%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP035^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:01 AM UTC 2026
% Result : Theorem 7.41s 2.40s
% Output : Refutation 7.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP035^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n028.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : ITP035^2 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.47 % Domain : Interactive Theorem Proving
% 0.28/0.47 % Problem : Sledgehammer Cartan problem prob_32__6530878_1
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Des21]
% 0.28/0.47 % Names : Cartan/prob_32__6530878_1 [Des21]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.28/0.47 % Syntax : Number of formulae : 500 ( 193 unt; 80 typ; 0 def)
% 0.28/0.47 % Number of atoms : 1017 ( 305 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.28/0.47 % Number of connectives : 3677 ( 42 ~; 23 |; 73 &;3098 @)
% 0.28/0.47 % ( 0 <=>; 441 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 18 ( 6 avg)
% 0.28/0.47 % Number of types : 4 ( 3 usr)
% 0.28/0.47 % Number of type conns : 284 ( 284 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 80 ( 77 usr; 5 con; 0-6 aty)
% 0.28/0.47 % Number of variables : 1042 ( 37 ^; 918 !; 15 ?;1042 :)
% 0.28/0.47 % ( 72 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.47 % SPC : TH1_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:23:02.925
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % Could-be-implicit typings (5)
% 0.28/0.47 thf(ty_t_Formal__Power__Series_Ofps,type,
% 0.28/0.47 formal_Power_fps: $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Complex_Ocomplex,type,
% 0.28/0.47 complex: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Real_Oreal,type,
% 0.28/0.47 real: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Set_Oset,type,
% 0.28/0.47 set: $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Nat_Onat,type,
% 0.28/0.47 nat: $tType ).
% 0.28/0.47
% 0.28/0.47 % Explicit typings (75)
% 0.28/0.47 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.28/0.47 finite_finite:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Oring__1,type,
% 0.28/0.47 ring_1:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.28/0.47 comm_monoid_add:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Osemiring__1,type,
% 0.28/0.47 semiring_1:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Osemiring__0,type,
% 0.28/0.47 semiring_0:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Ocomm__semiring__0,type,
% 0.28/0.47 comm_semiring_0:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.28/0.47 cancel_semigroup_add:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.28/0.47 group_add:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 0.28/0.47 real_V2090557954_space:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_HOL_Otype,type,
% 0.28/0.47 type:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Countable_Ocountable,type,
% 0.28/0.47 countable:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Oone,type,
% 0.28/0.47 one:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Ozero,type,
% 0.28/0.47 zero:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Fields_Ofield,type,
% 0.28/0.47 field:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Otimes,type,
% 0.28/0.47 times:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.28/0.47 ord:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Num_Oneg__numeral,type,
% 0.28/0.47 neg_numeral:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.28/0.47 order:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Omult__zero,type,
% 0.28/0.47 mult_zero:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Transcendental_Oln,type,
% 0.28/0.47 ln:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.28/0.47 monoid_mult:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.28/0.47 linorder:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.28/0.47 preorder:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Oordered__ring,type,
% 0.28/0.47 ordered_ring:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.28/0.47 zero_neq_one:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Fields_Ofield__char__0,type,
% 0.28/0.47 field_char_0:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.28/0.47 semigroup_mult:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.28/0.47 comm_semiring_1:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.28/0.47 linordered_idom:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Olinordered__ring,type,
% 0.28/0.47 linordered_ring:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Oordered__semiring,type,
% 0.28/0.47 ordered_semiring:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.28/0.47 comm_monoid_mult:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.28/0.47 ab_semigroup_mult:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Oordered__semiring__0,type,
% 0.28/0.47 ordered_semiring_0:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Oordered__comm__semiring,type,
% 0.28/0.47 ordere1490568538miring:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Topological__Spaces_Ot0__space,type,
% 0.28/0.47 topological_t0_space:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Topological__Spaces_Ot1__space,type,
