV756: $i,SV413: $i,SV34: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV34 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
| ( SV756 = SV1007 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3511,plain,
! [SV1008: $i,SV757: $i,SV414: $i,SV35: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SV414 @ SV35 @ tc_RealDef_Oreal @ SV757 ) @ SV1008 @ SV757 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV414 @ SV1008 @ SV757 @ SV35 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3512,plain,
! [SV36: $i,SV1009: $i,SV758: $i,SV415: $i] :
( ( ( c_Limits_OZfun @ SV415 @ SV758 @ SV1009 @ SV36 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SV415 @ SV36 @ tc_RealDef_Oreal @ SV1009 ) @ SV758 @ SV1009 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3513,plain,
! [SV1010: $i,SV37: $i,SV759: $i,SV416: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV416 ) )
= $true )
| ( ( c_Lim_OisCont @ ( c_COMBK @ SV759 @ SV416 @ SV37 ) @ SV1010 @ SV37 @ SV416 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3514,plain,
! [SV1011: $i,SV760: $i,SV417: $i,SV38: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SV417 @ SV38 @ SV38 @ SV760 ) @ SV1011 @ SV760 @ SV38 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV417 @ SV1011 @ SV760 @ SV38 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3515,plain,
! [SV41: $i,SV763: $i,SV420: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV420 )
= $false )
| ( ( ( c_Lim_OisUCont @ SV763 @ SV41 @ SV420 )
| ~ ( c_RealVector_Obounded__linear @ SV763 @ SV41 @ SV420 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3516,plain,
! [SV421: $i,SV42: $i,SV764: $i] :
( ( ( c_SEQ_OZseq @ SV764 @ SV42 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV42 ) @ SV421 ) @ SV764 @ SV42 @ SV42 @ tc_nat ) @ SV42 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3274]) ).
thf(3517,plain,
! [SV422: $i,SV43: $i,SV765: $i] :
( ( ( c_SEQ_OZseq @ SV765 @ SV43 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV43 ) @ SV422 ) @ SV765 @ SV43 @ SV43 @ tc_nat ) @ SV43 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3518,plain,
! [SV1012: $i,SV769: $i,SV426: $i,SV48: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV48 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV426 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3519,plain,
! [SV1166: $i,SV1013: $i,SV771: $i,SV429: $i,SV51: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV51 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV429 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SV1013 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3277]) ).
thf(3520,plain,
! [SV1167: $i,SV1014: $i,SV772: $i,SV430: $i,SV52: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV52 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV430 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SV1014 @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3521,plain,
! [SV1168: $i,SV1015: $i,SV773: $i,SV432: $i,SV56: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV56 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SV773 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV1015 ) @ SV1168 @ SV773 @ SV56 )
| ~ ( c_Limits_Otendsto @ SV432 @ SV1015 @ SV1168 @ SV773 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3522,plain,
! [SV1169: $i,SV1016: $i,SV774: $i,SV433: $i,SV57: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV57 )
= $false )
| ( ( ( c_Limits_Otendsto @ SV433 @ SV774 @ SV1016 @ SV1169 @ SV57 )
| ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SV1169 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV774 ) @ SV1016 @ SV1169 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3523,plain,
! [SV1221: $i,SV1170: $i,SV1017: $i,SV775: $i,SV434: $i,SV58: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV58 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV434 )
| ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3281]) ).
thf(3524,plain,
! [SV1031: $i,SV789: $i,SV450: $i,SV75: $i] :
( ( ( ~ ( class_HOL_Ozero @ SV75 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3525,plain,
! [SV451: $i,SV76: $i,SV790: $i] :
( ( ( c_Series_Osummable @ SV790 @ SV76 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ ( c_Series_Osuminf @ SV790 @ SV76 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV76 ) @ SV451 ) @ SV790 @ SV76 @ SV76 @ tc_nat ) @ SV76 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3526,plain,
! [SV1033: $i,SV797: $i,SV460: $i,SV85: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV85 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SV1033 @ SV797 @ SV85 )
| ~ ( c_Limits_OZfun @ SV460 @ SV1033 @ SV797 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3527,plain,
! [SV1222: $i,SV1171: $i,SV1034: $i,SV798: $i,SV461: $i,SV86: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV86 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SV1034 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV1171 ) @ SV1222 @ SV1034 @ SV86 )
| ~ ( c_Limits_Otendsto @ SV798 @ SV1171 @ SV1222 @ SV1034 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3528,plain,
! [SV1172: $i,SV1035: $i,SV799: $i,SV462: $i,SV87: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV87 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SV799 @ SV87 @ SV87 @ SV1035 ) @ SV1172 @ SV1035 @ SV87 )
| ~ ( c_Limits_OZfun @ SV799 @ SV1172 @ SV1035 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3302]) ).
thf(3529,plain,
! [SV1173: $i,SV1036: $i,SV800: $i,SV463: $i,SV88: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV88 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SV800 @ SV88 @ SV88 @ SV1036 ) @ SV1173 @ SV1036 @ SV88 )
| ~ ( c_Limits_OZfun @ SV800 @ SV1173 @ SV1036 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3530,plain,
! [SV464: $i,SV89: $i,SV801: $i] :
( ( ( SV801
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
= $true )
| ( ( SV464
= ( c_HOL_Ozero__class_Ozero @ SV89 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV89 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV464 ) @ SV801 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV464 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV89 ) @ SV801 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3531,plain,
! [SV465: $i,SV90: $i,SV802: $i] :
( ( ( SV802
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
= $true )
| ( ( SV465
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV90 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV465 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV465 ) @ SV802 ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV90 ) @ SV802 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3532,plain,
! [SV466: $i,SV92: $i,SV803: $i] :
( ( ( c_Series_Osummable @ SV803 @ SV92 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ ( c_Series_Osuminf @ SV803 @ SV92 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV92 ) @ SV466 ) @ SV803 @ SV92 @ SV92 @ tc_nat ) @ SV92 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3533,plain,
! [SV467: $i,SV93: $i,SV804: $i] :
( ( ( c_Series_Osummable @ SV804 @ SV93 )
= $false )
| ( ( ( c_Series_Osuminf @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ SV804 @ SV93 @ SV93 @ tc_nat ) @ SV93 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV93 ) @ SV467 ) @ ( c_Series_Osuminf @ SV804 @ SV93 ) ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3534,plain,
! [SV1174: $i,SV1037: $i,SV805: $i,SV468: $i,SV95: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV95 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV805 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1037 ) @ SV1174 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV468 ) @ SV1037 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV805 ) @ SV1174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3535,plain,
! [SV1223: $i,SV1175: $i,SV1038: $i,SV806: $i,SV469: $i,SV96: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV96 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV469 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1223 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SV1038 @ SV1175 @ SV1223 @ SV469 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3536,plain,
! [SV1039: $i,SV807: $i,SV97: $i,SV470: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SV470 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SV807 @ ( hAPP @ c_Complex_ORe @ SV1039 ) @ SV97 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV470 @ SV807 @ SV1039 @ SV97 @ tc_Complex_Ocomplex ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3310]) ).
thf(3537,plain,
! [SV98: $i,SV808: $i,SV471: $i] :
( ( ( c_Deriv_Odifferentiable @ SV471 @ SV808 @ SV98 )
= $false )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV98 ) @ SV471 @ SV98 @ SV98 @ SV98 ) @ SV808 @ SV98 )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3538,plain,
! [SV809: $i,SV472: $i,SV99: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV99 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ SV472 ) @ SV809 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV99 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV472 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV99 ) @ SV809 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3539,plain,
! [SV473: $i,SV100: $i,SV810: $i] :
( ( ( SV810
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
= $true )
| ( ( SV473
= ( c_HOL_Ozero__class_Ozero @ SV100 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ SV473 ) @ SV810 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV100 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV810 ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV100 ) @ SV473 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(3540,plain,
! [SV1176: $i,SV1040: $i,SV811: $i,SV474: $i,SV101: $i] :
( ( ( class_RealVector_Ometric__space @ SV101 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SV1176 @ SV474 @ SV101 )
| ( SV811 = SV1176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3541,plain,
! [SV1177: $i,SV1041: $i,SV812: $i,SV475: $i,SV102: $i] :
( ( ( class_RealVector_Ometric__space @ SV102 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
| ( SV812 = SV1041 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SV1177 @ SV1041 @ SV475 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3315]) ).
thf(3542,plain,
! [SV1178: $i,SV1042: $i,SV813: $i,SV477: $i,SV104: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV104 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ ( c_Finite__Set_Osetsum @ SV813 @ SV1042 @ SV1178 @ SV104 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV104 ) @ SV477 ) @ SV813 @ SV104 @ SV104 @ SV1178 ) @ SV1042 @ SV1178 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3543,plain,
! [SV1179: $i,SV1043: $i,SV814: $i,SV478: $i,SV105: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV105 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ ( c_Finite__Set_Osetsum @ SV814 @ SV1043 @ SV1179 @ SV105 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV105 ) @ SV478 ) @ SV814 @ SV105 @ SV105 @ SV1179 ) @ SV1043 @ SV1179 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3544,plain,
! [SV1180: $i,SV1044: $i,SV815: $i,SV480: $i,SV107: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV480 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
| ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3545,plain,
! [SV1045: $i,SV108: $i,SV816: $i,SV481: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV481 ) )
= $true )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SV1045 @ SV108 @ SV481 )
| ~ ( c_Lim_OisCont @ SV816 @ SV1045 @ SV108 @ SV481 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3546,plain,
! [SV1181: $i,SV1049: $i,SV820: $i,SV486: $i,SV114: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV114 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV114 )
| ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SV1181 @ SV820 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SV1049 @ SV1181 @ SV820 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3547,plain,
! [SV1050: $i,SV116: $i,SV821: $i,SV487: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV487 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1050 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SV1050 ) @ SV116 @ SV487 )
| ~ ( c_Lim_OisCont @ SV821 @ SV1050 @ SV116 @ SV487 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3325]) ).
thf(3548,plain,
! [SV117: $i,SV1051: $i,SV822: $i,SV488: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV488 ) )
= $true )
| ( ( ( c_Lim_OisCont @ SV822 @ SV1051 @ SV117 @ SV488 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV1051 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SV1051 ) @ SV117 @ SV488 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3326]) ).
thf(3549,plain,
! [SV119: $i,SV1052: $i,SV824: $i,SV490: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV490 ) )
= $true )
| ( ( ( c_Lim_OisCont @ SV824 @ SV1052 @ SV119 @ SV490 )
| ~ ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3550,plain,
! [SV1182: $i,SV1053: $i,SV825: $i,SV491: $i,SV120: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV120 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV491 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SV1053 @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3551,plain,
! [SV1183: $i,SV1054: $i,SV826: $i,SV492: $i,SV121: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV121 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV492 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SV1054 @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3552,plain,
! [SV1055: $i,SV827: $i,SV493: $i,SV122: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV827 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV1055 ) @ SV122 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV827 @ SV1055 @ SV122 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3330]) ).
thf(3553,plain,
! [SV494: $i,SV124: $i,SV828: $i] :
( ( ( c_Series_Osummable @ SV828 @ SV124 )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV124 ) @ SV494 ) @ SV828 @ SV124 @ SV124 @ tc_nat ) @ SV124 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3554,plain,
! [SV1184: $i,SV1056: $i,SV831: $i,SV497: $i,SV127: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV127 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV497 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV1184 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SV831 @ SV1056 @ SV1184 @ SV497 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3555,plain,
! [SV129: $i,SV1057: $i,SV832: $i,SV498: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV498 ) )
= $true )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
| ~ ( c_SEQ_OZseq @ SV1057 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3556,plain,
! [SV1238: $i,SV1224: $i,SV1185: $i,SV1058: $i,SV833: $i,SV499: $i,SV130: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV130 )
| ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3557,plain,
! [SV1186: $i,SV1059: $i,SV834: $i,SV500: $i,SV131: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV131 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV131 )
| ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3558,plain,
! [SV1060: $i,SV836: $i,SV502: $i,SV133: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV133 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3559,plain,
! [SV1061: $i,SV837: $i,SV503: $i,SV134: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV134 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3560,plain,
! [SV1239: $i,SV1225: $i,SV1187: $i,SV1062: $i,SV838: $i,SV504: $i,SV135: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV135 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(3561,plain,
! [SV1188: $i,SV1063: $i,SV839: $i,SV505: $i,SV136: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV136 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SV839 @ SV136 @ SV136 @ SV1063 ) @ SV1188 @ SV1063 @ SV136 )
| ~ ( c_Limits_OZfun @ SV839 @ SV1188 @ SV1063 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3562,plain,
! [SV1189: $i,SV1064: $i,SV840: $i,SV506: $i,SV137: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV137 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SV840 @ SV137 @ SV137 @ SV1064 ) @ SV1189 @ SV1064 @ SV137 )
| ~ ( c_Limits_OZfun @ SV840 @ SV1189 @ SV1064 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3563,plain,
! [SV139: $i,SV841: $i,SV508: $i] :
( ( ( ( hAPP @ SV508 @ SV841 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
= $true )
| ( ( ~ ( c_Deriv_Odifferentiable @ SV508 @ SV841 @ SV139 ) )
= $true )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SV508 @ SV139 @ SV139 @ SV139 ) @ SV841 @ SV139 )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3564,plain,
! [SV1240: $i,SV1226: $i,SV1190: $i,SV1065: $i,SV842: $i,SV509: $i,SV140: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV140 )
| ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3565,plain,
! [SV1066: $i,SV846: $i,SV145: $i,SV513: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV513 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV846 @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3566,plain,
! [SV146: $i,SV1067: $i,SV847: $i,SV514: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV514 ) )
= $true )
| ( ( ( c_Lim_OLIM @ SV847 @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3345]) ).
thf(3567,plain,
! [SV161: $i,SV1079: $i,SV862: $i,SV529: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV529 ) )
= $true )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
| ~ ( c_Series_Osummable @ SV1079 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3568,plain,
! [SV1192: $i,SV1080: $i,SV863: $i,SV530: $i,SV162: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV1080 ) @ SV1192 @ SV863 @ SV162 )
| ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SV530 @ SV1080 @ SV1192 @ SV863 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3569,plain,
! [SV1193: $i,SV1081: $i,SV864: $i,SV535: $i,SV167: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV167 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV535 ) @ SV864 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ SV1081 ) @ SV864 ) ) @ SV1193 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV167 ) @ SV535 ) @ SV1081 ) ) @ SV864 ) ) @ SV1193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3358]) ).
thf(3570,plain,
! [SV174: $i,SV1082: $i,SV865: $i,SV542: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV542 ) )
= $true )
| ( ( ( c_Lim_OisCont @ SV865 @ SV1082 @ SV174 @ SV542 )
| ~ ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3361]) ).
thf(3571,plain,
! [SV543: $i,SV175: $i] :
( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SV543 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SV543 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV543 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV175 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3362]) ).
thf(3572,plain,
! [SV1194: $i,SV1083: $i,SV866: $i,SV545: $i,SV177: $i] :
( ( ( class_RealVector_Oreal__vector @ SV177 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ ( c_Finite__Set_Osetsum @ SV866 @ SV1083 @ SV1194 @ SV177 ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV177 ) @ SV545 ) @ SV866 @ SV177 @ SV177 @ SV1194 ) @ SV1083 @ SV1194 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3573,plain,
! [SV1195: $i,SV1084: $i,SV867: $i,SV546: $i,SV179: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV179 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV546 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV1195 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV867 @ SV1084 @ SV1195 @ SV546 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3365]) ).
thf(3574,plain,
! [SV1228: $i,SV1196: $i,SV1087: $i,SV870: $i,SV552: $i,SV185: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV185 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV552 )
| ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
| ~ ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3370]) ).
thf(3575,plain,
! [SV568: $i,SV202: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SV568 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV568 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV202 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3576,plain,
! [SV1092: $i,SV206: $i,SV875: $i,SV572: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV572 ) )
= $true )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SV1092 @ SV206 @ SV572 )
| ~ ( c_Lim_OisCont @ SV875 @ SV1092 @ SV206 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3577,plain,
! [SV1197: $i,SV1093: $i,SV876: $i,SV573: $i,SV207: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV207 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV573 )
| ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SV1197 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SV1197 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3378]) ).
thf(3578,plain,
! [SV208: $i,SV1094: $i,SV877: $i,SV574: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV574 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
| ~ ( c_SEQ_OCauchy @ SV1094 @ SV208 )
| ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3579,plain,
! [SV1198: $i,SV1095: $i,SV878: $i,SV575: $i,SV209: $i] :
( ( ( class_RealVector_Ometric__space @ SV209 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV575 )
| ( c_Lim_OLIM @ SV878 @ SV1095 @ SV1198 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV1198 @ SV575 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(3580,plain,
! [SV1199: $i,SV1096: $i,SV879: $i,SV576: $i,SV210: $i] :
( ( ( class_RealVector_Ometric__space @ SV210 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV576 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SV1199 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SV879 @ SV1096 @ SV1199 @ SV576 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3581,plain,
! [SV211: $i,SV1097: $i,SV880: $i,SV577: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV577 ) )
= $true )
| ( ( ( c_Lim_OLIM @ SV880 @ SV1097 @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV1097 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3582,plain,
! [SV1098: $i,SV212: $i,SV881: $i,SV578: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV578 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV1098 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
| ~ ( c_Lim_OLIM @ SV881 @ SV1098 @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3583,plain,
! [SV579: $i,SV213: $i,SV882: $i] :
( ( ( c_Series_Osummable @ SV882 @ SV213 )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV213 ) @ SV579 ) @ SV882 @ SV213 @ SV213 @ tc_nat ) @ SV213 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3584,plain,
! [SV580: $i,SV214: $i,SV883: $i] :
( ( ( c_Series_Osummable @ SV883 @ SV214 )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV214 ) @ SV580 ) @ SV883 @ SV214 @ SV214 @ tc_nat ) @ SV214 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3585,plain,
! [SV1099: $i,SV884: $i,SV581: $i,SV215: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV884 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV1099 ) @ SV215 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV884 @ SV1099 @ SV215 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3586,plain,
! [SV1100: $i,SV885: $i,SV582: $i,SV216: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV885 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV1100 ) @ SV216 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV885 @ SV1100 @ SV216 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3587,plain,
! [SV218: $i,SV887: $i,SV584: $i] :
( ( ( c_Series_Osums @ SV584 @ SV887 @ SV218 )
= $false )
| ( ( c_Series_Osummable @ SV584 @ SV218 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3388]) ).