% 0.28/0.47 topological_t1_space:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 0.28/0.47 linord581940658strict:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 0.28/0.47 ring_11004092258visors:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 0.28/0.47 semiri1193490041visors:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.28/0.47 linord1659791738miring:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__field,type,
% 0.28/0.47 real_V758409581_field:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Topological__Spaces_Odiscrete__topology,type,
% 0.28/0.47 topolo2133971006pology:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 0.28/0.47 topolo503727757_space:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.28/0.47 canoni770627133id_add:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 0.28/0.47 semiri1923998003cancel:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Topological__Spaces_Ofirst__countable__topology,type,
% 0.28/0.47 topolo2135403230pology:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Complex__Analysis__Basics_Oholomorphic__on,type,
% 0.28/0.47 comple372758642hic_on: ( complex > complex ) > ( set @ complex ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Derivative_Oderiv,type,
% 0.28/0.47 deriv:
% 0.28/0.47 !>[A: $tType] : ( ( A > A ) > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Formal__Power__Series_Ofps__tan,type,
% 0.28/0.47 formal_Power_fps_tan:
% 0.28/0.47 !>[A: $tType] : ( A > ( formal_Power_fps @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Fun_Ocomp,type,
% 0.28/0.47 comp:
% 0.28/0.47 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Fun_Oid,type,
% 0.28/0.47 id:
% 0.28/0.47 !>[A: $tType] : ( A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.28/0.47 one_one:
% 0.28/0.47 !>[A: $tType] : A ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.28/0.47 times_times:
% 0.28/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.28/0.47 zero_zero:
% 0.28/0.47 !>[A: $tType] : A ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_If,type,
% 0.28/0.47 if:
% 0.28/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nat_Ocompow,type,
% 0.28/0.47 compow:
% 0.28/0.47 !>[A: $tType] : ( nat > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nat_Ofunpow,type,
% 0.28/0.47 funpow:
% 0.28/0.47 !>[A: $tType] : ( nat > ( A > A ) > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 0.28/0.47 neg_numeral_dbl_inc:
% 0.28/0.47 !>[A: $tType] : ( A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.28/0.47 ord_less_eq:
% 0.28/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect,type,
% 0.28/0.47 collect:
% 0.28/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oimage,type,
% 0.28/0.47 image:
% 0.28/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Topological__Spaces_Oopen__class_Oopen,type,
% 0.28/0.47 topolo1751647064n_open:
% 0.28/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconnected,type,
% 0.28/0.47 topolo1099314120nected:
% 0.28/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Transcendental_Oarcosh,type,
% 0.28/0.47 arcosh:
% 0.28/0.47 !>[A: $tType] : ( A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Transcendental_Oarsinh,type,
% 0.28/0.47 arsinh:
% 0.28/0.47 !>[A: $tType] : ( A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Transcendental_Oartanh,type,
% 0.28/0.47 artanh:
% 0.28/0.47 !>[A: $tType] : ( A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Transcendental_Oln__class_Oln,type,
% 0.28/0.47 ln_ln:
% 0.28/0.47 !>[A: $tType] : ( A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Transitive__Closure_Orelpowp,type,
% 0.28/0.47 transitive_relpowp:
% 0.28/0.47 !>[A: $tType] : ( nat > ( A > A > $o ) > A > A > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member,type,
% 0.28/0.47 member:
% 0.28/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_S,type,
% 0.28/0.47 s: set @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_T,type,
% 0.28/0.47 t: set @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_f,type,
% 0.28/0.47 f: complex > complex ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_g,type,
% 0.28/0.47 g: complex > complex ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_w,type,
% 0.28/0.47 w: complex ).
% 0.28/0.47
% 0.28/0.47 % Relevant facts (253)
% 0.28/0.47 thf(fact_0__092_060open_062_092_060And_062z_O_A_Ideriv_A_094_094_A1_J_Aid_Az_A_061_A_Iif_A1_A_061_A0_Athen_Az_Aelse_Aif_A1_A_061_A1_Athen_A1_058_058_063_Ha_Aelse_A_I0_058_058_063_Ha_J_J_092_060close_062,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V758409581_field @ A )
% 0.28/0.47 => ! [Z: A] :
% 0.28/0.47 ( ( ( ( one_one @ nat )
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 => ( ( compow @ ( ( A > A ) > A > A ) @ ( one_one @ nat ) @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 0.28/0.47 = Z ) )
% 0.28/0.47 & ( ( ( one_one @ nat )
% 0.28/0.47 != ( zero_zero @ nat ) )
% 0.28/0.47 => ( ( compow @ ( ( A > A ) > A > A ) @ ( one_one @ nat ) @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 0.28/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>\<And>z. (deriv ^^ 1) id z = (if 1 = 0 then z else if 1 = 1 then 1::?'a else (0::?'a))\<close>
% 0.28/0.47 thf(fact_1_assms_I7_J,axiom,
% 0.28/0.47 member @ complex @ w @ s ).
% 0.28/0.47
% 0.28/0.47 % assms(7)
% 0.28/0.47 thf(fact_2_deriv__id,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V758409581_field @ A )
% 0.28/0.47 => ( ( deriv @ A @ ( id @ A ) )
% 0.28/0.47 = ( ^ [Z2: A] : ( one_one @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % deriv_id
% 0.28/0.47 thf(fact_3_id__apply,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( id @ A )
% 0.28/0.47 = ( ^ [X: A] : X ) ) ).
% 0.28/0.47
% 0.28/0.47 % id_apply
% 0.28/0.47 thf(fact_4_id__def,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( id @ A )
% 0.28/0.47 = ( ^ [X: A] : X ) ) ).
% 0.28/0.47
% 0.28/0.47 % id_def
% 0.28/0.47 thf(fact_5_eq__id__iff,axiom,
% 0.28/0.47 ! [A: $tType,F: A > A] :
% 0.28/0.47 ( ( ! [X: A] :
% 0.28/0.47 ( ( F @ X )
% 0.28/0.47 = X ) )
% 0.28/0.47 = ( F
% 0.28/0.47 = ( id @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_id_iff
% 0.28/0.47 thf(fact_6_higher__deriv__id,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V758409581_field @ A )
% 0.28/0.47 => ! [N: nat,Z: A] :
% 0.28/0.47 ( ( ( N
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 => ( ( compow @ ( ( A > A ) > A > A ) @ N @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 0.28/0.47 = Z ) )
% 0.28/0.47 & ( ( N
% 0.28/0.47 != ( zero_zero @ nat ) )
% 0.28/0.47 => ( ( ( N
% 0.28/0.47 = ( one_one @ nat ) )
% 0.28/0.47 => ( ( compow @ ( ( A > A ) > A > A ) @ N @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 0.28/0.47 = ( one_one @ A ) ) )
% 0.28/0.47 & ( ( N
% 0.28/0.47 != ( one_one @ nat ) )
% 0.28/0.47 => ( ( compow @ ( ( A > A ) > A > A ) @ N @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % higher_deriv_id
% 0.28/0.47 thf(fact_7_one__reorient,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( one @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ( ( ( one_one @ A )
% 0.28/0.47 = X2 )
% 0.28/0.47 = ( X2
% 0.28/0.47 = ( one_one @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % one_reorient
% 0.28/0.47 thf(fact_8_id__funpow,axiom,
% 0.28/0.47 ! [A: $tType,N: nat] :
% 0.28/0.47 ( ( compow @ ( A > A ) @ N @ ( id @ A ) )
% 0.28/0.47 = ( id @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % id_funpow
% 0.28/0.47 thf(fact_9_calculation,axiom,
% 0.28/0.47 ( ( times_times @ complex @ ( deriv @ complex @ f @ w ) @ ( deriv @ complex @ g @ ( f @ w ) ) )
% 0.28/0.47 = ( deriv @ complex @ ( id @ complex ) @ w ) ) ).
% 0.28/0.47
% 0.28/0.47 % calculation
% 0.28/0.47 thf(fact_10__092_060open_062deriv_A_Ig_A_092_060circ_062_Af_J_Aw_A_061_Aderiv_Aid_Aw_092_060close_062,axiom,
% 0.28/0.47 ( ( deriv @ complex @ ( comp @ complex @ complex @ complex @ g @ f ) @ w )
% 0.28/0.47 = ( deriv @ complex @ ( id @ complex ) @ w ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>deriv (g \<circ> f) w = deriv id w\<close>
% 0.28/0.47 thf(fact_11_zero__neq__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( zero_neq_one @ A )
% 0.28/0.47 => ( ( zero_zero @ A )
% 0.28/0.47 != ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_neq_one
% 0.28/0.47 thf(fact_12__092_060open_062deriv_Af_Aw_A_K_Aderiv_Ag_A_If_Aw_J_A_061_Aderiv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_092_060close_062,axiom,
% 0.28/0.47 ( ( times_times @ complex @ ( deriv @ complex @ f @ w ) @ ( deriv @ complex @ g @ ( f @ w ) ) )
% 0.28/0.47 = ( times_times @ complex @ ( deriv @ complex @ g @ ( f @ w ) ) @ ( deriv @ complex @ f @ w ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>deriv f w * deriv g (f w) = deriv g (f w) * deriv f w\<close>
% 0.28/0.47 thf(fact_13_comp__apply,axiom,
% 0.28/0.47 ! [C: $tType,A: $tType,B: $tType] :
% 0.28/0.47 ( ( comp @ B @ A @ C )
% 0.28/0.47 = ( ^ [F2: B > A,G: C > B,X: C] : ( F2 @ ( G @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_apply
% 0.28/0.47 thf(fact_14_mult__zero__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( mult_zero @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_zero_left
% 0.28/0.47 thf(fact_15_mult__zero__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( mult_zero @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_zero_right
% 0.28/0.47 thf(fact_16_mult__eq__0__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semiri1193490041visors @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ B2 )