thf(3588,plain,
! [SV219: $i,SV888: $i,SV585: $i] :
( ( ( c_Series_Osums @ SV585 @ SV888 @ SV219 )
= $false )
| ( ( c_Series_Osummable @ SV585 @ SV219 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3589,plain,
! [SV1200: $i,SV1101: $i,SV890: $i,SV587: $i,SV221: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV221 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SV890 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV1101 ) @ SV1200 @ SV890 @ tc_RealDef_Oreal )
| ~ ( c_Limits_Otendsto @ SV587 @ SV1101 @ SV1200 @ SV890 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3590,plain,
! [SV595: $i,SV229: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SV595 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV595 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV229 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3591,plain,
! [SV1106: $i,SV236: $i,SV899: $i,SV601: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV601 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBK @ SV899 @ SV236 @ SV601 ) @ SV1106 @ SV899 @ SV601 @ SV236 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3592,plain,
! [SV1107: $i,SV900: $i,SV602: $i,SV237: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV237 ) )
= $true )
| ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SV602 @ SV900 @ SV1107 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SV602 @ tc_RealDef_Oreal @ SV237 @ SV1107 ) @ SV900 @ SV1107 @ SV237 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3593,plain,
! [SV901: $i,SV250: $i,SV615: $i] :
( ( ( c_Series_Osummable @ SV615 @ SV250 )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ SV615 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV901 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV250 @ tc_nat ) @ SV250 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3594,plain,
! [SV1229: $i,SV1201: $i,SV1108: $i,SV902: $i,SV616: $i,SV251: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV251 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV616 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1229 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SV1108 @ SV1201 @ SV1229 @ SV616 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3399]) ).
thf(3595,plain,
! [SV1202: $i,SV1110: $i,SV906: $i,SV620: $i,SV255: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV255 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV620 )
| ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
| ~ ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3401]) ).
thf(3596,plain,
! [SV257: $i,SV622: $i,SV907: $i] :
( ( ( c_Series_Osums @ SV907 @ SV622 @ SV257 )
= $false )
| ( ( SV622
= ( c_Series_Osuminf @ SV907 @ SV257 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3597,plain,
! [SV258: $i,SV908: $i,SV623: $i] :
( ( ( c_Series_Osums @ SV623 @ SV908 @ SV258 )
= $false )
| ( ( ( c_Series_Osuminf @ SV623 @ SV258 )
= SV908 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3598,plain,
! [SV268: $i,SV910: $i,SV630: $i] :
( ( ( c_Series_Osums @ SV630 @ SV910 @ SV268 )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV630 @ SV268 @ SV268 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV268 ) @ SV910 ) @ SV268 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3599,plain,
! [SV271: $i,SV1111: $i,SV911: $i,SV631: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV631 ) )
= $true )
| ( ( ( c_Lim_OLIM @ SV911 @ SV1111 @ ( hAPP @ SV911 @ SV1111 ) @ SV271 @ SV631 )
| ~ ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3409]) ).
thf(3600,plain,
! [SV632: $i,SV272: $i,SV912: $i] :
( ( ( c_SEQ_OZseq @ SV912 @ SV272 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV272 ) @ SV632 ) @ SV912 @ SV272 @ SV272 @ tc_nat ) @ SV272 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3601,plain,
! [SV633: $i,SV273: $i,SV913: $i] :
( ( ( c_SEQ_OZseq @ SV913 @ SV273 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV273 ) @ SV633 ) @ SV913 @ SV273 @ SV273 @ tc_nat ) @ SV273 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3602,plain,
! [SV276: $i,SV1112: $i,SV914: $i,SV636: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV636 ) )
= $true )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
| ~ ( c_SEQ_OCauchy @ SV1112 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3414]) ).
thf(3603,plain,
! [SV277: $i,SV1113: $i,SV915: $i,SV637: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV637 ) )
= $true )
| ( ( ( c_Lim_OisCont @ SV915 @ SV1113 @ SV277 @ SV637 )
| ~ ( c_Lim_OLIM @ SV915 @ SV1113 @ ( hAPP @ SV915 @ SV1113 ) @ SV277 @ SV637 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3415]) ).
thf(3604,plain,
! [SV278: $i,SV1114: $i,SV916: $i,SV638: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV638 ) )
= $true )
| ( ( ( c_Lim_OLIM @ SV916 @ SV1114 @ ( hAPP @ SV916 @ SV1114 ) @ SV278 @ SV638 )
| ~ ( c_Lim_OisCont @ SV916 @ SV1114 @ SV278 @ SV638 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3416]) ).
thf(3605,plain,
! [SV1230: $i,SV1203: $i,SV1115: $i,SV919: $i,SV641: $i,SV281: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV281 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV1203 ) @ SV1230 @ SV1115 @ SV281 )
| ~ ( c_Limits_Otendsto @ SV919 @ SV1203 @ SV1230 @ SV1115 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3417]) ).
thf(3606,plain,
! [SV642: $i,SV282: $i,SV920: $i] :
( ( ( c_SEQ_OCauchy @ SV920 @ SV282 )
= $false )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV282 ) @ SV642 ) @ SV920 @ SV282 @ SV282 @ tc_nat ) @ SV282 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3418]) ).
thf(3607,plain,
! [SV921: $i,SV644: $i,SV285: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV285 )
= $false )
| ( ( ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SV921 ) @ SV285 )
| ~ ( c_Series_Osums @ SV644 @ SV921 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3419]) ).
thf(3608,plain,
! [SV286: $i,SV1116: $i,SV922: $i,SV645: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV645 ) )
= $true )
| ( ( ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
| ~ ( c_Series_Osummable @ SV1116 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3420]) ).
thf(3609,plain,
! [SV1117: $i,SV287: $i,SV923: $i,SV646: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV646 ) )
= $true )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SV1117 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SV923 @ SV1117 @ SV287 @ SV646 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3421]) ).
thf(3610,plain,
! [SV294: $i,SV927: $i,SV652: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV652 @ SV927 @ SV294 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV652 @ SV294 @ SV294 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV294 ) @ SV927 ) @ SV294 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3611,plain,
! [SV928: $i,SV653: $i,SV295: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV653 @ SV295 @ SV295 @ tc_nat ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV295 ) @ SV928 ) @ SV295 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV653 @ SV928 @ SV295 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3612,plain,
! [SV297: $i,SV929: $i,SV654: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV654 @ SV929 @ SV297 )
= $false )
| ( ( c_SEQ_Oconvergent @ SV654 @ SV297 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3613,plain,
! [SV298: $i,SV930: $i,SV655: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV655 @ SV930 @ SV298 )
= $false )
| ( ( c_SEQ_Oconvergent @ SV655 @ SV298 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3614,plain,
! [SV931: $i,SV299: $i,SV656: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBK @ SV656 @ SV299 @ tc_nat ) @ SV931 @ SV299 )
= $false )
| ( ( SV656 = SV931 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3615,plain,
! [SV1241: $i,SV1232: $i,SV1205: $i,SV1119: $i,SV932: $i,SV657: $i,SV300: $i] :
( ( ~ ( class_RealVector_Ometric__space @ SV300 )
| ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3616,plain,
! [SV303: $i,SV933: $i,SV660: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV660 @ SV933 @ SV303 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV660 @ SV303 @ tc_RealDef_Oreal @ tc_nat ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV303 ) @ SV933 ) @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3617,plain,
! [SV1120: $i,SV305: $i,SV934: $i,SV662: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV662 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV934 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SV1120 @ SV305 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV662 @ SV1120 @ SV305 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3432]) ).
thf(3618,plain,
! [SV1121: $i,SV306: $i,SV935: $i,SV663: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV663 @ SV935 @ SV306 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV663 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1121 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SV935 @ SV306 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3433]) ).
thf(3619,plain,
! [SV307: $i,SV936: $i,SV664: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV664 @ SV936 @ SV307 )
= $false )
| ( ( ( c_SEQ_Olim @ SV664 @ SV307 )
= SV936 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3620,plain,
! [SV1206: $i,SV1123: $i,SV938: $i,SV668: $i,SV312: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV312 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV668 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3621,plain,
! [SV1233: $i,SV1207: $i,SV1124: $i,SV939: $i,SV669: $i,SV313: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV313 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV669 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3437]) ).
thf(3622,plain,
! [SV941: $i,SV671: $i,SV315: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV315 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SV941 ) @ SV315 )
| ~ ( c_SEQ_OLIMSEQ @ SV671 @ SV941 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3623,plain,
! [SV1234: $i,SV1208: $i,SV1125: $i,SV943: $i,SV675: $i,SV320: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV320 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV675 )
| ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3439]) ).
thf(3624,plain,
! [SV321: $i,SV1126: $i,SV944: $i,SV676: $i] :
( ( ( SV676 = SV944 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV944 @ SV321 )
| ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV676 @ SV321 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(3625,plain,
! [SV1127: $i,SV945: $i,SV677: $i,SV322: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV945 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV1127 ) @ SV322 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV945 @ SV1127 @ SV322 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV322 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(3626,plain,
! [SV1128: $i,SV323: $i,SV946: $i,SV678: $i] :
( ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SV1128 @ SV323 )
= $true )
| ( ( ~ ( c_Deriv_Odifferentiable @ SV946 @ SV1128 @ SV323 )
| ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SV1128 ) @ SV323 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(3627,plain,
! [SV1129: $i,SV947: $i,SV679: $i,SV324: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV947 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV1129 ) @ SV324 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV947 @ SV1129 @ SV324 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3443]) ).
thf(3628,plain,
! [SV326: $i,SV948: $i,SV680: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV680 @ SV948 @ SV326 )
= $false )
| ( ( c_SEQ_OCauchy @ SV680 @ SV326 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3629,plain,
! [SV327: $i,SV949: $i,SV681: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV681 @ SV949 @ SV327 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV681 @ c_Suc @ tc_nat @ SV327 @ tc_nat ) @ SV949 @ SV327 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3630,plain,
! [SV950: $i,SV328: $i,SV682: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV682 @ c_Suc @ tc_nat @ SV328 @ tc_nat ) @ SV950 @ SV328 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV682 @ SV950 @ SV328 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3631,plain,
! [SV684: $i,SV330: $i,SV952: $i] :
( ( ( SV952
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV684 @ SV952 @ SV330 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV684 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV952 ) @ SV330 )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3448]) ).
thf(3632,plain,
! [SV1131: $i,SV953: $i,SV331: $i,SV685: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SV685 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SV953 @ ( hAPP @ c_Complex_OIm @ SV1131 ) @ SV331 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV685 @ SV953 @ SV1131 @ SV331 @ tc_Complex_Ocomplex ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(3633,plain,
! [SV957: $i,SV691: $i,SV339: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV691 ) @ SV691 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV957 ) @ SV957 ) )
= $false )
| ( ( ( SV691
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SV957 ) )
| ( SV691 = SV957 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3634,plain,
! [SV1134: $i,SV958: $i,SV692: $i,SV340: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV692 ) @ SV958 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1134 ) @ SV958 ) )
= $true )
| ( ( SV692 = SV1134 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3453]) ).
thf(3635,plain,
! [SV959: $i,SV693: $i,SV342: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SV693 ) @ SV959 )
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
= $false )
| ( ( ( SV693
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
| ( SV959
= ( c_HOL_Ozero__class_Ozero @ SV342 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3636,plain,
! [SV1212: $i,SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV345 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV345 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
| ( SV961 = SV1212 )
| ( SV696 = SV1135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3637,plain,
! [SV962: $i,SV698: $i,SV347: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV962 ) )
= $false )
| ( ( ( SV698 = SV962 )
| ( SV962
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3638,plain,
! [SV963: $i,SV699: $i,SV348: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ SV699 ) @ SV963 )
= ( c_HOL_Ozero__class_Ozero @ SV348 ) )
= $false )
| ( ( SV699
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV348 ) @ SV963 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3459]) ).
thf(3639,plain,
! [SV964: $i,SV700: $i,SV349: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV700 ) @ SV700 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV349 ) @ SV964 ) @ SV964 ) )
= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
= $false )
| ( ( SV700
= ( c_HOL_Ozero__class_Ozero @ SV349 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3640,plain,
! [SV965: $i,SV701: $i,SV350: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SV701 ) @ SV965 )
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
= $false )
| ( ( ( SV965
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ SV350 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3641,plain,
! [SV1213: $i,SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV352 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV352 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
| ( SV967 = SV1213 )
| ( SV703 = SV1137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3642,plain,
! [SV1138: $i,SV968: $i,SV705: $i,SV354: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV968 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV1138 ) )
= $true )
| ( ( ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV968 = SV1138 ) )
= $true )
| ( ( class_RealVector_Oreal__vector @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3465]) ).
thf(3643,plain,
! [SV970: $i,SV708: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SV708 ) @ SV970 )
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $false )
| ( ( ( SV970
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
| ( SV708
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
= $true )
| ( ( class_RealVector_Oreal__vector @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3644,plain,
! [SV1139: $i,SV971: $i,SV709: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV971 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV1139 ) )
= $true )
| ( ( SV971 = SV1139 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3467]) ).
thf(3645,plain,
! [SV973: $i,SV711: $i,SV360: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV711 ) @ SV973 )
= ( c_HOL_Ozero__class_Ozero @ SV360 ) )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV360 ) @ SV711 )
= SV973 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3646,plain,
! [SV974: $i,SV712: $i,SV361: $i] :
( ( ( class_Int_Onumber__ring @ SV361 )
= $false )
| ( ( ( SV712
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SV974 ) )
| ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3469]) ).
thf(3647,plain,
! [SV975: $i,SV713: $i,SV362: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SV713 ) @ SV975 )
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
= $false )
| ( ( ( SV975
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV362 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3470]) ).
thf(3648,plain,
! [SV714: $i,SV363: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SV714 )
!= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
= $true )
| ( ( SV714
= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV363 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(3649,plain,
! [SV976: $i,SV715: $i,SV364: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV715 ) @ SV715 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV364 ) @ SV976 ) @ SV976 ) )
= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
= $false )
| ( ( SV976
= ( c_HOL_Ozero__class_Ozero @ SV364 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3650,plain,
! [SV977: $i,SV716: $i,SV365: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV716 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV365 ) @ SV977 ) )
= $false )
| ( ( SV716 = SV977 )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3651,plain,
! [SV1140: $i,SV978: $i,SV717: $i,SV366: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SV978 )
!= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV1140 ) @ SV978 ) )
= $true )
| ( ( ( SV978
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SV717 = SV1140 ) )
= $true )
| ( ( class_RealVector_Oreal__vector @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3474]) ).
thf(3652,plain,
! [SV980: $i,SV724: $i,SV373: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
= $false )
| ( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV980 ) )
| ( SV724 = SV980 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3653,plain,
! [SV981: $i,SV725: $i,SV374: $i] :
( ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV725 )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV374 ) @ SV981 ) )
= $false )
| ( ( SV725 = SV981 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV374 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3654,plain,
! [SV1142: $i,SV982: $i,SV726: $i,SV375: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV375 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV1142 ) )
| ( SV982 = SV1142 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3483]) ).
thf(3655,plain,
! [SV983: $i,SV727: $i,SV376: $i] :
( ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV727 )
= ( hAPP @ ( c_RealVector_Oof__real @ SV376 ) @ SV983 ) )
= $false )
| ( ( SV727 = SV983 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3484]) ).
thf(3656,plain,
! [SV1214: $i,SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV377 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
| ( SV1143 = SV1214 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3657,plain,
! [SV1144: $i,SV985: $i,SV729: $i,SV379: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV985 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV1144 ) )
= $true )
| ( ( SV985 = SV1144 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3486]) ).
thf(3658,plain,
! [SV1215: $i,SV1145: $i,SV986: $i,SV731: $i,SV381: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV381 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1145 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1215 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SV1145 )
= SV1215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3487]) ).
thf(3659,plain,
! [SV1146: $i,SV987: $i,SV732: $i,SV382: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV987 ) @ SV1146 ) )
!= SV987 )
= $true )
| ( ( SV732
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SV1146 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(3660,plain,
! [SV1147: $i,SV988: $i,SV733: $i,SV2: $i,SV383: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV383 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SV733 @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3489]) ).
thf(3661,plain,
! [SV1148: $i,SV989: $i,SV734: $i,SV3: $i,SV384: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV384 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SV734 @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3490]) ).
thf(3662,plain,
! [SV1216: $i,SV1149: $i,SV990: $i,SV735: $i,SV385: $i,SV4: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV4 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SV990 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV1149 ) @ SV990 ) @ SV1216 @ SV735 @ SV4 )
| ~ ( c_Limits_Otendsto @ SV385 @ SV1149 @ SV1216 @ SV735 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3491]) ).
thf(3663,plain,
! [SV1150: $i,SV991: $i,SV736: $i,SV386: $i,SV5: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SV736 ) @ SV991 @ SV736 @ SV5 @ SV5 ) @ SV1150 @ SV736 @ SV5 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV386 @ SV1150 @ SV736 @ SV5 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3664,plain,
! [SV1151: $i,SV992: $i,SV737: $i,SV387: $i,SV6: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SV737 ) @ SV992 @ SV737 @ SV6 @ SV6 ) @ SV1151 @ SV737 @ SV6 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV387 @ SV1151 @ SV737 @ SV6 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(3665,plain,
! [SV1217: $i,SV1152: $i,SV993: $i,SV738: $i,SV388: $i,SV7: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV7 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV388 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV1217 ) @ SV993 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SV1152 @ SV1217 @ SV388 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3666,plain,
! [SV1218: $i,SV1156: $i,SV997: $i,SV742: $i,SV392: $i,SV11: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV11 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV392 )
| ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV1218 ) @ SV997 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SV1156 @ SV1218 @ SV392 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3667,plain,
! [SV1157: $i,SV998: $i,SV743: $i,SV393: $i,SV12: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SV743 ) @ SV998 @ SV743 @ SV12 @ SV12 ) @ SV1157 @ SV743 @ SV12 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV393 @ SV1157 @ SV743 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3499]) ).