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 = ( ( A2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( B2
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_eq_0_iff
% 0.28/0.47 thf(fact_17_mult__cancel__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semiri1923998003cancel @ A )
% 0.28/0.47 => ! [C2: A,A2: A,B2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ C2 @ A2 )
% 0.28/0.47 = ( times_times @ A @ C2 @ B2 ) )
% 0.28/0.47 = ( ( C2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel_left
% 0.28/0.47 thf(fact_18_mult__cancel__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semiri1923998003cancel @ A )
% 0.28/0.47 => ! [A2: A,C2: A,B2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ C2 )
% 0.28/0.47 = ( times_times @ A @ B2 @ C2 ) )
% 0.28/0.47 = ( ( C2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel_right
% 0.28/0.47 thf(fact_19_mult_Oright__neutral,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( monoid_mult @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult.right_neutral
% 0.28/0.47 thf(fact_20_mult_Oleft__neutral,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( monoid_mult @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult.left_neutral
% 0.28/0.47 thf(fact_21_id__comp,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,G2: A > B] :
% 0.28/0.47 ( ( comp @ B @ B @ A @ ( id @ B ) @ G2 )
% 0.28/0.47 = G2 ) ).
% 0.28/0.47
% 0.28/0.47 % id_comp
% 0.28/0.47 thf(fact_22_comp__id,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: A > B] :
% 0.28/0.47 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 0.28/0.47 = F ) ).
% 0.28/0.47
% 0.28/0.47 % comp_id
% 0.28/0.47 thf(fact_23_funpow__0,axiom,
% 0.28/0.47 ! [A: $tType,F: A > A,X2: A] :
% 0.28/0.47 ( ( compow @ ( A > A ) @ ( zero_zero @ nat ) @ F @ X2 )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % funpow_0
% 0.28/0.47 thf(fact_24_assms_I3_J,axiom,
% 0.28/0.47 topolo1751647064n_open @ complex @ s ).
% 0.28/0.47
% 0.28/0.47 % assms(3)
% 0.28/0.47 thf(fact_25__092_060open_062deriv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_A_061_Aderiv_A_Ig_A_092_060circ_062_Af_J_Aw_092_060close_062,axiom,
% 0.28/0.47 ( ( times_times @ complex @ ( deriv @ complex @ g @ ( f @ w ) ) @ ( deriv @ complex @ f @ w ) )
% 0.28/0.47 = ( deriv @ complex @ ( comp @ complex @ complex @ complex @ g @ f ) @ w ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>deriv g (f w) * deriv f w = deriv (g \<circ> f) w\<close>
% 0.28/0.47 thf(fact_26_mult__cancel__right2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ring_11004092258visors @ A )
% 0.28/0.47 => ! [A2: A,C2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ C2 )
% 0.28/0.47 = C2 )
% 0.28/0.47 = ( ( C2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( A2
% 0.28/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel_right2
% 0.28/0.47 thf(fact_27_mult__cancel__right1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ring_11004092258visors @ A )
% 0.28/0.47 => ! [C2: A,B2: A] :
% 0.28/0.47 ( ( C2
% 0.28/0.47 = ( times_times @ A @ B2 @ C2 ) )
% 0.28/0.47 = ( ( C2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( B2
% 0.28/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel_right1
% 0.28/0.47 thf(fact_28_mult__cancel__left2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ring_11004092258visors @ A )
% 0.28/0.47 => ! [C2: A,A2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ C2 @ A2 )
% 0.28/0.47 = C2 )
% 0.28/0.47 = ( ( C2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( A2
% 0.28/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel_left2
% 0.28/0.47 thf(fact_29_mult__cancel__left1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ring_11004092258visors @ A )
% 0.28/0.47 => ! [C2: A,B2: A] :
% 0.28/0.47 ( ( C2
% 0.28/0.47 = ( times_times @ A @ C2 @ B2 ) )
% 0.28/0.47 = ( ( C2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( B2
% 0.28/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel_left1
% 0.28/0.47 thf(fact_30_assms_I6_J,axiom,
% 0.28/0.47 ! [Z: complex] :
% 0.28/0.47 ( ( member @ complex @ Z @ s )
% 0.28/0.47 => ( ( g @ ( f @ Z ) )
% 0.28/0.47 = Z ) ) ).