thf(3668,plain,
! [SV1158: $i,SV999: $i,SV744: $i,SV394: $i,SV13: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SV744 ) @ SV999 @ SV744 @ SV13 @ SV13 ) @ SV1158 @ SV744 @ SV13 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV394 @ SV1158 @ SV744 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(3669,plain,
! [SV1219: $i,SV1159: $i,SV1000: $i,SV745: $i,SV395: $i,SV14: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV14 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SV1000 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV1159 ) @ SV1000 ) @ SV1219 @ SV745 @ SV14 )
| ~ ( c_Limits_Otendsto @ SV395 @ SV1159 @ SV1219 @ SV745 @ tc_RealDef_Oreal ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3670,plain,
! [SV15: $i,SV396: $i] :
( ( ( c_SEQ_OCauchy @ SV396 @ tc_RealDef_Oreal )
= $false )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV15 ) @ SV396 @ tc_RealDef_Oreal @ SV15 @ tc_nat ) @ SV15 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV15 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3671,plain,
! [SV1004: $i,SV25: $i,SV750: $i,SV404: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
= $false )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
| ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3672,plain,
! [SV1163: $i,SV1005: $i,SV754: $i,SV31: $i,SV410: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV410 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SV754 @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(3673,plain,
! [SV1164: $i,SV1006: $i,SV755: $i,SV32: $i,SV411: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV411 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SV755 @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3674,plain,
! [SV1220: $i,SV1165: $i,SV1007: $i,SV756: $i,SV413: $i,SV34: $i] :
( ( ( class_RealVector_Ometric__space @ SV34 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
| ( SV756 = SV1007 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(3675,plain,
! [SV35: $i,SV757: $i,SV1008: $i,SV414: $i] :
( ( ( c_Limits_OZfun @ SV414 @ SV1008 @ SV757 @ SV35 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV35 ) @ SV414 @ SV35 @ tc_RealDef_Oreal @ SV757 ) @ SV1008 @ SV757 @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(3676,plain,
! [SV758: $i,SV1009: $i,SV415: $i,SV36: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV36 ) @ SV415 @ SV36 @ tc_RealDef_Oreal @ SV1009 ) @ SV758 @ SV1009 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Limits_OZfun @ SV415 @ SV758 @ SV1009 @ SV36 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3512]) ).
thf(3677,plain,
! [SV1010: $i,SV37: $i,SV759: $i,SV416: $i] :
( ( ( class_RealVector_Ometric__space @ SV416 )
= $false )
| ( ( c_Lim_OisCont @ ( c_COMBK @ SV759 @ SV416 @ SV37 ) @ SV1010 @ SV37 @ SV416 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(3678,plain,
! [SV38: $i,SV760: $i,SV1011: $i,SV417: $i] :
( ( ( c_Limits_OZfun @ SV417 @ SV1011 @ SV760 @ SV38 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV38 ) @ SV417 @ SV38 @ SV38 @ SV760 ) @ SV1011 @ SV760 @ SV38 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(3679,plain,
! [SV420: $i,SV41: $i,SV763: $i] :
( ( ( c_Lim_OisUCont @ SV763 @ SV41 @ SV420 )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV763 @ SV41 @ SV420 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV420 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(3680,plain,
! [SV1012: $i,SV769: $i,SV426: $i,SV48: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV48 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV426 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3681,plain,
! [SV1166: $i,SV1013: $i,SV771: $i,SV51: $i,SV429: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV429 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SV1013 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(3682,plain,
! [SV1167: $i,SV1014: $i,SV772: $i,SV52: $i,SV430: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV430 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SV1014 @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3683,plain,
! [SV1168: $i,SV1015: $i,SV773: $i,SV432: $i,SV56: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SV773 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV1015 ) @ SV1168 @ SV773 @ SV56 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV432 @ SV1015 @ SV1168 @ SV773 @ SV56 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3521]) ).
thf(3684,plain,
! [SV57: $i,SV1169: $i,SV1016: $i,SV774: $i,SV433: $i] :
( ( ( c_Limits_Otendsto @ SV433 @ SV774 @ SV1016 @ SV1169 @ SV57 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SV1169 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV774 ) @ SV1016 @ SV1169 @ SV57 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3522]) ).
thf(3685,plain,
! [SV1221: $i,SV1170: $i,SV1017: $i,SV775: $i,SV434: $i,SV58: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV434 )
| ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3686,plain,
! [SV1031: $i,SV789: $i,SV450: $i,SV75: $i] :
( ( ( class_HOL_Ozero @ SV75 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3524]) ).
thf(3687,plain,
! [SV1033: $i,SV797: $i,SV460: $i,SV85: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV85 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SV1033 @ SV797 @ SV85 )
| ~ ( c_Limits_OZfun @ SV460 @ SV1033 @ SV797 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3526]) ).
thf(3688,plain,
! [SV1222: $i,SV1171: $i,SV1034: $i,SV798: $i,SV461: $i,SV86: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV86 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SV1034 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV1171 ) @ SV1222 @ SV1034 @ SV86 )
| ~ ( c_Limits_Otendsto @ SV798 @ SV1171 @ SV1222 @ SV1034 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3527]) ).
thf(3689,plain,
! [SV1172: $i,SV1035: $i,SV799: $i,SV462: $i,SV87: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SV799 @ SV87 @ SV87 @ SV1035 ) @ SV1172 @ SV1035 @ SV87 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV799 @ SV1172 @ SV1035 @ SV87 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3528]) ).
thf(3690,plain,
! [SV1173: $i,SV1036: $i,SV800: $i,SV463: $i,SV88: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SV800 @ SV88 @ SV88 @ SV1036 ) @ SV1173 @ SV1036 @ SV88 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV800 @ SV1173 @ SV1036 @ SV88 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(3691,plain,
! [SV1223: $i,SV1175: $i,SV1038: $i,SV806: $i,SV469: $i,SV96: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV96 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV469 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1223 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SV1038 @ SV1175 @ SV1223 @ SV469 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3692,plain,
! [SV97: $i,SV1039: $i,SV807: $i,SV470: $i] :
( ( ( c_Lim_OLIM @ SV470 @ SV807 @ SV1039 @ SV97 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_ORe @ SV470 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV97 ) @ SV807 @ ( hAPP @ c_Complex_ORe @ SV1039 ) @ SV97 @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Ometric__space @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3693,plain,
! [SV1176: $i,SV1040: $i,SV101: $i,SV811: $i,SV474: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV474 ) )
= $true )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SV1176 @ SV474 @ SV101 )
| ( SV811 = SV1176 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3540]) ).
thf(3694,plain,
! [SV1177: $i,SV102: $i,SV1041: $i,SV812: $i,SV475: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV475 ) )
= $true )
| ( ( ( SV812 = SV1041 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SV1177 @ SV1041 @ SV475 @ SV102 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3695,plain,
! [SV1180: $i,SV1044: $i,SV815: $i,SV107: $i,SV480: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV480 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
| ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3696,plain,
! [SV1045: $i,SV108: $i,SV816: $i,SV481: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV481 )
= $false )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SV1045 @ SV108 @ SV481 )
| ~ ( c_Lim_OisCont @ SV816 @ SV1045 @ SV108 @ SV481 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3545]) ).
thf(3697,plain,
! [SV1181: $i,SV1049: $i,SV820: $i,SV486: $i,SV114: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV114 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SV1181 @ SV820 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SV1049 @ SV1181 @ SV820 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3546]) ).
thf(3698,plain,
! [SV1050: $i,SV116: $i,SV821: $i,SV487: $i] :
( ( ( class_RealVector_Ometric__space @ SV487 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1050 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SV1050 ) @ SV116 @ SV487 )
| ~ ( c_Lim_OisCont @ SV821 @ SV1050 @ SV116 @ SV487 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3699,plain,
! [SV117: $i,SV1051: $i,SV822: $i,SV488: $i] :
( ( ( class_RealVector_Ometric__space @ SV488 )
= $false )
| ( ( ( c_Lim_OisCont @ SV822 @ SV1051 @ SV117 @ SV488 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV1051 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SV1051 ) @ SV117 @ SV488 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3700,plain,
! [SV119: $i,SV1052: $i,SV824: $i,SV490: $i] :
( ( ( class_RealVector_Ometric__space @ SV490 )
= $false )
| ( ( ( c_Lim_OisCont @ SV824 @ SV1052 @ SV119 @ SV490 )
| ~ ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3549]) ).
thf(3701,plain,
! [SV1182: $i,SV1053: $i,SV825: $i,SV120: $i,SV491: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV491 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SV1053 @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3550]) ).
thf(3702,plain,
! [SV1183: $i,SV1054: $i,SV826: $i,SV121: $i,SV492: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV492 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SV1054 @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3551]) ).
thf(3703,plain,
! [SV493: $i,SV122: $i,SV1055: $i,SV827: $i] :
( ( ( c_Series_Osums @ SV827 @ SV1055 @ SV122 )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV827 @ SV122 @ SV122 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV122 ) @ SV493 ) @ SV1055 ) @ SV122 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3704,plain,
! [SV1184: $i,SV1056: $i,SV831: $i,SV127: $i,SV497: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV497 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV1184 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SV831 @ SV1056 @ SV1184 @ SV497 @ SV127 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(3705,plain,
! [SV129: $i,SV1057: $i,SV832: $i,SV498: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV498 )
= $false )
| ( ( ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
| ~ ( c_SEQ_OZseq @ SV1057 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3706,plain,
! [SV1238: $i,SV1224: $i,SV1185: $i,SV1058: $i,SV833: $i,SV499: $i,SV130: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV130 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(3707,plain,
! [SV1186: $i,SV1059: $i,SV834: $i,SV500: $i,SV131: $i] :
( ( ( ~ ( class_RealVector_Oreal__algebra__1 @ SV131 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3557]) ).
thf(3708,plain,
! [SV1060: $i,SV836: $i,SV502: $i,SV133: $i] :
( ( ( class_Int_Onumber__ring @ SV133 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV1060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV133 ) @ SV502 ) @ SV836 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3709,plain,
! [SV1061: $i,SV837: $i,SV503: $i,SV134: $i] :
( ( ( class_Int_Onumber__ring @ SV134 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV134 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV1061 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV134 ) @ SV503 ) @ SV837 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(3710,plain,
! [SV1239: $i,SV1225: $i,SV1187: $i,SV1062: $i,SV838: $i,SV504: $i,SV135: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV135 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3711,plain,
! [SV1188: $i,SV1063: $i,SV839: $i,SV505: $i,SV136: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SV839 @ SV136 @ SV136 @ SV1063 ) @ SV1188 @ SV1063 @ SV136 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV839 @ SV1188 @ SV1063 @ SV136 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3561]) ).
thf(3712,plain,
! [SV1189: $i,SV1064: $i,SV840: $i,SV506: $i,SV137: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SV840 @ SV137 @ SV137 @ SV1064 ) @ SV1189 @ SV1064 @ SV137 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV840 @ SV1189 @ SV1064 @ SV137 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3562]) ).
thf(3713,plain,
! [SV139: $i,SV841: $i,SV508: $i] :
( ( ( c_Deriv_Odifferentiable @ SV508 @ SV841 @ SV139 )
= $false )
| ( ( ( hAPP @ SV508 @ SV841 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
= $true )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV139 ) @ SV508 @ SV139 @ SV139 @ SV139 ) @ SV841 @ SV139 )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3714,plain,
! [SV1240: $i,SV1226: $i,SV1190: $i,SV1065: $i,SV842: $i,SV509: $i,SV140: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV140 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(3715,plain,
! [SV1066: $i,SV846: $i,SV145: $i,SV513: $i] :
( ( ( class_RealVector_Ometric__space @ SV513 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV846 @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(3716,plain,
! [SV146: $i,SV1067: $i,SV847: $i,SV514: $i] :
( ( ( class_RealVector_Ometric__space @ SV514 )
= $false )
| ( ( ( c_Lim_OLIM @ SV847 @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3566]) ).
thf(3717,plain,
! [SV161: $i,SV1079: $i,SV862: $i,SV529: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV529 )
= $false )
| ( ( ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
| ~ ( c_Series_Osummable @ SV1079 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(3718,plain,
! [SV1192: $i,SV1080: $i,SV863: $i,SV530: $i,SV162: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV1080 ) @ SV1192 @ SV863 @ SV162 )
= $true )
| ( ( ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
| ~ ( c_Limits_Otendsto @ SV530 @ SV1080 @ SV1192 @ SV863 @ SV162 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3568]) ).
thf(3719,plain,
! [SV174: $i,SV1082: $i,SV865: $i,SV542: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV542 )
= $false )
| ( ( ( c_Lim_OisCont @ SV865 @ SV1082 @ SV174 @ SV542 )
| ~ ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3720,plain,
! [SV175: $i,SV543: $i] :
( ( ( c_Series_Osummable @ SV543 @ tc_RealDef_Oreal )
= $false )
| ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV175 ) @ ( c_Series_Osuminf @ SV543 @ tc_RealDef_Oreal ) )
= ( c_Series_Osuminf @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV175 ) @ SV543 @ tc_RealDef_Oreal @ SV175 @ tc_nat ) @ SV175 ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV175 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3571]) ).
thf(3721,plain,
! [SV1195: $i,SV1084: $i,SV867: $i,SV179: $i,SV546: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV546 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV1195 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV867 @ SV1084 @ SV1195 @ SV546 @ SV179 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(3722,plain,
! [SV1228: $i,SV1196: $i,SV1087: $i,SV870: $i,SV552: $i,SV185: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV185 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV552 )
| ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
| ~ ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(3723,plain,
! [SV202: $i,SV568: $i] :
( ( ( c_Series_Osummable @ SV568 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV202 ) @ SV568 @ tc_RealDef_Oreal @ SV202 @ tc_nat ) @ SV202 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV202 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3575]) ).
thf(3724,plain,
! [SV1092: $i,SV206: $i,SV875: $i,SV572: $i] :
( ( ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
= $false )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SV1092 @ SV206 @ SV572 )
| ~ ( c_Lim_OisCont @ SV875 @ SV1092 @ SV206 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3725,plain,
! [SV1197: $i,SV1093: $i,SV207: $i,SV876: $i,SV573: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV573 ) )
= $true )
| ( ( ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SV1197 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SV1197 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3577]) ).
thf(3726,plain,
! [SV208: $i,SV1094: $i,SV877: $i,SV574: $i] :
( ( ( class_RealVector_Ometric__space @ SV574 )
= $false )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
| ~ ( c_SEQ_OCauchy @ SV1094 @ SV208 )
| ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3578]) ).
thf(3727,plain,
! [SV209: $i,SV1198: $i,SV1095: $i,SV878: $i,SV575: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV575 ) )
= $true )
| ( ( ( c_Lim_OLIM @ SV878 @ SV1095 @ SV1198 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV1198 @ SV575 @ SV209 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3579]) ).
thf(3728,plain,
! [SV1199: $i,SV210: $i,SV1096: $i,SV879: $i,SV576: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV576 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SV1199 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SV879 @ SV1096 @ SV1199 @ SV576 @ SV210 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(3729,plain,
! [SV211: $i,SV1097: $i,SV880: $i,SV577: $i] :
( ( ( class_RealVector_Ometric__space @ SV577 )
= $false )
| ( ( ( c_Lim_OLIM @ SV880 @ SV1097 @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV1097 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3581]) ).
thf(3730,plain,
! [SV1098: $i,SV212: $i,SV881: $i,SV578: $i] :
( ( ( class_RealVector_Ometric__space @ SV578 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV1098 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
| ~ ( c_Lim_OLIM @ SV881 @ SV1098 @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3731,plain,
! [SV581: $i,SV215: $i,SV1099: $i,SV884: $i] :
( ( ( c_Series_Osums @ SV884 @ SV1099 @ SV215 )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV884 @ SV215 @ SV215 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV215 ) @ SV581 ) @ SV1099 ) @ SV215 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3585]) ).
thf(3732,plain,
! [SV582: $i,SV216: $i,SV1100: $i,SV885: $i] :
( ( ( c_Series_Osums @ SV885 @ SV1100 @ SV216 )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV885 @ SV216 @ SV216 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV216 ) @ SV582 ) @ SV1100 ) @ SV216 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3733,plain,
! [SV1200: $i,SV1101: $i,SV890: $i,SV587: $i,SV221: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SV890 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV1101 ) @ SV1200 @ SV890 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV587 @ SV1101 @ SV1200 @ SV890 @ SV221 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(3734,plain,
! [SV229: $i,SV595: $i] :
( ( ( c_SEQ_OZseq @ SV595 @ tc_RealDef_Oreal )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV229 ) @ SV595 @ tc_RealDef_Oreal @ SV229 @ tc_nat ) @ SV229 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV229 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3735,plain,
! [SV1106: $i,SV236: $i,SV899: $i,SV601: $i] :
( ( ( class_RealVector_Ometric__space @ SV601 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBK @ SV899 @ SV236 @ SV601 ) @ SV1106 @ SV899 @ SV601 @ SV236 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(3736,plain,
! [SV1107: $i,SV900: $i,SV602: $i,SV237: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV237 )
= $false )
| ( ( ( hAPP @ ( c_RealVector_Oof__real @ SV237 ) @ ( c_Finite__Set_Osetsum @ SV602 @ SV900 @ SV1107 @ tc_RealDef_Oreal ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV237 ) @ SV602 @ tc_RealDef_Oreal @ SV237 @ SV1107 ) @ SV900 @ SV1107 @ SV237 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3737,plain,
! [SV1229: $i,SV1201: $i,SV1108: $i,SV902: $i,SV616: $i,SV251: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV251 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV616 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1229 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SV1108 @ SV1201 @ SV1229 @ SV616 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3594]) ).
thf(3738,plain,
! [SV1202: $i,SV255: $i,SV1110: $i,SV906: $i,SV620: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV620 ) )
= $true )
| ( ( ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
| ~ ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(3739,plain,
! [SV271: $i,SV1111: $i,SV911: $i,SV631: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV631 )
= $false )
| ( ( ( c_Lim_OLIM @ SV911 @ SV1111 @ ( hAPP @ SV911 @ SV1111 ) @ SV271 @ SV631 )
| ~ ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(3740,plain,
! [SV276: $i,SV1112: $i,SV914: $i,SV636: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV636 )
= $false )
| ( ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
| ~ ( c_SEQ_OCauchy @ SV1112 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3602]) ).
thf(3741,plain,
! [SV277: $i,SV1113: $i,SV915: $i,SV637: $i] :
( ( ( class_RealVector_Ometric__space @ SV637 )
= $false )
| ( ( ( c_Lim_OisCont @ SV915 @ SV1113 @ SV277 @ SV637 )
| ~ ( c_Lim_OLIM @ SV915 @ SV1113 @ ( hAPP @ SV915 @ SV1113 ) @ SV277 @ SV637 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3603]) ).
thf(3742,plain,
! [SV278: $i,SV1114: $i,SV916: $i,SV638: $i] :
( ( ( class_RealVector_Ometric__space @ SV638 )
= $false )
| ( ( ( c_Lim_OLIM @ SV916 @ SV1114 @ ( hAPP @ SV916 @ SV1114 ) @ SV278 @ SV638 )
| ~ ( c_Lim_OisCont @ SV916 @ SV1114 @ SV278 @ SV638 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3604]) ).
thf(3743,plain,
! [SV1230: $i,SV1203: $i,SV1115: $i,SV919: $i,SV641: $i,SV281: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV281 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV1203 ) @ SV1230 @ SV1115 @ SV281 )
| ~ ( c_Limits_Otendsto @ SV919 @ SV1203 @ SV1230 @ SV1115 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3605]) ).
thf(3744,plain,
! [SV921: $i,SV644: $i,SV285: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SV921 ) @ SV285 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV644 @ SV921 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV285 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(3745,plain,
! [SV286: $i,SV1116: $i,SV922: $i,SV645: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV645 )
= $false )
| ( ( ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
| ~ ( c_Series_Osummable @ SV1116 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(3746,plain,
! [SV1117: $i,SV287: $i,SV923: $i,SV646: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV646 )
= $false )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SV1117 @ SV287 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OisCont @ SV923 @ SV1117 @ SV287 @ SV646 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3609]) ).
thf(3747,plain,
! [SV1241: $i,SV1232: $i,SV1205: $i,SV1119: $i,SV932: $i,SV657: $i,SV300: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV300 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3615]) ).
thf(3748,plain,
! [SV934: $i,SV305: $i,SV1120: $i,SV662: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV662 @ SV1120 @ SV305 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV662 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV934 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV305 @ tc_nat ) @ SV1120 @ SV305 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3617]) ).
thf(3749,plain,
! [SV935: $i,SV306: $i,SV1121: $i,SV663: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV663 @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1121 @ tc_nat @ tc_nat @ tc_nat ) @ tc_nat @ SV306 @ tc_nat ) @ SV935 @ SV306 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV663 @ SV935 @ SV306 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3750,plain,
! [SV1206: $i,SV312: $i,SV1123: $i,SV938: $i,SV668: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV668 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(3751,plain,
! [SV1233: $i,SV1207: $i,SV1124: $i,SV939: $i,SV669: $i,SV313: $i] :
( ( ( class_RealVector_Ometric__space @ SV313 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV669 )
| ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(3752,plain,
! [SV941: $i,SV671: $i,SV315: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SV941 ) @ SV315 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV671 @ SV941 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV315 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3622]) ).
thf(3753,plain,
! [SV1234: $i,SV1208: $i,SV1125: $i,SV943: $i,SV675: $i,SV320: $i] :
( ( ( class_RealVector_Ometric__space @ SV320 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV675 )
| ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(3754,plain,
! [SV676: $i,SV321: $i,SV944: $i,SV1126: $i] :
( ( ( ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV944 @ SV321 ) )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV676 @ SV321 ) )
= $true )
| ( ( SV676 = SV944 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(3755,plain,
! [SV677: $i,SV322: $i,SV1127: $i,SV945: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV945 @ SV1127 @ SV322 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV945 @ SV322 @ SV322 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV322 ) @ SV677 ) @ SV1127 ) @ SV322 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3756,plain,
! [SV678: $i,SV323: $i,SV1128: $i,SV946: $i] :
( ( ( ~ ( c_Deriv_Odifferentiable @ SV946 @ SV1128 @ SV323 ) )
= $true )
| ( ( ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SV1128 ) @ SV323 ) )
= $true )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SV1128 @ SV323 )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(3757,plain,
! [SV679: $i,SV324: $i,SV1129: $i,SV947: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV947 @ SV1129 @ SV324 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV947 @ SV324 @ SV324 @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV324 ) @ SV679 ) @ SV1129 ) @ SV324 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3758,plain,
! [SV330: $i,SV952: $i,SV684: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV684 @ SV952 @ SV330 )
= $false )
| ( ( SV952
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV684 @ SV330 @ SV330 @ tc_nat ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV330 ) @ SV952 ) @ SV330 )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3631]) ).
thf(3759,plain,
! [SV331: $i,SV1131: $i,SV953: $i,SV685: $i] :
( ( ( c_Lim_OLIM @ SV685 @ SV953 @ SV1131 @ SV331 @ tc_Complex_Ocomplex )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ c_Complex_OIm @ SV685 @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ SV331 ) @ SV953 @ ( hAPP @ c_Complex_OIm @ SV1131 ) @ SV331 @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Ometric__space @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3632]) ).
thf(3760,plain,
! [SV957: $i,SV339: $i,SV691: $i] :
( ( ( SV691
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV339 ) @ SV957 ) )
= $true )
| ( ( SV691 = SV957 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV691 ) @ SV691 )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV339 ) @ SV957 ) @ SV957 ) )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(3761,plain,
! [SV1134: $i,SV958: $i,SV692: $i,SV340: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV692 ) @ SV958 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1134 ) @ SV958 ) )
= $false )
| ( ( SV692 = SV1134 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3634]) ).
thf(3762,plain,
! [SV959: $i,SV342: $i,SV693: $i] :
( ( ( SV693
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
= $true )
| ( ( SV959
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV342 ) @ SV693 ) @ SV959 )
= ( c_HOL_Ozero__class_Ozero @ SV342 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV342 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3635]) ).
thf(3763,plain,
! [SV1212: $i,SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV345 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
| ( SV961 = SV1212 )
| ( SV696 = SV1135 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(3764,plain,
! [SV347: $i,SV962: $i,SV698: $i] :
( ( ( SV698 = SV962 )
= $true )
| ( ( ( SV962
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
| ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV962 ) )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3637]) ).
thf(3765,plain,
! [SV701: $i,SV350: $i,SV965: $i] :
( ( ( SV965
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
= $true )
| ( ( SV701
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV350 ) @ SV701 ) @ SV965 )
= ( c_HOL_Ozero__class_Ozero @ SV350 ) )
= $false )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3640]) ).
thf(3766,plain,
! [SV1213: $i,SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV352 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
| ( SV967 = SV1213 )
| ( SV703 = SV1137 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3641]) ).
thf(3767,plain,
! [SV1138: $i,SV968: $i,SV705: $i,SV354: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV968 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV1138 ) )
= $false )
| ( ( ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( SV968 = SV1138 ) )
= $true )
| ( ( class_RealVector_Oreal__vector @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3768,plain,
! [SV708: $i,SV357: $i,SV970: $i] :
( ( ( SV970
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $true )
| ( ( SV708
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV357 ) @ SV708 ) @ SV970 )
= ( c_HOL_Ozero__class_Ozero @ SV357 ) )
= $false )
| ( ( class_RealVector_Oreal__vector @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(3769,plain,
! [SV1139: $i,SV971: $i,SV709: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV971 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV358 ) @ SV709 ) @ SV1139 ) )
= $false )
| ( ( SV971 = SV1139 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3644]) ).
thf(3770,plain,
! [SV974: $i,SV361: $i,SV712: $i] :
( ( ( SV712
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SV974 ) )
= $true )
| ( ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV361 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3646]) ).
thf(3771,plain,
! [SV713: $i,SV362: $i,SV975: $i] :
( ( ( SV975
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
= $true )
| ( ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV362 ) @ SV713 ) @ SV975 )
= ( c_HOL_Ozero__class_Ozero @ SV362 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3647]) ).
thf(3772,plain,
! [SV714: $i,SV363: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV363 ) @ SV714 )
= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
= $false )
| ( ( SV714
= ( c_HOL_Ozero__class_Ozero @ SV363 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV363 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3648]) ).
thf(3773,plain,
! [SV1140: $i,SV978: $i,SV717: $i,SV366: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SV978 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV1140 ) @ SV978 ) )
= $false )
| ( ( ( SV978
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
| ( SV717 = SV1140 ) )
= $true )
| ( ( class_RealVector_Oreal__vector @ SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(3774,plain,
! [SV980: $i,SV724: $i,SV373: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
!= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV980 ) )
= $true )
| ( ( SV724 = SV980 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV373 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3652]) ).
thf(3775,plain,
! [SV1142: $i,SV982: $i,SV726: $i,SV375: $i] :
( ( ( class_Int_Onumber__ring @ SV375 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV1142 ) )
| ( SV982 = SV1142 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3654]) ).
thf(3776,plain,
! [SV1214: $i,SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV377 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
| ( SV1143 = SV1214 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3777,plain,
! [SV1144: $i,SV985: $i,SV729: $i,SV379: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV985 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV729 ) @ SV1144 ) )
= $false )
| ( ( SV985 = SV1144 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3778,plain,
! [SV1215: $i,SV1145: $i,SV986: $i,SV731: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1145 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1215 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SV1145 )
= SV1215 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3658]) ).
thf(3779,plain,
! [SV1146: $i,SV987: $i,SV732: $i,SV382: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV382 ) @ SV987 ) @ SV1146 ) )
= SV987 )
= $false )
| ( ( SV732
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV382 ) @ SV1146 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3780,plain,
! [SV1147: $i,SV988: $i,SV733: $i,SV2: $i,SV383: $i] :
( ( ( class_RealVector_Ometric__space @ SV383 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
| ~ ( c_Lim_OLIM @ SV733 @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3781,plain,
! [SV1148: $i,SV989: $i,SV734: $i,SV3: $i,SV384: $i] :
( ( ( class_RealVector_Ometric__space @ SV384 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
| ~ ( c_Lim_OLIM @ SV734 @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3661]) ).
thf(3782,plain,
! [SV1216: $i,SV1149: $i,SV990: $i,SV735: $i,SV385: $i,SV4: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SV990 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV1149 ) @ SV990 ) @ SV1216 @ SV735 @ SV4 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV385 @ SV1149 @ SV1216 @ SV735 @ SV4 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3662]) ).
thf(3783,plain,
! [SV991: $i,SV5: $i,SV736: $i,SV1150: $i,SV386: $i] :
( ( ( c_Limits_OZfun @ SV386 @ SV1150 @ SV736 @ SV5 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV5 ) @ SV386 @ SV5 @ ( tc_fun @ SV5 @ SV5 ) @ SV736 ) @ SV991 @ SV736 @ SV5 @ SV5 ) @ SV1150 @ SV736 @ SV5 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(3784,plain,
! [SV992: $i,SV6: $i,SV737: $i,SV1151: $i,SV387: $i] :
( ( ( c_Limits_OZfun @ SV387 @ SV1151 @ SV737 @ SV6 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV6 ) @ SV387 @ SV6 @ ( tc_fun @ SV6 @ SV6 ) @ SV737 ) @ SV992 @ SV737 @ SV6 @ SV6 ) @ SV1151 @ SV737 @ SV6 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3664]) ).
thf(3785,plain,
! [SV1217: $i,SV1152: $i,SV993: $i,SV738: $i,SV7: $i,SV388: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV388 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV1217 ) @ SV993 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SV1152 @ SV1217 @ SV388 @ SV7 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3665]) ).
thf(3786,plain,
! [SV1218: $i,SV1156: $i,SV997: $i,SV742: $i,SV11: $i,SV392: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV392 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV1218 ) @ SV997 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SV1156 @ SV1218 @ SV392 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(3787,plain,
! [SV998: $i,SV12: $i,SV743: $i,SV1157: $i,SV393: $i] :
( ( ( c_Limits_OZfun @ SV393 @ SV1157 @ SV743 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV12 ) @ SV393 @ tc_RealDef_Oreal @ ( tc_fun @ SV12 @ SV12 ) @ SV743 ) @ SV998 @ SV743 @ SV12 @ SV12 ) @ SV1157 @ SV743 @ SV12 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3667]) ).
thf(3788,plain,
! [SV999: $i,SV13: $i,SV744: $i,SV1158: $i,SV394: $i] :
( ( ( c_Limits_OZfun @ SV394 @ SV1158 @ SV744 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV13 ) @ SV394 @ tc_RealDef_Oreal @ ( tc_fun @ SV13 @ SV13 ) @ SV744 ) @ SV999 @ SV744 @ SV13 @ SV13 ) @ SV1158 @ SV744 @ SV13 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(3789,plain,
! [SV1219: $i,SV1159: $i,SV1000: $i,SV745: $i,SV395: $i,SV14: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SV1000 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV1159 ) @ SV1000 ) @ SV1219 @ SV745 @ SV14 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV395 @ SV1159 @ SV1219 @ SV745 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3669]) ).
thf(3790,plain,
! [SV1004: $i,SV25: $i,SV750: $i,SV404: $i] :
( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
= $true )
| ( ( ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
| ~ ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3671]) ).
thf(3791,plain,
! [SV1163: $i,SV1005: $i,SV754: $i,SV31: $i,SV410: $i] :
( ( ( class_RealVector_Ometric__space @ SV410 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
| ~ ( c_Lim_OLIM @ SV754 @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(3792,plain,
! [SV1164: $i,SV1006: $i,SV755: $i,SV32: $i,SV411: $i] :
( ( ( class_RealVector_Ometric__space @ SV411 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
| ~ ( c_Lim_OLIM @ SV755 @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(3793,plain,
! [SV34: $i,SV1220: $i,SV1165: $i,SV1007: $i,SV756: $i,SV413: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV413 ) )
= $true )
| ( ( ( SV756 = SV1007 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3674]) ).
thf(3794,plain,
! [SV420: $i,SV41: $i,SV763: $i] :
( ( ( c_RealVector_Obounded__linear @ SV763 @ SV41 @ SV420 )
= $false )
| ( ( c_Lim_OisUCont @ SV763 @ SV41 @ SV420 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV420 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(3795,plain,
! [SV1012: $i,SV769: $i,SV48: $i,SV426: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV426 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV48 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(3796,plain,
! [SV1166: $i,SV1013: $i,SV771: $i,SV51: $i,SV429: $i] :
( ( ( class_RealVector_Ometric__space @ SV429 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
| ~ ( c_Lim_OLIM @ SV1013 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(3797,plain,
! [SV1167: $i,SV1014: $i,SV772: $i,SV52: $i,SV430: $i] :
( ( ( class_RealVector_Ometric__space @ SV430 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
| ~ ( c_Lim_OLIM @ SV1014 @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3682]) ).
thf(3798,plain,
! [SV56: $i,SV773: $i,SV1168: $i,SV1015: $i,SV432: $i] :
( ( ( c_Limits_Otendsto @ SV432 @ SV1015 @ SV1168 @ SV773 @ SV56 )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV432 @ SV56 @ SV56 @ SV773 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV56 ) @ SV1015 ) @ SV1168 @ SV773 @ SV56 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3683]) ).
thf(3799,plain,
! [SV1016: $i,SV774: $i,SV1169: $i,SV433: $i,SV57: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV433 @ SV57 @ SV57 @ SV1169 ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV57 ) @ SV774 ) @ SV1016 @ SV1169 @ SV57 )
= $false )
| ( ( c_Limits_Otendsto @ SV433 @ SV774 @ SV1016 @ SV1169 @ SV57 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(3800,plain,
! [SV1221: $i,SV58: $i,SV1170: $i,SV1017: $i,SV775: $i,SV434: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV434 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(3801,plain,
! [SV1031: $i,SV75: $i,SV789: $i,SV450: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV450 ) )
= $true )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true )
| ( ( class_HOL_Ozero @ SV75 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(3802,plain,
! [SV1033: $i,SV797: $i,SV460: $i,SV85: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SV1033 @ SV797 @ SV85 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV460 @ SV1033 @ SV797 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV85 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3687]) ).
thf(3803,plain,
! [SV1222: $i,SV1171: $i,SV1034: $i,SV798: $i,SV461: $i,SV86: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SV1034 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV1171 ) @ SV1222 @ SV1034 @ SV86 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV798 @ SV1171 @ SV1222 @ SV1034 @ SV86 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(3804,plain,
! [SV462: $i,SV87: $i,SV1035: $i,SV1172: $i,SV799: $i] :
( ( ( c_Limits_OZfun @ SV799 @ SV1172 @ SV1035 @ SV87 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV87 ) @ SV462 ) @ SV799 @ SV87 @ SV87 @ SV1035 ) @ SV1172 @ SV1035 @ SV87 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(3805,plain,
! [SV463: $i,SV88: $i,SV1036: $i,SV1173: $i,SV800: $i] :
( ( ( c_Limits_OZfun @ SV800 @ SV1173 @ SV1036 @ SV88 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV88 ) @ SV463 ) @ SV800 @ SV88 @ SV88 @ SV1036 ) @ SV1173 @ SV1036 @ SV88 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(3806,plain,
! [SV1223: $i,SV1175: $i,SV1038: $i,SV806: $i,SV96: $i,SV469: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV469 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1223 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SV1038 @ SV1175 @ SV1223 @ SV469 @ SV96 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3691]) ).
thf(3807,plain,
! [SV1176: $i,SV1040: $i,SV101: $i,SV811: $i,SV474: $i] :
( ( ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
= $false )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SV1176 @ SV474 @ SV101 )
| ( SV811 = SV1176 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3693]) ).