% 0.28/0.47
% 0.28/0.47 % assms(6)
% 0.28/0.47 thf(fact_31_assms_I1_J,axiom,
% 0.28/0.47 comple372758642hic_on @ f @ s ).
% 0.28/0.47
% 0.28/0.47 % assms(1)
% 0.28/0.47 thf(fact_32_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ab_semigroup_mult @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ab_semigroup_mult_class.mult_ac(1)
% 0.28/0.47 thf(fact_33_comp__def,axiom,
% 0.28/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.28/0.47 ( ( comp @ B @ C @ A )
% 0.28/0.47 = ( ^ [F2: B > C,G: A > B,X: A] : ( F2 @ ( G @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_def
% 0.28/0.47 thf(fact_34_comp__assoc,axiom,
% 0.28/0.47 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G2: C > D,H: A > C] :
% 0.28/0.47 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G2 ) @ H )
% 0.28/0.47 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G2 @ H ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_assoc
% 0.28/0.47 thf(fact_35_comp__funpow,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,N: nat,F: A > A] :
% 0.28/0.47 ( ( compow @ ( ( B > A ) > B > A ) @ N @ ( comp @ A @ A @ B @ F ) )
% 0.28/0.47 = ( comp @ A @ A @ B @ ( compow @ ( A > A ) @ N @ F ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_funpow
% 0.28/0.47 thf(fact_36_comp__eq__dest,axiom,
% 0.28/0.47 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.28/0.47 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.28/0.47 => ( ( A2 @ ( B2 @ V ) )
% 0.28/0.47 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_eq_dest
% 0.28/0.47 thf(fact_37_comp__eq__elim,axiom,
% 0.28/0.47 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.28/0.47 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.28/0.47 => ! [V2: A] :
% 0.28/0.47 ( ( A2 @ ( B2 @ V2 ) )
% 0.28/0.47 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_eq_elim
% 0.28/0.47 thf(fact_38_funpow__swap1,axiom,
% 0.28/0.47 ! [A: $tType,F: A > A,N: nat,X2: A] :
% 0.28/0.47 ( ( F @ ( compow @ ( A > A ) @ N @ F @ X2 ) )
% 0.28/0.47 = ( compow @ ( A > A ) @ N @ F @ ( F @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % funpow_swap1
% 0.28/0.47 thf(fact_39_comp__eq__dest__lhs,axiom,
% 0.28/0.47 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.28/0.47 = C2 )
% 0.28/0.47 => ( ( A2 @ ( B2 @ V ) )
% 0.28/0.47 = ( C2 @ V ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_eq_dest_lhs
% 0.28/0.47 thf(fact_40_zero__reorient,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( zero @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ( ( ( zero_zero @ A )
% 0.28/0.47 = X2 )
% 0.28/0.47 = ( X2
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_reorient
% 0.28/0.47 thf(fact_41_mult__not__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( mult_zero @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ B2 )
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( A2
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 & ( B2
% 0.28/0.47 != ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_not_zero
% 0.28/0.47 thf(fact_42_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.28/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.28/0.47 = ( P @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_43_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] :
% 0.28/0.47 ( ( collect @ A
% 0.28/0.47 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 0.28/0.47 = A3 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_44_Collect__cong,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 = ( Q @ X3 ) )
% 0.28/0.47 => ( ( collect @ A @ P )
% 0.28/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_cong
% 0.28/0.47 thf(fact_45_ext,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( F @ X3 )
% 0.28/0.47 = ( G2 @ X3 ) )
% 0.28/0.47 => ( F = G2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % ext
% 0.28/0.47 thf(fact_46_mult_Oassoc,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semigroup_mult @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult.assoc
% 0.28/0.47 thf(fact_47_mult_Ocommute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ab_semigroup_mult @ A )
% 0.28/0.47 => ( ( times_times @ A )
% 0.28/0.47 = ( ^ [A4: A,B3: A] : ( times_times @ A @ B3 @ A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult.commute
% 0.28/0.47 thf(fact_48_mult_Oleft__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ab_semigroup_mult @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.28/0.47 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C2 ) )
% 0.28/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult.left_commute
% 0.28/0.47 thf(fact_49_divisors__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semiri1193490041visors @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ B2 )