thf(3808,plain,
! [SV1177: $i,SV102: $i,SV1041: $i,SV812: $i,SV475: $i] :
( ( ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
= $false )
| ( ( ( SV812 = SV1041 )
| ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SV1177 @ SV1041 @ SV475 @ SV102 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3809,plain,
! [SV1180: $i,SV1044: $i,SV815: $i,SV107: $i,SV480: $i] :
( ( ( class_RealVector_Ometric__space @ SV480 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
| ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3695]) ).
thf(3810,plain,
! [SV1045: $i,SV108: $i,SV816: $i,SV481: $i] :
( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SV1045 @ SV108 @ SV481 )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV816 @ SV1045 @ SV108 @ SV481 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV481 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3696]) ).
thf(3811,plain,
! [SV1181: $i,SV1049: $i,SV820: $i,SV486: $i,SV114: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV114 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SV1181 @ SV820 @ SV114 )
| ~ ( c_Limits_Otendsto @ SV486 @ SV1049 @ SV1181 @ SV820 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3812,plain,
! [SV487: $i,SV1050: $i,SV116: $i,SV821: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1050 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SV1050 ) @ SV116 @ SV487 )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV821 @ SV1050 @ SV116 @ SV487 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV487 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3698]) ).
thf(3813,plain,
! [SV488: $i,SV117: $i,SV1051: $i,SV822: $i] :
( ( ( c_Lim_OisCont @ SV822 @ SV1051 @ SV117 @ SV488 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV1051 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SV1051 ) @ SV117 @ SV488 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV488 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(3814,plain,
! [SV490: $i,SV119: $i,SV1052: $i,SV824: $i] :
( ( ( c_Lim_OisCont @ SV824 @ SV1052 @ SV119 @ SV490 )
= $true )
| ( ( ~ ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV490 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3700]) ).
thf(3815,plain,
! [SV1182: $i,SV1053: $i,SV825: $i,SV120: $i,SV491: $i] :
( ( ( class_RealVector_Ometric__space @ SV491 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
| ~ ( c_Lim_OLIM @ SV1053 @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(3816,plain,
! [SV1183: $i,SV1054: $i,SV826: $i,SV121: $i,SV492: $i] :
( ( ( class_RealVector_Ometric__space @ SV492 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
| ~ ( c_Lim_OLIM @ SV1054 @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3817,plain,
! [SV1184: $i,SV1056: $i,SV831: $i,SV127: $i,SV497: $i] :
( ( ( class_RealVector_Ometric__space @ SV497 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV1184 ) @ SV497 @ SV127 )
| ~ ( c_Lim_OLIM @ SV831 @ SV1056 @ SV1184 @ SV497 @ SV127 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(3818,plain,
! [SV498: $i,SV129: $i,SV1057: $i,SV832: $i] :
( ( ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
= $true )
| ( ( ~ ( c_SEQ_OZseq @ SV1057 @ SV129 )
| ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV498 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3705]) ).
thf(3819,plain,
! [SV1238: $i,SV1224: $i,SV1185: $i,SV1058: $i,SV833: $i,SV499: $i,SV130: $i] :
( ( ( class_RealVector_Ometric__space @ SV130 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV499 )
| ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(3820,plain,
! [SV1186: $i,SV1059: $i,SV834: $i,SV500: $i,SV131: $i] :
( ( ( class_RealVector_Oreal__algebra__1 @ SV131 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV500 )
| ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(3821,plain,
! [SV1239: $i,SV1225: $i,SV1187: $i,SV1062: $i,SV838: $i,SV504: $i,SV135: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV504 )
| ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(3822,plain,
! [SV505: $i,SV136: $i,SV1063: $i,SV1188: $i,SV839: $i] :
( ( ( c_Limits_OZfun @ SV839 @ SV1188 @ SV1063 @ SV136 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV136 ) @ SV505 ) @ SV839 @ SV136 @ SV136 @ SV1063 ) @ SV1188 @ SV1063 @ SV136 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3823,plain,
! [SV506: $i,SV137: $i,SV1064: $i,SV1189: $i,SV840: $i] :
( ( ( c_Limits_OZfun @ SV840 @ SV1189 @ SV1064 @ SV137 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV137 ) @ SV506 ) @ SV840 @ SV137 @ SV137 @ SV1064 ) @ SV1189 @ SV1064 @ SV137 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(3824,plain,
! [SV1240: $i,SV1226: $i,SV1190: $i,SV1065: $i,SV842: $i,SV509: $i,SV140: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV140 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV509 )
| ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3714]) ).
thf(3825,plain,
! [SV1066: $i,SV513: $i,SV846: $i,SV145: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV846 @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV513 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3715]) ).
thf(3826,plain,
! [SV514: $i,SV146: $i,SV1067: $i,SV847: $i] :
( ( ( c_Lim_OLIM @ SV847 @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV514 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3716]) ).
thf(3827,plain,
! [SV529: $i,SV161: $i,SV1079: $i,SV862: $i] :
( ( ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV1079 @ SV161 )
| ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV529 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3717]) ).
thf(3828,plain,
! [SV863: $i,SV1192: $i,SV530: $i,SV162: $i,SV1080: $i] :
( ( ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV530 @ SV1080 @ SV1192 @ SV863 @ SV162 ) )
= $true )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV1080 ) @ SV1192 @ SV863 @ SV162 )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3718]) ).
thf(3829,plain,
! [SV542: $i,SV174: $i,SV1082: $i,SV865: $i] :
( ( ( c_Lim_OisCont @ SV865 @ SV1082 @ SV174 @ SV542 )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV542 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3719]) ).
thf(3830,plain,
! [SV1195: $i,SV1084: $i,SV867: $i,SV179: $i,SV546: $i] :
( ( ( class_RealVector_Ometric__space @ SV546 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV1195 ) @ SV546 @ tc_RealDef_Oreal )
| ~ ( c_Lim_OLIM @ SV867 @ SV1084 @ SV1195 @ SV546 @ SV179 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3831,plain,
! [SV1228: $i,SV1196: $i,SV185: $i,SV1087: $i,SV870: $i,SV552: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV552 ) )
= $true )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
| ~ ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3722]) ).
thf(3832,plain,
! [SV1092: $i,SV206: $i,SV875: $i,SV572: $i] :
( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SV1092 @ SV206 @ SV572 )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV875 @ SV1092 @ SV206 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3724]) ).
thf(3833,plain,
! [SV1197: $i,SV1093: $i,SV207: $i,SV876: $i,SV573: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV573 )
= $false )
| ( ( ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SV1197 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SV1197 ) ) )
| ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3834,plain,
! [SV574: $i,SV208: $i,SV1094: $i,SV877: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV1094 @ SV208 )
| ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV574 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(3835,plain,
! [SV209: $i,SV1198: $i,SV1095: $i,SV878: $i,SV575: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV575 )
= $false )
| ( ( ( c_Lim_OLIM @ SV878 @ SV1095 @ SV1198 @ SV575 @ SV209 )
| ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV1198 @ SV575 @ SV209 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3727]) ).
thf(3836,plain,
! [SV1199: $i,SV210: $i,SV1096: $i,SV879: $i,SV576: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV576 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SV1199 @ SV576 @ SV210 )
| ~ ( c_Lim_OLIM @ SV879 @ SV1096 @ SV1199 @ SV576 @ SV210 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3728]) ).
thf(3837,plain,
! [SV577: $i,SV211: $i,SV1097: $i,SV880: $i] :
( ( ( c_Lim_OLIM @ SV880 @ SV1097 @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV1097 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV577 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(3838,plain,
! [SV578: $i,SV1098: $i,SV212: $i,SV881: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV1098 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV881 @ SV1098 @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV578 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(3839,plain,
! [SV221: $i,SV890: $i,SV1200: $i,SV1101: $i,SV587: $i] :
( ( ( c_Limits_Otendsto @ SV587 @ SV1101 @ SV1200 @ SV890 @ SV221 )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV587 @ SV221 @ tc_RealDef_Oreal @ SV890 ) @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV221 ) @ SV1101 ) @ SV1200 @ SV890 @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3733]) ).
thf(3840,plain,
! [SV1229: $i,SV1201: $i,SV1108: $i,SV902: $i,SV251: $i,SV616: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV616 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1229 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SV1108 @ SV1201 @ SV1229 @ SV616 @ SV251 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3737]) ).
thf(3841,plain,
! [SV1202: $i,SV255: $i,SV1110: $i,SV906: $i,SV620: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV620 )
= $false )
| ( ( ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
| ~ ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3738]) ).
thf(3842,plain,
! [SV631: $i,SV271: $i,SV1111: $i,SV911: $i] :
( ( ( c_Lim_OLIM @ SV911 @ SV1111 @ ( hAPP @ SV911 @ SV1111 ) @ SV271 @ SV631 )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV631 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(3843,plain,
! [SV636: $i,SV276: $i,SV1112: $i,SV914: $i] :
( ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
= $true )
| ( ( ~ ( c_SEQ_OCauchy @ SV1112 @ SV276 )
| ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV636 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(3844,plain,
! [SV637: $i,SV277: $i,SV1113: $i,SV915: $i] :
( ( ( c_Lim_OisCont @ SV915 @ SV1113 @ SV277 @ SV637 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV915 @ SV1113 @ ( hAPP @ SV915 @ SV1113 ) @ SV277 @ SV637 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV637 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3741]) ).
thf(3845,plain,
! [SV638: $i,SV278: $i,SV1114: $i,SV916: $i] :
( ( ( c_Lim_OLIM @ SV916 @ SV1114 @ ( hAPP @ SV916 @ SV1114 ) @ SV278 @ SV638 )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV916 @ SV1114 @ SV278 @ SV638 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV638 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(3846,plain,
! [SV1230: $i,SV1203: $i,SV1115: $i,SV919: $i,SV641: $i,SV281: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV1203 ) @ SV1230 @ SV1115 @ SV281 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV919 @ SV1203 @ SV1230 @ SV1115 @ SV281 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(3847,plain,
! [SV285: $i,SV921: $i,SV644: $i] :
( ( ( c_Series_Osums @ SV644 @ SV921 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV285 ) @ SV644 @ tc_RealDef_Oreal @ SV285 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV285 ) @ SV921 ) @ SV285 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV285 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3744]) ).
thf(3848,plain,
! [SV645: $i,SV286: $i,SV1116: $i,SV922: $i] :
( ( ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
= $true )
| ( ( ~ ( c_Series_Osummable @ SV1116 @ SV286 )
| ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV645 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(3849,plain,
! [SV1117: $i,SV287: $i,SV923: $i,SV646: $i] :
( ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SV1117 @ SV287 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV923 @ SV1117 @ SV287 @ SV646 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV646 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(3850,plain,
! [SV1241: $i,SV1232: $i,SV1205: $i,SV1119: $i,SV932: $i,SV657: $i,SV300: $i] :
( ( ( class_RealVector_Ometric__space @ SV300 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV657 )
| ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3747]) ).
thf(3851,plain,
! [SV1206: $i,SV312: $i,SV1123: $i,SV938: $i,SV668: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV668 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
| ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3750]) ).
thf(3852,plain,
! [SV1233: $i,SV1207: $i,SV313: $i,SV1124: $i,SV939: $i,SV669: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV669 ) )
= $true )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3751]) ).
thf(3853,plain,
! [SV315: $i,SV941: $i,SV671: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV671 @ SV941 @ tc_RealDef_Oreal )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV315 ) @ SV671 @ tc_RealDef_Oreal @ SV315 @ tc_nat ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV315 ) @ SV941 ) @ SV315 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV315 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3854,plain,
! [SV1234: $i,SV320: $i,SV1208: $i,SV1125: $i,SV943: $i,SV675: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV675 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3753]) ).
thf(3855,plain,
! [SV676: $i,SV321: $i,SV944: $i,SV1126: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV1126 @ SV944 @ SV321 )
= $false )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV1126 @ SV676 @ SV321 ) )
= $true )
| ( ( SV676 = SV944 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(3856,plain,
! [SV678: $i,SV323: $i,SV1128: $i,SV946: $i] :
( ( ( c_Deriv_Odifferentiable @ SV946 @ SV1128 @ SV323 )
= $false )
| ( ( ~ ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SV1128 ) @ SV323 ) )
= $true )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SV1128 @ SV323 )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3857,plain,
! [SV1212: $i,SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ( class_Int_Onumber__ring @ SV345 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
| ( SV961 = SV1212 )
| ( SV696 = SV1135 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3763]) ).
thf(3858,plain,
! [SV698: $i,SV347: $i,SV962: $i] :
( ( ( SV962
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
= $true )
| ( ( SV698
= ( c_HOL_Ozero__class_Ozero @ SV347 ) )
= $true )
| ( ( SV698 = SV962 )
= $true )
| ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV698 )
= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV347 ) @ SV962 ) )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3764]) ).
thf(3859,plain,
! [SV1213: $i,SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ( class_Int_Onumber__ring @ SV352 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
| ( SV967 = SV1213 )
| ( SV703 = SV1137 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3766]) ).
thf(3860,plain,
! [SV354: $i,SV1138: $i,SV968: $i,SV705: $i] :
( ( ( SV705
= ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= $true )
| ( ( SV968 = SV1138 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV968 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV354 ) @ SV705 ) @ SV1138 ) )
= $false )
| ( ( class_RealVector_Oreal__vector @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3767]) ).
thf(3861,plain,
! [SV974: $i,SV361: $i,SV712: $i] :
( ( ( SV712
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV712 ) @ SV974 ) )
= $false )
| ( ( SV974
= ( c_HOL_Ozero__class_Ozero @ SV361 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV361 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3862,plain,
! [SV1140: $i,SV717: $i,SV366: $i,SV978: $i] :
( ( ( SV978
= ( c_HOL_Ozero__class_Ozero @ SV366 ) )
= $true )
| ( ( SV717 = SV1140 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV717 ) @ SV978 )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV366 ) @ SV1140 ) @ SV978 ) )
= $false )
| ( ( class_RealVector_Oreal__vector @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3863,plain,
! [SV980: $i,SV724: $i,SV373: $i] :
( ( ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV724 )
= ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV373 ) @ SV980 ) )
= $false )
| ( ( SV724 = SV980 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3864,plain,
! [SV1142: $i,SV982: $i,SV726: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV1142 ) )
= $true )
| ( ( SV982 = SV1142 )
= $true )
| ( ( class_Int_Onumber__ring @ SV375 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3775]) ).
thf(3865,plain,
! [SV1214: $i,SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
| ( SV1143 = SV1214 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3866,plain,
! [SV1215: $i,SV1145: $i,SV986: $i,SV731: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1145 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV986 ) @ SV1215 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV731 ) @ SV1145 )
= SV1215 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3867,plain,
! [SV1147: $i,SV988: $i,SV383: $i,SV733: $i,SV2: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV733 @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV383 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3780]) ).
thf(3868,plain,
! [SV1148: $i,SV989: $i,SV384: $i,SV734: $i,SV3: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV734 @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV384 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(3869,plain,
! [SV990: $i,SV4: $i,SV735: $i,SV1216: $i,SV1149: $i,SV385: $i] :
( ( ( c_Limits_Otendsto @ SV385 @ SV1149 @ SV1216 @ SV735 @ SV4 )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV385 @ SV4 @ ( tc_fun @ SV4 @ SV4 ) @ SV735 ) @ SV990 @ SV735 @ SV4 @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV4 ) @ SV1149 ) @ SV990 ) @ SV1216 @ SV735 @ SV4 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(3870,plain,
! [SV1217: $i,SV1152: $i,SV993: $i,SV738: $i,SV7: $i,SV388: $i] :
( ( ( class_RealVector_Ometric__space @ SV388 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV1217 ) @ SV993 ) @ SV388 @ SV7 )
| ~ ( c_Lim_OLIM @ SV738 @ SV1152 @ SV1217 @ SV388 @ SV7 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3785]) ).
thf(3871,plain,
! [SV1218: $i,SV1156: $i,SV997: $i,SV742: $i,SV11: $i,SV392: $i] :
( ( ( class_RealVector_Ometric__space @ SV392 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV1218 ) @ SV997 ) @ SV392 @ SV11 )
| ~ ( c_Lim_OLIM @ SV742 @ SV1156 @ SV1218 @ SV392 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3872,plain,
! [SV1000: $i,SV14: $i,SV745: $i,SV1219: $i,SV1159: $i,SV395: $i] :
( ( ( c_Limits_Otendsto @ SV395 @ SV1159 @ SV1219 @ SV745 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV395 @ tc_RealDef_Oreal @ ( tc_fun @ SV14 @ SV14 ) @ SV745 ) @ SV1000 @ SV745 @ SV14 @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV14 ) @ SV1159 ) @ SV1000 ) @ SV1219 @ SV745 @ SV14 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(3873,plain,
! [SV25: $i,SV404: $i,SV1004: $i,SV750: $i] :
( ( ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 ) )
= $true )
| ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3790]) ).
thf(3874,plain,
! [SV1163: $i,SV1005: $i,SV410: $i,SV754: $i,SV31: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV754 @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV410 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(3875,plain,
! [SV1164: $i,SV1006: $i,SV411: $i,SV755: $i,SV32: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV755 @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV411 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(3876,plain,
! [SV34: $i,SV1220: $i,SV1165: $i,SV1007: $i,SV756: $i,SV413: $i] :
( ( ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
= $false )
| ( ( ( SV756 = SV1007 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3877,plain,
! [SV1012: $i,SV769: $i,SV48: $i,SV426: $i] :
( ( ( class_RealVector_Ometric__space @ SV426 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
| ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV48 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(3878,plain,
! [SV1166: $i,SV429: $i,SV1013: $i,SV771: $i,SV51: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1013 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV429 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(3879,plain,
! [SV1167: $i,SV430: $i,SV1014: $i,SV772: $i,SV52: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1014 @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV430 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3797]) ).
thf(3880,plain,
! [SV1221: $i,SV58: $i,SV1170: $i,SV1017: $i,SV775: $i,SV434: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV434 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV775 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(3881,plain,
! [SV1031: $i,SV75: $i,SV789: $i,SV450: $i] :
( ( ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
= $false )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true )
| ( ( class_HOL_Ozero @ SV75 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3882,plain,
! [SV85: $i,SV797: $i,SV1033: $i,SV460: $i] :
( ( ( c_Limits_OZfun @ SV460 @ SV1033 @ SV797 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV85 ) @ SV460 @ tc_RealDef_Oreal @ SV85 @ SV797 ) @ SV1033 @ SV797 @ SV85 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV85 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(3883,plain,
! [SV461: $i,SV86: $i,SV1034: $i,SV1222: $i,SV1171: $i,SV798: $i] :
( ( ( c_Limits_Otendsto @ SV798 @ SV1171 @ SV1222 @ SV1034 @ SV86 )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV798 @ SV86 @ SV86 @ SV1034 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV86 ) @ SV461 ) @ SV1171 ) @ SV1222 @ SV1034 @ SV86 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3803]) ).