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 => ( ( A2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( B2
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % divisors_zero
% 0.28/0.47 thf(fact_50_no__zero__divisors,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semiri1193490041visors @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( times_times @ A @ A2 @ B2 )
% 0.28/0.47 != ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % no_zero_divisors
% 0.28/0.47 thf(fact_51_mult__left__cancel,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semiri1923998003cancel @ A )
% 0.28/0.47 => ! [C2: A,A2: A,B2: A] :
% 0.28/0.47 ( ( C2
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ( times_times @ A @ C2 @ A2 )
% 0.28/0.47 = ( times_times @ A @ C2 @ B2 ) )
% 0.28/0.47 = ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_left_cancel
% 0.28/0.47 thf(fact_52_mult__right__cancel,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semiri1923998003cancel @ A )
% 0.28/0.47 => ! [C2: A,A2: A,B2: A] :
% 0.28/0.47 ( ( C2
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ( times_times @ A @ A2 @ C2 )
% 0.28/0.47 = ( times_times @ A @ B2 @ C2 ) )
% 0.28/0.47 = ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_right_cancel
% 0.28/0.47 thf(fact_53_comp__eq__id__dest,axiom,
% 0.28/0.47 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.28/0.47 = ( comp @ B @ B @ A @ ( id @ B ) @ C2 ) )
% 0.28/0.47 => ( ( A2 @ ( B2 @ V ) )
% 0.28/0.47 = ( C2 @ V ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % comp_eq_id_dest
% 0.28/0.47 thf(fact_54_mult_Ocomm__neutral,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_monoid_mult @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult.comm_neutral
% 0.28/0.47 thf(fact_55_comm__monoid__mult__class_Omult__1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_monoid_mult @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % comm_monoid_mult_class.mult_1
% 0.28/0.47 thf(fact_56_funpow__simps__right_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,F: A > A] :
% 0.28/0.47 ( ( compow @ ( A > A ) @ ( zero_zero @ nat ) @ F )
% 0.28/0.47 = ( id @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % funpow_simps_right(1)
% 0.28/0.47 thf(fact_57_fun_Omap__id,axiom,
% 0.28/0.47 ! [A: $tType,D: $tType,T: D > A] :
% 0.28/0.47 ( ( comp @ A @ A @ D @ ( id @ A ) @ T )
% 0.28/0.47 = T ) ).
% 0.28/0.47
% 0.28/0.47 % fun.map_id
% 0.28/0.47 thf(fact_58_vector__space__over__itself_Oscale__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ( ( times_times @ A @ ( one_one @ A ) @ X2 )
% 0.28/0.47 = X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_one
% 0.28/0.47 thf(fact_59_vector__space__over__itself_Oscale__eq__0__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [A2: A,X2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ X2 )
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 = ( ( A2
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 | ( X2
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_eq_0_iff
% 0.28/0.47 thf(fact_60_vector__space__over__itself_Oscale__zero__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ( ( times_times @ A @ ( zero_zero @ A ) @ X2 )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_zero_left
% 0.28/0.47 thf(fact_61_vector__space__over__itself_Oscale__zero__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_zero_right
% 0.28/0.47 thf(fact_62_vector__space__over__itself_Oscale__cancel__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [A2: A,X2: A,Y: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ X2 )
% 0.28/0.47 = ( times_times @ A @ A2 @ Y ) )
% 0.28/0.47 = ( ( X2 = Y )
% 0.28/0.47 | ( A2
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_cancel_left
% 0.28/0.47 thf(fact_63_vector__space__over__itself_Oscale__cancel__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [A2: A,X2: A,B2: A] :
% 0.28/0.47 ( ( ( times_times @ A @ A2 @ X2 )
% 0.28/0.47 = ( times_times @ A @ B2 @ X2 ) )
% 0.28/0.47 = ( ( A2 = B2 )
% 0.28/0.47 | ( X2
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_cancel_right
% 0.28/0.47 thf(fact_64_mult__if__delta,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_semiring_1 @ A )
% 0.28/0.47 => ! [P: $o,Q2: A] :
% 0.28/0.47 ( ( P
% 0.28/0.47 => ( ( times_times @ A @ ( if @ A @ P @ ( one_one @ A ) @ ( zero_zero @ A ) ) @ Q2 )
% 0.28/0.47 = Q2 ) )
% 0.28/0.47 & ( ~ P
% 0.28/0.47 => ( ( times_times @ A @ ( if @ A @ P @ ( one_one @ A ) @ ( zero_zero @ A ) ) @ Q2 )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_if_delta
% 0.28/0.47 thf(fact_65_relpowp__1,axiom,
% 0.28/0.47 ! [A: $tType,P: A > A > $o] :
% 0.28/0.47 ( ( compow @ ( A > A > $o ) @ ( one_one @ nat ) @ P )
% 0.28/0.47 = P ) ).