thf(3884,plain,
! [SV1223: $i,SV1175: $i,SV1038: $i,SV806: $i,SV96: $i,SV469: $i] :
( ( ( class_RealVector_Ometric__space @ SV469 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1223 ) @ SV469 @ SV96 )
| ~ ( c_Lim_OLIM @ SV1038 @ SV1175 @ SV1223 @ SV469 @ SV96 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(3885,plain,
! [SV1176: $i,SV1040: $i,SV474: $i,SV101: $i,SV811: $i] :
( ( ( ~ ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SV1176 @ SV474 @ SV101 ) )
= $true )
| ( ( SV811 = SV1176 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(3886,plain,
! [SV1177: $i,SV475: $i,SV102: $i,SV1041: $i,SV812: $i] :
( ( ( SV812 = SV1041 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SV1177 @ SV1041 @ SV475 @ SV102 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3808]) ).
thf(3887,plain,
! [SV1180: $i,SV1044: $i,SV480: $i,SV815: $i,SV107: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
= $true )
| ( ( ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
| ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV480 )
= $false )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3809]) ).
thf(3888,plain,
! [SV481: $i,SV108: $i,SV1045: $i,SV816: $i] :
( ( ( c_Lim_OisCont @ SV816 @ SV1045 @ SV108 @ SV481 )
= $false )
| ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV481 ) @ SV816 @ SV481 @ SV481 @ SV108 ) @ SV1045 @ SV108 @ SV481 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV481 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(3889,plain,
! [SV1181: $i,SV1049: $i,SV820: $i,SV486: $i,SV114: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SV1181 @ SV820 @ SV114 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV486 @ SV1049 @ SV1181 @ SV820 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV114 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3811]) ).
thf(3890,plain,
! [SV487: $i,SV116: $i,SV1050: $i,SV821: $i] :
( ( ( c_Lim_OisCont @ SV821 @ SV1050 @ SV116 @ SV487 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV821 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1050 ) @ SV116 @ SV487 @ SV116 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( hAPP @ SV821 @ SV1050 ) @ SV116 @ SV487 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV487 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3891,plain,
! [SV488: $i,SV1051: $i,SV117: $i,SV822: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV822 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV1051 ) @ SV117 @ SV488 @ SV117 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( hAPP @ SV822 @ SV1051 ) @ SV117 @ SV488 )
= $false )
| ( ( c_Lim_OisCont @ SV822 @ SV1051 @ SV117 @ SV488 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV488 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3813]) ).
thf(3892,plain,
! [SV1052: $i,SV490: $i,SV119: $i,SV824: $i] :
( ( ( c_Lim_OisUCont @ SV824 @ SV119 @ SV490 )
= $false )
| ( ( c_Lim_OisCont @ SV824 @ SV1052 @ SV119 @ SV490 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV490 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(3893,plain,
! [SV1182: $i,SV491: $i,SV1053: $i,SV825: $i,SV120: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1053 @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV491 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(3894,plain,
! [SV1183: $i,SV492: $i,SV1054: $i,SV826: $i,SV121: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1054 @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV492 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3816]) ).
thf(3895,plain,
! [SV1184: $i,SV1056: $i,SV497: $i,SV831: $i,SV127: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV1184 ) @ SV497 @ SV127 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV831 @ SV1056 @ SV1184 @ SV497 @ SV127 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV497 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(3896,plain,
! [SV498: $i,SV832: $i,SV129: $i,SV1057: $i] :
( ( ( ~ ( c_SEQ_OZseq @ SV1057 @ SV129 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV498 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(3897,plain,
! [SV1238: $i,SV1224: $i,SV130: $i,SV1185: $i,SV1058: $i,SV833: $i,SV499: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV499 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(3898,plain,
! [SV1186: $i,SV1059: $i,SV834: $i,SV131: $i,SV500: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV500 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV131 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3820]) ).
thf(3899,plain,
! [SV1239: $i,SV1225: $i,SV135: $i,SV1187: $i,SV1062: $i,SV838: $i,SV504: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV504 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(3900,plain,
! [SV1240: $i,SV1226: $i,SV1190: $i,SV140: $i,SV1065: $i,SV842: $i,SV509: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV509 ) )
= $true )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(3901,plain,
! [SV513: $i,SV145: $i,SV1066: $i,SV846: $i] :
( ( ( c_Lim_OLIM @ SV846 @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ SV145 ) @ SV513 @ SV145 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV145 ) @ SV846 @ SV145 @ tc_RealDef_Oreal @ SV513 ) @ SV1066 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV513 @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Ometric__space @ SV513 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(3902,plain,
! [SV1067: $i,SV514: $i,SV847: $i,SV146: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV146 ) @ SV847 @ SV146 @ tc_RealDef_Oreal @ SV514 ) @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV514 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Lim_OLIM @ SV847 @ SV1067 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV514 @ SV146 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV514 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(3903,plain,
! [SV529: $i,SV862: $i,SV161: $i,SV1079: $i] :
( ( ( ~ ( c_Series_Osummable @ SV1079 @ SV161 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true )
| ( ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV529 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(3904,plain,
! [SV162: $i,SV863: $i,SV1192: $i,SV1080: $i,SV530: $i] :
( ( ( c_Limits_Otendsto @ SV530 @ SV1080 @ SV1192 @ SV863 @ SV162 )
= $false )
| ( ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV162 ) )
= $true )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV530 @ SV162 @ SV162 @ SV863 ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV162 ) @ SV1080 ) @ SV1192 @ SV863 @ SV162 )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(3905,plain,
! [SV1082: $i,SV542: $i,SV174: $i,SV865: $i] :
( ( ( c_RealVector_Obounded__linear @ SV865 @ SV174 @ SV542 )
= $false )
| ( ( c_Lim_OisCont @ SV865 @ SV1082 @ SV174 @ SV542 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV542 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3829]) ).
thf(3906,plain,
! [SV1195: $i,SV1084: $i,SV546: $i,SV867: $i,SV179: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV1195 ) @ SV546 @ tc_RealDef_Oreal )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV867 @ SV1084 @ SV1195 @ SV546 @ SV179 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV546 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3830]) ).
thf(3907,plain,
! [SV1228: $i,SV1196: $i,SV185: $i,SV1087: $i,SV870: $i,SV552: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV552 )
= $false )
| ( ( ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
| ~ ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(3908,plain,
! [SV572: $i,SV206: $i,SV1092: $i,SV875: $i] :
( ( ( c_Lim_OisCont @ SV875 @ SV1092 @ SV206 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV572 ) @ SV875 @ tc_RealDef_Oreal @ SV572 @ SV206 ) @ SV1092 @ SV206 @ SV572 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV572 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(3909,plain,
! [SV573: $i,SV1197: $i,SV1093: $i,SV207: $i,SV876: $i] :
( ( ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SV1197 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SV1197 ) ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV573 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3833]) ).
thf(3910,plain,
! [SV574: $i,SV877: $i,SV208: $i,SV1094: $i] :
( ( ( ~ ( c_SEQ_OCauchy @ SV1094 @ SV208 ) )
= $true )
| ( ( ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV574 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3834]) ).
thf(3911,plain,
! [SV209: $i,SV575: $i,SV1198: $i,SV1095: $i,SV878: $i] :
( ( ( c_Lim_OLIM @ SV878 @ SV1095 @ SV1198 @ SV575 @ SV209 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV1198 @ SV575 @ SV209 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV575 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3835]) ).
thf(3912,plain,
! [SV1199: $i,SV210: $i,SV1096: $i,SV576: $i,SV879: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SV1199 @ SV576 @ SV210 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV879 @ SV1096 @ SV1199 @ SV576 @ SV210 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV576 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(3913,plain,
! [SV577: $i,SV1097: $i,SV211: $i,SV880: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV880 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV1097 ) @ SV211 @ SV577 @ SV211 ) @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
= $false )
| ( ( c_Lim_OLIM @ SV880 @ SV1097 @ ( hAPP @ SV880 @ SV1097 ) @ SV211 @ SV577 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV577 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(3914,plain,
! [SV578: $i,SV212: $i,SV1098: $i,SV881: $i] :
( ( ( c_Lim_OLIM @ SV881 @ SV1098 @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV881 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV212 ) @ SV1098 ) @ SV212 @ SV578 @ SV212 ) @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ ( hAPP @ SV881 @ SV1098 ) @ SV212 @ SV578 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV578 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(3915,plain,
! [SV1229: $i,SV1201: $i,SV1108: $i,SV902: $i,SV251: $i,SV616: $i] :
( ( ( class_RealVector_Ometric__space @ SV616 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1229 ) @ SV616 @ SV251 )
| ~ ( c_Lim_OLIM @ SV1108 @ SV1201 @ SV1229 @ SV616 @ SV251 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3840]) ).
thf(3916,plain,
! [SV1202: $i,SV620: $i,SV255: $i,SV1110: $i,SV906: $i] :
( ( ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
= $true )
| ( ( ~ ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
| ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV620 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3841]) ).
thf(3917,plain,
! [SV1111: $i,SV631: $i,SV271: $i,SV911: $i] :
( ( ( c_RealVector_Obounded__linear @ SV911 @ SV271 @ SV631 )
= $false )
| ( ( c_Lim_OLIM @ SV911 @ SV1111 @ ( hAPP @ SV911 @ SV1111 ) @ SV271 @ SV631 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV631 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3842]) ).
thf(3918,plain,
! [SV636: $i,SV914: $i,SV276: $i,SV1112: $i] :
( ( ( ~ ( c_SEQ_OCauchy @ SV1112 @ SV276 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV636 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3843]) ).
thf(3919,plain,
! [SV637: $i,SV277: $i,SV1113: $i,SV915: $i] :
( ( ( c_Lim_OLIM @ SV915 @ SV1113 @ ( hAPP @ SV915 @ SV1113 ) @ SV277 @ SV637 )
= $false )
| ( ( c_Lim_OisCont @ SV915 @ SV1113 @ SV277 @ SV637 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV637 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(3920,plain,
! [SV638: $i,SV278: $i,SV1114: $i,SV916: $i] :
( ( ( c_Lim_OisCont @ SV916 @ SV1114 @ SV278 @ SV638 )
= $false )
| ( ( c_Lim_OLIM @ SV916 @ SV1114 @ ( hAPP @ SV916 @ SV1114 ) @ SV278 @ SV638 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV638 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(3921,plain,
! [SV641: $i,SV281: $i,SV1115: $i,SV1230: $i,SV1203: $i,SV919: $i] :
( ( ( c_Limits_Otendsto @ SV919 @ SV1203 @ SV1230 @ SV1115 @ SV281 )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV919 @ SV281 @ SV281 @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV281 ) @ SV641 ) @ SV1203 ) @ SV1230 @ SV1115 @ SV281 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3846]) ).
thf(3922,plain,
! [SV645: $i,SV922: $i,SV286: $i,SV1116: $i] :
( ( ( ~ ( c_Series_Osummable @ SV1116 @ SV286 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true )
| ( ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV645 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(3923,plain,
! [SV646: $i,SV287: $i,SV1117: $i,SV923: $i] :
( ( ( c_Lim_OisCont @ SV923 @ SV1117 @ SV287 @ SV646 )
= $false )
| ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV646 ) @ SV923 @ SV646 @ tc_RealDef_Oreal @ SV287 ) @ SV1117 @ SV287 @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV646 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(3924,plain,
! [SV1241: $i,SV1232: $i,SV300: $i,SV1205: $i,SV1119: $i,SV932: $i,SV657: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV657 ) )
= $true )
| ( ( ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(3925,plain,
! [SV1206: $i,SV668: $i,SV312: $i,SV1123: $i,SV938: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
| ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV668 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(3926,plain,
! [SV1233: $i,SV1207: $i,SV313: $i,SV1124: $i,SV939: $i,SV669: $i] :
( ( ( class_RealVector_Ometric__space @ SV669 )
= $false )
| ( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
| ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(3927,plain,
! [SV1234: $i,SV320: $i,SV1208: $i,SV1125: $i,SV943: $i,SV675: $i] :
( ( ( class_RealVector_Ometric__space @ SV675 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV943 )
| ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(3928,plain,
! [SV944: $i,SV321: $i,SV676: $i,SV1126: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV1126 @ SV676 @ SV321 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV1126 @ SV944 @ SV321 )
= $false )
| ( ( SV676 = SV944 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3855]) ).
thf(3929,plain,
! [SV323: $i,SV1128: $i,SV946: $i,SV678: $i] :
( ( ( c_Deriv_Odifferentiable @ SV678 @ ( hAPP @ SV946 @ SV1128 ) @ SV323 )
= $false )
| ( ( c_Deriv_Odifferentiable @ SV946 @ SV1128 @ SV323 )
= $false )
| ( ( c_Deriv_Odifferentiable @ ( c_COMBB @ SV678 @ SV946 @ SV323 @ SV323 @ SV323 ) @ SV1128 @ SV323 )
= $true )
| ( ( class_RealVector_Oreal__normed__field @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(3930,plain,
! [SV1212: $i,SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
= $true )
| ( ( ( SV961 = SV1212 )
| ( SV696 = SV1135 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV345 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3857]) ).
thf(3931,plain,
! [SV1213: $i,SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
= $true )
| ( ( ( SV967 = SV1213 )
| ( SV703 = SV1137 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV352 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(3932,plain,
! [SV1142: $i,SV982: $i,SV726: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV982 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV375 ) @ SV726 ) @ SV1142 ) )
= $false )
| ( ( SV982 = SV1142 )
= $true )
| ( ( class_Int_Onumber__ring @ SV375 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(3933,plain,
! [SV1214: $i,SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
= $true )
| ( ( ( SV1143 = SV1214 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3865]) ).
thf(3934,plain,
! [SV988: $i,SV383: $i,SV2: $i,SV1147: $i,SV733: $i] :
( ( ( c_Lim_OLIM @ SV733 @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV2 ) @ SV733 @ SV2 @ ( tc_fun @ SV2 @ SV2 ) @ SV383 ) @ SV988 @ SV383 @ SV2 @ SV2 ) @ SV1147 @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV383 @ SV2 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV383 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(3935,plain,
! [SV989: $i,SV384: $i,SV3: $i,SV1148: $i,SV734: $i] :
( ( ( c_Lim_OLIM @ SV734 @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV3 ) @ SV734 @ SV3 @ ( tc_fun @ SV3 @ SV3 ) @ SV384 ) @ SV989 @ SV384 @ SV3 @ SV3 ) @ SV1148 @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV384 @ SV3 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV384 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3868]) ).
thf(3936,plain,
! [SV1217: $i,SV1152: $i,SV993: $i,SV388: $i,SV738: $i,SV7: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV1217 ) @ SV993 ) @ SV388 @ SV7 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV738 @ SV1152 @ SV1217 @ SV388 @ SV7 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV388 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3870]) ).
thf(3937,plain,
! [SV1218: $i,SV1156: $i,SV997: $i,SV392: $i,SV742: $i,SV11: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV1218 ) @ SV997 ) @ SV392 @ SV11 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV742 @ SV1156 @ SV1218 @ SV392 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV392 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3871]) ).
thf(3938,plain,
! [SV404: $i,SV25: $i,SV1004: $i,SV750: $i] :
( ( ( c_Lim_OisCont @ SV750 @ SV1004 @ SV25 @ SV404 )
= $false )
| ( ( ( hAPP @ SV750 @ SV1004 )
= ( c_HOL_Ozero__class_Ozero @ SV404 ) )
= $true )
| ( ( c_Lim_OisCont @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV404 ) @ SV750 @ SV404 @ SV404 @ SV25 ) @ SV1004 @ SV25 @ SV404 )
= $true )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV404 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(3939,plain,
! [SV1005: $i,SV31: $i,SV410: $i,SV1163: $i,SV754: $i] :
( ( ( c_Lim_OLIM @ SV754 @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV410 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV31 ) @ SV754 @ tc_RealDef_Oreal @ ( tc_fun @ SV31 @ SV31 ) @ SV410 ) @ SV1005 @ SV410 @ SV31 @ SV31 ) @ SV1163 @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV410 @ SV31 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV410 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3874]) ).
thf(3940,plain,
! [SV1006: $i,SV32: $i,SV411: $i,SV1164: $i,SV755: $i] :
( ( ( c_Lim_OLIM @ SV755 @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV411 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV32 ) @ SV755 @ tc_RealDef_Oreal @ ( tc_fun @ SV32 @ SV32 ) @ SV411 ) @ SV1006 @ SV411 @ SV32 @ SV32 ) @ SV1164 @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV411 @ SV32 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV411 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(3941,plain,
! [SV34: $i,SV413: $i,SV1220: $i,SV1165: $i,SV1007: $i,SV756: $i] :
( ( ( SV756 = SV1007 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
| ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3876]) ).
thf(3942,plain,
! [SV1012: $i,SV426: $i,SV769: $i,SV48: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV426 )
= $false )
| ( ( class_RealVector_Oreal__algebra__1 @ SV48 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(3943,plain,
! [SV771: $i,SV429: $i,SV51: $i,SV1166: $i,SV1013: $i] :
( ( ( c_Lim_OLIM @ SV1013 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV51 ) @ SV771 ) @ SV1013 @ SV51 @ SV51 @ SV429 ) @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV429 @ SV51 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV429 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(3944,plain,
! [SV772: $i,SV430: $i,SV52: $i,SV1167: $i,SV1014: $i] :
( ( ( c_Lim_OLIM @ SV1014 @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV52 ) @ SV772 ) @ SV1014 @ SV52 @ SV52 @ SV430 ) @ SV1167 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV430 @ SV52 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV430 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(3945,plain,
! [SV1221: $i,SV58: $i,SV434: $i,SV1170: $i,SV1017: $i,SV775: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV775 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV434 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(3946,plain,
! [SV1031: $i,SV450: $i,SV75: $i,SV789: $i] :
( ( ( ~ ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 ) )
= $true )
| ( ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
= $false )
| ( ( class_HOL_Ozero @ SV75 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(3947,plain,
! [SV1223: $i,SV1175: $i,SV469: $i,SV1038: $i,SV806: $i,SV96: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1223 ) @ SV469 @ SV96 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1038 @ SV1175 @ SV1223 @ SV469 @ SV96 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV469 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3884]) ).
thf(3948,plain,
! [SV1176: $i,SV1040: $i,SV474: $i,SV101: $i,SV811: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBK @ SV811 @ SV101 @ SV474 ) @ SV1040 @ SV1176 @ SV474 @ SV101 )
= $false )
| ( ( SV811 = SV1176 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV474 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(3949,plain,
! [SV1041: $i,SV1177: $i,SV475: $i,SV102: $i,SV812: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBK @ SV812 @ SV102 @ SV475 ) @ SV1177 @ SV1041 @ SV475 @ SV102 )
= $false )
| ( ( SV812 = SV1041 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV475 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(3950,plain,
! [SV480: $i,SV1044: $i,SV815: $i,SV107: $i,SV1180: $i] :
( ( ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV480 )
= $false )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3887]) ).
thf(3951,plain,
! [SV114: $i,SV820: $i,SV1181: $i,SV1049: $i,SV486: $i] :
( ( ( c_Limits_Otendsto @ SV486 @ SV1049 @ SV1181 @ SV820 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV114 ) @ SV486 @ tc_RealDef_Oreal @ SV114 @ SV820 ) @ ( hAPP @ ( c_RealVector_Oof__real @ SV114 ) @ SV1049 ) @ SV1181 @ SV820 @ SV114 )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV114 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3889]) ).
thf(3952,plain,
! [SV825: $i,SV491: $i,SV120: $i,SV1182: $i,SV1053: $i] :
( ( ( c_Lim_OLIM @ SV1053 @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV120 ) @ SV825 ) @ SV1053 @ SV120 @ SV120 @ SV491 ) @ SV1182 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV491 @ SV120 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV491 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3893]) ).
thf(3953,plain,
! [SV826: $i,SV492: $i,SV121: $i,SV1183: $i,SV1054: $i] :
( ( ( c_Lim_OLIM @ SV1054 @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV121 ) @ SV826 ) @ SV1054 @ SV121 @ SV121 @ SV492 ) @ SV1183 @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV492 @ SV121 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV492 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3894]) ).
thf(3954,plain,
! [SV127: $i,SV497: $i,SV1184: $i,SV1056: $i,SV831: $i] :
( ( ( c_Lim_OLIM @ SV831 @ SV1056 @ SV1184 @ SV497 @ SV127 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV831 @ SV127 @ SV127 @ SV497 ) @ SV1056 @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV127 ) @ SV1184 ) @ SV497 @ SV127 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV497 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3895]) ).
thf(3955,plain,
! [SV498: $i,SV832: $i,SV129: $i,SV1057: $i] :
( ( ( c_SEQ_OZseq @ SV1057 @ SV129 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 ) )
= $true )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV498 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3896]) ).
thf(3956,plain,
! [SV1238: $i,SV1224: $i,SV130: $i,SV1185: $i,SV1058: $i,SV833: $i,SV499: $i] :
( ( ( class_RealVector_Ometric__space @ SV499 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV833 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3897]) ).
thf(3957,plain,
! [SV1186: $i,SV1059: $i,SV834: $i,SV131: $i,SV500: $i] :
( ( ( class_RealVector_Ometric__space @ SV500 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
| ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Oreal__algebra__1 @ SV131 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3898]) ).
thf(3958,plain,
! [SV1239: $i,SV1225: $i,SV135: $i,SV1187: $i,SV1062: $i,SV838: $i,SV504: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV504 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV838 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(3959,plain,
! [SV1240: $i,SV1226: $i,SV1190: $i,SV140: $i,SV1065: $i,SV842: $i,SV509: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV509 )
= $false )
| ( ( ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
| ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3900]) ).
thf(3960,plain,
! [SV529: $i,SV862: $i,SV161: $i,SV1079: $i] :
( ( ( c_Series_Osummable @ SV1079 @ SV161 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 ) )
= $true )
| ( ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV529 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3903]) ).
thf(3961,plain,
! [SV179: $i,SV546: $i,SV1195: $i,SV1084: $i,SV867: $i] :
( ( ( c_Lim_OLIM @ SV867 @ SV1084 @ SV1195 @ SV546 @ SV179 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV867 @ SV179 @ tc_RealDef_Oreal @ SV546 ) @ SV1084 @ ( hAPP @ ( c_RealVector_Onorm__class_Onorm @ SV179 ) @ SV1195 ) @ SV546 @ tc_RealDef_Oreal )
= $true )
| ( ( class_RealVector_Ometric__space @ SV546 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3906]) ).
thf(3962,plain,
! [SV1228: $i,SV1196: $i,SV185: $i,SV552: $i,SV1087: $i,SV870: $i] :
( ( ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
= $true )
| ( ( ~ ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
| ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV552 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3907]) ).
thf(3963,plain,
! [SV1197: $i,SV1093: $i,SV573: $i,SV207: $i,SV876: $i] :
( ( ( c_RealVector_Obounded__linear @ SV876 @ SV207 @ SV573 )
= $false )
| ( ( ( hAPP @ SV876 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV207 ) @ SV1093 ) @ SV1197 ) )
= ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV573 ) @ SV1093 ) @ ( hAPP @ SV876 @ SV1197 ) ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV573 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(3964,plain,
! [SV574: $i,SV877: $i,SV208: $i,SV1094: $i] :
( ( ( c_SEQ_OCauchy @ SV1094 @ SV208 )
= $false )
| ( ( ~ ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 ) )
= $true )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV574 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3910]) ).
thf(3965,plain,
! [SV1198: $i,SV209: $i,SV1095: $i,SV575: $i,SV878: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV878 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1095 ) @ SV575 @ SV209 @ SV575 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV1198 @ SV575 @ SV209 )
= $false )
| ( ( c_Lim_OLIM @ SV878 @ SV1095 @ SV1198 @ SV575 @ SV209 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV575 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(3966,plain,
! [SV210: $i,SV576: $i,SV1199: $i,SV1096: $i,SV879: $i] :
( ( ( c_Lim_OLIM @ SV879 @ SV1096 @ SV1199 @ SV576 @ SV210 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV879 @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1096 ) @ SV576 @ SV210 @ SV576 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ SV1199 @ SV576 @ SV210 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV576 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3912]) ).
thf(3967,plain,
! [SV1229: $i,SV1201: $i,SV616: $i,SV1108: $i,SV902: $i,SV251: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1229 ) @ SV616 @ SV251 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1108 @ SV1201 @ SV1229 @ SV616 @ SV251 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV616 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3915]) ).
thf(3968,plain,
! [SV620: $i,SV906: $i,SV255: $i,SV1202: $i,SV1110: $i] :
( ( ( ~ ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true )
| ( ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV620 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3916]) ).
thf(3969,plain,
! [SV636: $i,SV914: $i,SV276: $i,SV1112: $i] :
( ( ( c_SEQ_OCauchy @ SV1112 @ SV276 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 ) )
= $true )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV636 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(3970,plain,
! [SV645: $i,SV922: $i,SV286: $i,SV1116: $i] :
( ( ( c_Series_Osummable @ SV1116 @ SV286 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 ) )
= $true )
| ( ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV645 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(3971,plain,
! [SV1241: $i,SV1232: $i,SV300: $i,SV1205: $i,SV1119: $i,SV932: $i,SV657: $i] :
( ( ( class_RealVector_Ometric__space @ SV657 )
= $false )
| ( ( ~ ( class_RealVector_Ometric__space @ SV932 )
| ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3924]) ).
thf(3972,plain,
! [SV668: $i,SV938: $i,SV312: $i,SV1206: $i,SV1123: $i] :
( ( ( ~ ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV668 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(3973,plain,
! [SV1233: $i,SV1207: $i,SV313: $i,SV669: $i,SV1124: $i,SV939: $i] :
( ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
= $true )
| ( ( ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
| ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV669 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(3974,plain,
! [SV1234: $i,SV320: $i,SV675: $i,SV1208: $i,SV1125: $i,SV943: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV943 ) )
= $true )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV675 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3927]) ).
thf(3975,plain,
! [SV1212: $i,SV1135: $i,SV961: $i,SV696: $i,SV345: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
= $false )
| ( ( ( SV961 = SV1212 )
| ( SV696 = SV1135 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV345 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3930]) ).
thf(3976,plain,
! [SV1213: $i,SV1137: $i,SV967: $i,SV703: $i,SV352: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
= $false )
| ( ( ( SV967 = SV1213 )
| ( SV703 = SV1137 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV352 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3931]) ).
thf(3977,plain,
! [SV1214: $i,SV1143: $i,SV984: $i,SV728: $i,SV377: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
= $false )
| ( ( ( SV1143 = SV1214 )
| ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3933]) ).
thf(3978,plain,
! [SV993: $i,SV7: $i,SV388: $i,SV1217: $i,SV1152: $i,SV738: $i] :
( ( ( c_Lim_OLIM @ SV738 @ SV1152 @ SV1217 @ SV388 @ SV7 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV738 @ SV7 @ ( tc_fun @ SV7 @ SV7 ) @ SV388 ) @ SV993 @ SV388 @ SV7 @ SV7 ) @ SV1152 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV7 ) @ SV1217 ) @ SV993 ) @ SV388 @ SV7 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV388 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3936]) ).
thf(3979,plain,
! [SV997: $i,SV11: $i,SV392: $i,SV1218: $i,SV1156: $i,SV742: $i] :
( ( ( c_Lim_OLIM @ SV742 @ SV1156 @ SV1218 @ SV392 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBC @ ( c_COMBB @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV742 @ tc_RealDef_Oreal @ ( tc_fun @ SV11 @ SV11 ) @ SV392 ) @ SV997 @ SV392 @ SV11 @ SV11 ) @ SV1156 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV11 ) @ SV1218 ) @ SV997 ) @ SV392 @ SV11 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV392 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3937]) ).
thf(3980,plain,
! [SV756: $i,SV34: $i,SV413: $i,SV1007: $i,SV1220: $i,SV1165: $i] :
( ( ( ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 ) )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true )
| ( ( SV756 = SV1007 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(3981,plain,
! [SV48: $i,SV426: $i,SV1012: $i,SV769: $i] :
( ( ( c_Lim_OLIM @ SV769 @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ SV426 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV48 ) @ SV769 @ tc_RealDef_Oreal @ SV48 @ SV426 ) @ SV1012 @ ( c_HOL_Ozero__class_Ozero @ SV48 ) @ SV426 @ SV48 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV426 )
= $false )
| ( ( class_RealVector_Oreal__algebra__1 @ SV48 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(3982,plain,
! [SV1221: $i,SV58: $i,SV434: $i,SV1170: $i,SV1017: $i,SV775: $i] :
( ( ( class_RealVector_Ometric__space @ SV775 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
| ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV434 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(3983,plain,
! [SV1031: $i,SV450: $i,SV75: $i,SV789: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBK @ SV789 @ SV75 @ SV450 ) @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV75 ) @ SV450 @ SV75 )
= $false )
| ( ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV75 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV450 )
= $false )
| ( ( class_HOL_Ozero @ SV75 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(3984,plain,
! [SV806: $i,SV96: $i,SV469: $i,SV1223: $i,SV1175: $i,SV1038: $i] :
( ( ( c_Lim_OLIM @ SV1038 @ SV1175 @ SV1223 @ SV469 @ SV96 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1038 @ SV96 @ SV96 @ SV469 ) @ SV1175 @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV96 ) @ SV806 ) @ SV1223 ) @ SV469 @ SV96 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV469 )
= $false )
| ( ( class_RealVector_Oreal__normed__algebra @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3947]) ).
thf(3985,plain,
! [SV107: $i,SV480: $i,SV1180: $i,SV1044: $i,SV815: $i] :
( ( ( c_Lim_OLIM @ SV815 @ SV1044 @ SV1180 @ SV480 @ SV107 )
= $false )
| ( ( SV1180
= ( c_HOL_Ozero__class_Ozero @ SV107 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV815 @ SV107 @ SV107 @ SV480 ) @ SV1044 @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ SV107 ) @ SV1180 ) @ SV480 @ SV107 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV480 )
= $false )
| ( ( class_RealVector_Oreal__normed__div__algebra @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(3986,plain,
! [SV1057: $i,SV498: $i,SV129: $i,SV832: $i] :
( ( ( c_RealVector_Obounded__linear @ SV832 @ SV129 @ SV498 )
= $false )
| ( ( c_SEQ_OZseq @ SV1057 @ SV129 )
= $false )
| ( ( c_SEQ_OZseq @ ( c_COMBB @ SV832 @ SV1057 @ SV129 @ SV498 @ tc_nat ) @ SV498 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV498 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(3987,plain,
! [SV1238: $i,SV1224: $i,SV499: $i,SV130: $i,SV1185: $i,SV1058: $i,SV833: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV833 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV499 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3956]) ).
thf(3988,plain,
! [SV1186: $i,SV1059: $i,SV500: $i,SV834: $i,SV131: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV500 )
= $false )
| ( ( class_RealVector_Oreal__algebra__1 @ SV131 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(3989,plain,
! [SV1239: $i,SV1225: $i,SV504: $i,SV135: $i,SV1187: $i,SV1062: $i,SV838: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV838 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV504 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3958]) ).
thf(3990,plain,
! [SV1240: $i,SV1226: $i,SV1190: $i,SV140: $i,SV509: $i,SV1065: $i,SV842: $i] :
( ( ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
= $true )
| ( ( ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
| ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV509 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(3991,plain,
! [SV1079: $i,SV529: $i,SV161: $i,SV862: $i] :
( ( ( c_RealVector_Obounded__linear @ SV862 @ SV161 @ SV529 )
= $false )
| ( ( c_Series_Osummable @ SV1079 @ SV161 )
= $false )
| ( ( c_Series_Osummable @ ( c_COMBB @ SV862 @ SV1079 @ SV161 @ SV529 @ tc_nat ) @ SV529 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV529 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3960]) ).
thf(3992,plain,
! [SV185: $i,SV870: $i,SV552: $i,SV1196: $i,SV1228: $i,SV1087: $i] :
( ( ( ~ ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true )
| ( ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV552 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3962]) ).
thf(3993,plain,
! [SV1094: $i,SV574: $i,SV208: $i,SV877: $i] :
( ( ( c_Lim_OisUCont @ SV877 @ SV208 @ SV574 )
= $false )
| ( ( c_SEQ_OCauchy @ SV1094 @ SV208 )
= $false )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV877 @ SV1094 @ SV208 @ SV574 @ tc_nat ) @ SV574 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV574 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(3994,plain,
! [SV902: $i,SV251: $i,SV616: $i,SV1229: $i,SV1201: $i,SV1108: $i] :
( ( ( c_Lim_OLIM @ SV1108 @ SV1201 @ SV1229 @ SV616 @ SV251 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1108 @ SV251 @ SV251 @ SV616 ) @ SV1201 @ ( hAPP @ ( hAPP @ ( c_RealVector_OscaleR__class_OscaleR @ SV251 ) @ SV902 ) @ SV1229 ) @ SV616 @ SV251 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV616 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3967]) ).
thf(3995,plain,
! [SV620: $i,SV906: $i,SV255: $i,SV1202: $i,SV1110: $i] :
( ( ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 ) )
= $true )
| ( ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV620 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3968]) ).
thf(3996,plain,
! [SV1112: $i,SV636: $i,SV276: $i,SV914: $i] :
( ( ( c_RealVector_Obounded__linear @ SV914 @ SV276 @ SV636 )
= $false )
| ( ( c_SEQ_OCauchy @ SV1112 @ SV276 )
= $false )
| ( ( c_SEQ_OCauchy @ ( c_COMBB @ SV914 @ SV1112 @ SV276 @ SV636 @ tc_nat ) @ SV636 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV636 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3969]) ).
thf(3997,plain,
! [SV1116: $i,SV645: $i,SV286: $i,SV922: $i] :
( ( ( c_RealVector_Obounded__linear @ SV922 @ SV286 @ SV645 )
= $false )
| ( ( c_Series_Osummable @ SV1116 @ SV286 )
= $false )
| ( ( ( hAPP @ SV922 @ ( c_Series_Osuminf @ SV1116 @ SV286 ) )
= ( c_Series_Osuminf @ ( c_COMBB @ SV922 @ SV1116 @ SV286 @ SV645 @ tc_nat ) @ SV645 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV645 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3970]) ).
thf(3998,plain,
! [SV1241: $i,SV1232: $i,SV657: $i,SV300: $i,SV1205: $i,SV1119: $i,SV932: $i] :
( ( ( ~ ( class_RealVector_Ometric__space @ SV932 ) )
= $true )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV657 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3971]) ).
thf(3999,plain,
! [SV668: $i,SV938: $i,SV312: $i,SV1206: $i,SV1123: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV668 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4000,plain,
! [SV313: $i,SV1207: $i,SV939: $i,SV669: $i,SV1233: $i,SV1124: $i] :
( ( ( ~ ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 ) )
= $true )
| ( ( ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV669 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3973]) ).
thf(4001,plain,
! [SV1234: $i,SV320: $i,SV675: $i,SV1208: $i,SV1125: $i,SV943: $i] :
( ( ( class_RealVector_Ometric__space @ SV943 )
= $false )
| ( ( ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV675 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4002,plain,
! [SV345: $i,SV1135: $i,SV696: $i,SV1212: $i,SV961: $i] :
( ( ( SV961 = SV1212 )
= $true )
| ( ( SV696 = SV1135 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV1212 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV696 ) @ SV1212 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV345 ) @ SV1135 ) @ SV961 ) ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV345 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3975]) ).