% 0.28/0.47
% 0.28/0.47 % relpowp_1
% 0.28/0.47 thf(fact_66_set__times__intro,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( times @ A )
% 0.28/0.47 => ! [A2: A,C3: set @ A,B2: A,D3: set @ A] :
% 0.28/0.47 ( ( member @ A @ A2 @ C3 )
% 0.28/0.47 => ( ( member @ A @ B2 @ D3 )
% 0.28/0.47 => ( member @ A @ ( times_times @ A @ A2 @ B2 ) @ ( times_times @ ( set @ A ) @ C3 @ D3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_times_intro
% 0.28/0.47 thf(fact_67_funpow__code__def,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( funpow @ A )
% 0.28/0.47 = ( compow @ ( A > A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % funpow_code_def
% 0.28/0.47 thf(fact_68_assms_I4_J,axiom,
% 0.28/0.47 topolo1751647064n_open @ complex @ t ).
% 0.28/0.47
% 0.28/0.47 % assms(4)
% 0.28/0.47 thf(fact_69_assms_I2_J,axiom,
% 0.28/0.47 comple372758642hic_on @ g @ t ).
% 0.28/0.47
% 0.28/0.47 % assms(2)
% 0.28/0.47 thf(fact_70_mult__cancel2,axiom,
% 0.28/0.47 ! [M: nat,K: nat,N: nat] :
% 0.28/0.47 ( ( ( times_times @ nat @ M @ K )
% 0.28/0.47 = ( times_times @ nat @ N @ K ) )
% 0.28/0.47 = ( ( M = N )
% 0.28/0.47 | ( K
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel2
% 0.28/0.47 thf(fact_71_mult__cancel1,axiom,
% 0.28/0.47 ! [K: nat,M: nat,N: nat] :
% 0.28/0.47 ( ( ( times_times @ nat @ K @ M )
% 0.28/0.47 = ( times_times @ nat @ K @ N ) )
% 0.28/0.47 = ( ( M = N )
% 0.28/0.47 | ( K
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_cancel1
% 0.28/0.47 thf(fact_72_mult__0__right,axiom,
% 0.28/0.47 ! [M: nat] :
% 0.28/0.47 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_0_right
% 0.28/0.47 thf(fact_73_mult__is__0,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( ( times_times @ nat @ M @ N )
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 = ( ( M
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 | ( N
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_is_0
% 0.28/0.47 thf(fact_74_nat__mult__eq__1__iff,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( ( times_times @ nat @ M @ N )
% 0.28/0.47 = ( one_one @ nat ) )
% 0.28/0.47 = ( ( M
% 0.28/0.47 = ( one_one @ nat ) )
% 0.28/0.47 & ( N
% 0.28/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_mult_eq_1_iff
% 0.28/0.47 thf(fact_75_nat__1__eq__mult__iff,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( ( one_one @ nat )
% 0.28/0.47 = ( times_times @ nat @ M @ N ) )
% 0.28/0.47 = ( ( M
% 0.28/0.47 = ( one_one @ nat ) )
% 0.28/0.47 & ( N
% 0.28/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_1_eq_mult_iff
% 0.28/0.47 thf(fact_76_relpowp__Suc__D2_H,axiom,
% 0.28/0.47 ! [A: $tType,N: nat,P: A > A > $o,X4: A,Y2: A,Z3: A] :
% 0.28/0.47 ( ( ( compow @ ( A > A > $o ) @ N @ P @ X4 @ Y2 )
% 0.28/0.47 & ( P @ Y2 @ Z3 ) )
% 0.28/0.47 => ? [W: A] :
% 0.28/0.47 ( ( P @ X4 @ W )
% 0.28/0.47 & ( compow @ ( A > A > $o ) @ N @ P @ W @ Z3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % relpowp_Suc_D2'
% 0.28/0.47 thf(fact_77_higher__deriv__transform__within__open,axiom,
% 0.28/0.47 ! [F: complex > complex,S: set @ complex,G2: complex > complex,Z: complex,I: nat] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S )
% 0.28/0.47 => ( ( comple372758642hic_on @ G2 @ S )
% 0.28/0.47 => ( ( topolo1751647064n_open @ complex @ S )
% 0.28/0.47 => ( ( member @ complex @ Z @ S )
% 0.28/0.47 => ( ! [W: complex] :