thf(4003,plain,
! [SV352: $i,SV1137: $i,SV703: $i,SV1213: $i,SV967: $i] :
( ( ( SV967 = SV1213 )
= $true )
| ( ( SV703 = SV1137 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV967 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV1213 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV703 ) @ SV1213 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV352 ) @ SV1137 ) @ SV967 ) ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV352 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3976]) ).
thf(4004,plain,
! [SV728: $i,SV377: $i,SV984: $i,SV1214: $i,SV1143: $i] :
( ( ( SV1143 = SV1214 )
= $true )
| ( ( SV984
= ( c_HOL_Ozero__class_Ozero @ SV377 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1143 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV377 ) @ SV728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ SV377 ) @ SV984 ) @ SV1214 ) ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV377 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3977]) ).
thf(4005,plain,
! [SV756: $i,SV34: $i,SV413: $i,SV1007: $i,SV1220: $i,SV1165: $i] :
( ( ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
= $false )
| ( ( ~ ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 ) )
= $true )
| ( ( SV756 = SV1007 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4006,plain,
! [SV1221: $i,SV775: $i,SV58: $i,SV434: $i,SV1170: $i,SV1017: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
| ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV775 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV434 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3982]) ).
thf(4007,plain,
! [SV1238: $i,SV1224: $i,SV499: $i,SV130: $i,SV1185: $i,SV1058: $i,SV833: $i] :
( ( ( class_RealVector_Ometric__space @ SV833 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
| ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV499 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3987]) ).
thf(4008,plain,
! [SV131: $i,SV500: $i,SV1186: $i,SV1059: $i,SV834: $i] :
( ( ( c_Lim_OLIM @ SV834 @ SV1059 @ SV1186 @ SV500 @ tc_RealDef_Oreal )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ ( c_RealVector_Oof__real @ SV131 ) @ SV834 @ tc_RealDef_Oreal @ SV131 @ SV500 ) @ SV1059 @ ( hAPP @ ( c_RealVector_Oof__real @ SV131 ) @ SV1186 ) @ SV500 @ SV131 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV500 )
= $false )
| ( ( class_RealVector_Oreal__algebra__1 @ SV131 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3988]) ).
thf(4009,plain,
! [SV1239: $i,SV1225: $i,SV504: $i,SV135: $i,SV1187: $i,SV1062: $i,SV838: $i] :
( ( ( class_RealVector_Ometric__space @ SV838 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
| ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV504 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4010,plain,
! [SV140: $i,SV842: $i,SV509: $i,SV1190: $i,SV1240: $i,SV1226: $i,SV1065: $i] :
( ( ( ~ ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV509 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3990]) ).
thf(4011,plain,
! [SV185: $i,SV870: $i,SV552: $i,SV1196: $i,SV1228: $i,SV1087: $i] :
( ( ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 ) )
= $true )
| ( ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV552 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4012,plain,
! [SV1202: $i,SV1110: $i,SV620: $i,SV255: $i,SV906: $i] :
( ( ( c_RealVector_Obounded__linear @ SV906 @ SV255 @ SV620 )
= $false )
| ( ( c_Series_Osums @ SV1110 @ SV1202 @ SV255 )
= $false )
| ( ( c_Series_Osums @ ( c_COMBB @ SV906 @ SV1110 @ SV255 @ SV620 @ tc_nat ) @ ( hAPP @ SV906 @ SV1202 ) @ SV620 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV620 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4013,plain,
! [SV1241: $i,SV1232: $i,SV657: $i,SV300: $i,SV1205: $i,SV1119: $i,SV932: $i] :
( ( ( class_RealVector_Ometric__space @ SV932 )
= $false )
| ( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
| ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV657 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3998]) ).
thf(4014,plain,
! [SV1206: $i,SV1123: $i,SV668: $i,SV312: $i,SV938: $i] :
( ( ( c_RealVector_Obounded__linear @ SV938 @ SV312 @ SV668 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ SV1123 @ SV1206 @ SV312 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV938 @ SV1123 @ SV312 @ SV668 @ tc_nat ) @ ( hAPP @ SV938 @ SV1206 ) @ SV668 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV668 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4015,plain,
! [SV313: $i,SV1207: $i,SV939: $i,SV669: $i,SV1233: $i,SV1124: $i] :
( ( ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
= $false )
| ( ( ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
| ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV669 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4000]) ).
thf(4016,plain,
! [SV1234: $i,SV320: $i,SV675: $i,SV943: $i,SV1208: $i,SV1125: $i] :
( ( ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
| ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV943 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV675 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4001]) ).
thf(4017,plain,
! [SV1007: $i,SV34: $i,SV413: $i,SV756: $i,SV1220: $i,SV1165: $i] :
( ( ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV756 @ SV413 @ SV34 )
= $false )
| ( ( c_Lim_OLIM @ SV1165 @ SV1220 @ SV1007 @ SV413 @ SV34 )
= $false )
| ( ( SV756 = SV1007 )
= $true )
| ( ( class_RealVector_Oreal__normed__algebra__1 @ SV413 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4005]) ).
thf(4018,plain,
! [SV58: $i,SV1017: $i,SV775: $i,SV434: $i,SV1221: $i,SV1170: $i] :
( ( ( ~ ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV775 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV434 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4019,plain,
! [SV1238: $i,SV1224: $i,SV833: $i,SV499: $i,SV130: $i,SV1185: $i,SV1058: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
| ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV833 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV499 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4007]) ).
thf(4020,plain,
! [SV1239: $i,SV1225: $i,SV838: $i,SV504: $i,SV135: $i,SV1187: $i,SV1062: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
| ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV838 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV504 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4021,plain,
! [SV140: $i,SV842: $i,SV509: $i,SV1190: $i,SV1240: $i,SV1226: $i,SV1065: $i] :
( ( ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 ) )
= $true )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV509 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4010]) ).
thf(4022,plain,
! [SV1196: $i,SV1228: $i,SV1087: $i,SV185: $i,SV552: $i,SV870: $i] :
( ( ( c_RealVector_Obounded__linear @ SV870 @ SV552 @ SV185 )
= $false )
| ( ( c_Limits_OZfun @ SV1087 @ SV1228 @ SV1196 @ SV552 )
= $false )
| ( ( c_Limits_OZfun @ ( c_COMBB @ SV870 @ SV1087 @ SV552 @ SV185 @ SV1196 ) @ SV1228 @ SV1196 @ SV185 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV552 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4023,plain,
! [SV1241: $i,SV1232: $i,SV932: $i,SV657: $i,SV300: $i,SV1205: $i,SV1119: $i] :
( ( ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
| ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true )
| ( ( class_RealVector_Ometric__space @ SV932 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV657 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4024,plain,
! [SV313: $i,SV1207: $i,SV939: $i,SV669: $i,SV1233: $i,SV1124: $i] :
( ( ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 ) )
= $true )
| ( ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV669 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4015]) ).
thf(4025,plain,
! [SV320: $i,SV675: $i,SV943: $i,SV1234: $i,SV1208: $i,SV1125: $i] :
( ( ( ~ ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 ) )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true )
| ( ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV943 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV675 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4016]) ).
thf(4026,plain,
! [SV58: $i,SV1017: $i,SV775: $i,SV434: $i,SV1221: $i,SV1170: $i] :
( ( ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV775 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV434 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4027,plain,
! [SV499: $i,SV1058: $i,SV130: $i,SV833: $i,SV1238: $i,SV1224: $i,SV1185: $i] :
( ( ( ~ ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 ) )
= $true )
| ( ( ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV833 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV499 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4028,plain,
! [SV504: $i,SV1062: $i,SV135: $i,SV838: $i,SV1239: $i,SV1225: $i,SV1187: $i] :
( ( ( ~ ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 ) )
= $true )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV838 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV504 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4020]) ).
thf(4029,plain,
! [SV1190: $i,SV1240: $i,SV1226: $i,SV1065: $i,SV140: $i,SV509: $i,SV842: $i] :
( ( ( c_RealVector_Obounded__linear @ SV842 @ SV509 @ SV140 )
= $false )
| ( ( c_Limits_Otendsto @ SV1065 @ SV1226 @ SV1240 @ SV1190 @ SV509 )
= $false )
| ( ( c_Limits_Otendsto @ ( c_COMBB @ SV842 @ SV1065 @ SV509 @ SV140 @ SV1190 ) @ ( hAPP @ SV842 @ SV1226 ) @ SV1240 @ SV1190 @ SV140 )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV509 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4030,plain,
! [SV657: $i,SV1119: $i,SV300: $i,SV932: $i,SV1241: $i,SV1232: $i,SV1205: $i] :
( ( ( ~ ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 ) )
= $true )
| ( ( ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV932 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV657 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4031,plain,
! [SV1124: $i,SV313: $i,SV669: $i,SV1207: $i,SV1233: $i,SV939: $i] :
( ( ( c_Lim_OLIM @ SV939 @ SV1233 @ SV1207 @ SV669 @ SV313 )
= $false )
| ( ( ( hAPP @ SV1124 @ ( c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 @ SV1124 @ SV1233 @ SV669 ) )
= SV1233 )
= $true )
| ( ( c_SEQ_OLIMSEQ @ SV1124 @ SV1233 @ SV669 )
= $false )
| ( ( c_SEQ_OLIMSEQ @ ( c_COMBB @ SV939 @ SV1124 @ SV669 @ SV313 @ tc_nat ) @ SV1207 @ SV313 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV669 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4024]) ).
thf(4032,plain,
! [SV320: $i,SV675: $i,SV943: $i,SV1234: $i,SV1208: $i,SV1125: $i] :
( ( ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
= $false )
| ( ( ~ ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 ) )
= $true )
| ( ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV943 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV675 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4025]) ).
thf(4033,plain,
! [SV775: $i,SV1221: $i,SV1170: $i,SV58: $i,SV434: $i,SV1017: $i] :
( ( ( c_RealVector_Obounded__linear @ SV1017 @ SV434 @ SV58 )
= $false )
| ( ( c_Lim_OLIM @ SV1170 @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV775 @ SV434 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1017 @ SV1170 @ SV434 @ SV58 @ SV775 ) @ SV1221 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV775 @ SV58 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV775 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV434 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4034,plain,
! [SV499: $i,SV1058: $i,SV130: $i,SV833: $i,SV1238: $i,SV1224: $i,SV1185: $i] :
( ( ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
= $false )
| ( ( ~ ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV833 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV499 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4027]) ).
thf(4035,plain,
! [SV504: $i,SV1062: $i,SV135: $i,SV838: $i,SV1239: $i,SV1225: $i,SV1187: $i] :
( ( ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
= $false )
| ( ( ~ ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV838 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV504 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4028]) ).
thf(4036,plain,
! [SV657: $i,SV1119: $i,SV300: $i,SV932: $i,SV1241: $i,SV1232: $i,SV1205: $i] :
( ( ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
= $false )
| ( ( ~ ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 ) )
= $true )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV932 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV657 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4030]) ).
thf(4037,plain,
! [SV675: $i,SV1125: $i,SV943: $i,SV320: $i,SV1234: $i,SV1208: $i] :
( ( ( c_Lim_OisCont @ SV1208 @ SV1234 @ SV320 @ SV943 )
= $false )
| ( ( c_Lim_OisCont @ SV1125 @ ( hAPP @ SV1208 @ SV1234 ) @ SV943 @ SV675 )
= $false )
| ( ( c_Lim_OisCont @ ( c_COMBB @ SV1125 @ SV1208 @ SV943 @ SV675 @ SV320 ) @ SV1234 @ SV320 @ SV675 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV943 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV675 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4032]) ).
thf(4038,plain,
! [SV833: $i,SV1224: $i,SV1185: $i,SV499: $i,SV130: $i,SV1238: $i,SV1058: $i] :
( ( ( c_Lim_OisCont @ SV1058 @ SV1238 @ SV130 @ SV499 )
= $false )
| ( ( c_Lim_OLIM @ SV1185 @ SV1224 @ SV1238 @ SV833 @ SV130 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1058 @ SV1185 @ SV130 @ SV499 @ SV833 ) @ SV1224 @ ( hAPP @ SV1058 @ SV1238 ) @ SV833 @ SV499 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV833 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV499 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4039,plain,
! [SV838: $i,SV1239: $i,SV1225: $i,SV1187: $i,SV504: $i,SV135: $i,SV1062: $i] :
( ( ( c_RealVector_Obounded__linear @ SV1062 @ SV135 @ SV504 )
= $false )
| ( ( c_Lim_OLIM @ SV1187 @ SV1225 @ SV1239 @ SV838 @ SV135 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1062 @ SV1187 @ SV135 @ SV504 @ SV838 ) @ SV1225 @ ( hAPP @ SV1062 @ SV1239 ) @ SV838 @ SV504 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV838 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV504 )
= $false )
| ( ( class_RealVector_Oreal__normed__vector @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4040,plain,
! [SV932: $i,SV1232: $i,SV1205: $i,SV657: $i,SV300: $i,SV1241: $i,SV1119: $i] :
( ( ( c_Lim_OLIM @ SV1119 @ SV1241 @ ( hAPP @ SV1119 @ SV1241 ) @ SV300 @ SV657 )
= $false )
| ( ( c_Lim_OLIM @ SV1205 @ SV1232 @ SV1241 @ SV932 @ SV300 )
= $false )
| ( ( c_Lim_OLIM @ ( c_COMBB @ SV1119 @ SV1205 @ SV300 @ SV657 @ SV932 ) @ SV1232 @ ( hAPP @ SV1119 @ SV1241 ) @ SV932 @ SV657 )
= $true )
| ( ( class_RealVector_Ometric__space @ SV932 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV657 )
= $false )
| ( ( class_RealVector_Ometric__space @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4041,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1286,4040,4039,4038,4037,4033,4031,4029,4022,4017,4014,4012,4008,4004,4003,4002,3997,3996,3994,3993,3991,3986,3985,3984,3983,3981,3979,3978,3966,3965,3963,3961,3954,3953,3952,3951,3949,3948,3944,3943,3940,3939,3938,3935,3934,3932,3929,3928,3923,3921,3920,3919,3917,3914,3913,3908,3905,3904,3902,3901,3892,3891,3890,3888,3883,3882,3872,3869,3866,3863,3862,3861,3860,3858,3853,3847,3839,3823,3822,3805,3804,3799,3798,3794,3788,3787,3784,3783,3779,3777,3772,3771,3769,3768,3765,3762,3761,3760,3759,3758,3757,3755,3749,3748,3736,3735,3734,3732,3731,3723,3720,3713,3709,3708,3703,3692,3678,3677,3676,3675,3670,3655,3653,3650,3649,3645,3639,3638,3630,3629,3628,3619,3616,3614,3613,3612,3611,3610,3606,3601,3600,3598,3597,3596,3593,3588,3587,3584,3583,3572,3569,3553,3543,3542,3539,3538,3537,3534,3533,3532,3531,3530,3525,3517,3516,3507,3505,3504,3503,3497,3496,3495,3480,3479,3478,3477,3476,3475,3464,3462,3457,3455,3451,3450,3447,3435,3430,3429,3422,3413,3412,3407,3406,3405,3402,3400,3395,3393,3392,3391,3376,3375,3374,3372,3371,3369,3368,3367,3366,3363,3360,3359,3355,3354,3353,3352,3351,3350,3349,3348,3347,3346,3341,3323,3322,3321,3320,3299,3296,3295,3294,3293,3292,3291,3290,3289,3288,3287,3286,3285,3284,3283,3282,3267,3263,3262,3260,3256,3220,3217,3205,3201,3187,3169,3168,3162,3161,3151,3142,3141,3138,3135,3134,3133,3127,3125,3122,3101,3087,3075,3074,3073,3060,3059,3053,3041,3024,3023,3022,3021,3020,2998,2995,2993,2992,2991,2987,2986,2977,2973,2971,2970,2948,2925,2905,2892,2891,2887,2886,2871,2868,2849,2846,2836,2835,2834,2833,2832,2831,2830,2829,2828,2827,2826,2814,2792,2791,2790,2789,2788,2787,2786,2785,2784,2782,2781,2780,2778,2766,2765,2764,2763,2759,2758,2757,2756,2753,2687,2682,2659,2656,2624,2563,2562,2548,2545,2540,2528,2517,2504,2503,2500,2495,2470,2425,2416,2389,2388,2380,2370,2366,2354,2352,2334,2331,2296,2287,2263,2242,2237,2200,2196,2164,2145,2094,2085,2084,1969,1820,1806,1772,1742,1604,1541,1481,1431,1430,1429,1428,1427,1426,1425,1424,1423,1422,1421,1420,1419,1418,1417,1416,1415,1414,1413,1412,1411,1410,1409,1408,1407,1406,1405,1404,1403,1402,1401,1400,1399,1398,1397,1396,1395,1394,1393,1392,1391,1390,1389,1388,1387,1386,1385,1384,1383,1382,1381,1380,1379,1378,1377,1376,1375,1374,1373,1372,1371,1370,1369,1368,1367,1366,1365,1364,1363,1362,1361,1360,1359,1358,1357,1356,1355,1354,1353,1352,1351,1350,1349,1348,1347,1345,1340,1333,1330,1316,1309,1304,1295]) ).
thf(4042,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4041]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG365-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 18:17:43 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 126.04/25.72 ...
% 126.04/25.72
% 126.04/25.72 No.of.Axioms: 477
% 126.04/25.72
% 126.04/25.72 Length.of.Defs: 0
% 126.04/25.72
% 126.04/25.72 Contains.Choice.Funs: false
% 126.04/25.72 ..........................................................................................................................................
% 126.04/25.72
% 126.04/25.72 ********************************
% 126.04/25.72 * All subproblems solved! *
% 126.04/25.72 ********************************
% 126.04/25.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:477,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4041,loop_count:0,foatp_calls:1,translation:fof_full)
% 126.04/25.72
% 126.04/25.72 %**** Beginning of derivation protocol ****
% 126.04/25.72 % SZS output start CNFRefutation
% See solution above
% 126.04/25.75
% 126.04/25.75 %**** End of derivation protocol ****
% 126.04/25.75 %**** no. of clauses in derivation: 4042 ****
% 126.04/25.75 %**** clause counter: 4041 ****
% 126.04/25.75
% 126.04/25.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:477,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4041,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------