% 0.28/0.47 ( ( member @ complex @ W @ S )
% 0.28/0.47 => ( ( F @ W )
% 0.28/0.47 = ( G2 @ W ) ) )
% 0.28/0.47 => ( ( compow @ ( ( complex > complex ) > complex > complex ) @ I @ ( deriv @ complex ) @ F @ Z )
% 0.28/0.47 = ( compow @ ( ( complex > complex ) > complex > complex ) @ I @ ( deriv @ complex ) @ G2 @ Z ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % higher_deriv_transform_within_open
% 0.28/0.47 thf(fact_78_holomorphic__higher__deriv,axiom,
% 0.28/0.47 ! [F: complex > complex,S: set @ complex,N: nat] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S )
% 0.28/0.47 => ( ( topolo1751647064n_open @ complex @ S )
% 0.28/0.47 => ( comple372758642hic_on @ ( compow @ ( ( complex > complex ) > complex > complex ) @ N @ ( deriv @ complex ) @ F ) @ S ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_higher_deriv
% 0.28/0.47 thf(fact_79_holomorphic__deriv,axiom,
% 0.28/0.47 ! [F: complex > complex,S: set @ complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S )
% 0.28/0.47 => ( ( topolo1751647064n_open @ complex @ S )
% 0.28/0.47 => ( comple372758642hic_on @ ( deriv @ complex @ F ) @ S ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_deriv
% 0.28/0.47 thf(fact_80_mult__0,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_0
% 0.28/0.47 thf(fact_81_nat__mult__1__right,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 0.28/0.47 = N ) ).
% 0.28/0.47
% 0.28/0.47 % nat_mult_1_right
% 0.28/0.47 thf(fact_82_nat__mult__1,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 0.28/0.47 = N ) ).
% 0.28/0.47
% 0.28/0.47 % nat_mult_1
% 0.28/0.47 thf(fact_83_funpow__mult,axiom,
% 0.28/0.47 ! [A: $tType,N: nat,M: nat,F: A > A] :
% 0.28/0.47 ( ( compow @ ( A > A ) @ N @ ( compow @ ( A > A ) @ M @ F ) )
% 0.28/0.47 = ( compow @ ( A > A ) @ ( times_times @ nat @ M @ N ) @ F ) ) ).
% 0.28/0.47
% 0.28/0.47 % funpow_mult
% 0.28/0.47 thf(fact_84_mult__eq__self__implies__10,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( M
% 0.28/0.47 = ( times_times @ nat @ M @ N ) )
% 0.28/0.47 => ( ( N
% 0.28/0.47 = ( one_one @ nat ) )
% 0.28/0.47 | ( M
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_eq_self_implies_10
% 0.28/0.47 thf(fact_85_vector__space__over__itself_Oscale__left__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [A2: A,B2: A,X2: A] :
% 0.28/0.47 ( ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ X2 ) )
% 0.28/0.47 = ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_left_commute
% 0.28/0.47 thf(fact_86_vector__space__over__itself_Oscale__scale,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [A2: A,B2: A,X2: A] :
% 0.28/0.47 ( ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ X2 ) )
% 0.28/0.47 = ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_scale
% 0.28/0.47 thf(fact_87_set__times__elim,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( times @ A )
% 0.28/0.47 => ! [X2: A,A3: set @ A,B4: set @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( times_times @ ( set @ A ) @ A3 @ B4 ) )
% 0.28/0.47 => ~ ! [A5: A,B5: A] :
% 0.28/0.47 ( ( X2
% 0.28/0.47 = ( times_times @ A @ A5 @ B5 ) )
% 0.28/0.47 => ( ( member @ A @ A5 @ A3 )
% 0.28/0.47 => ~ ( member @ A @ B5 @ B4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_times_elim
% 0.28/0.47 thf(fact_88_relpowp__0__I,axiom,
% 0.28/0.47 ! [A: $tType,P: A > A > $o,X2: A] : ( compow @ ( A > A > $o ) @ ( zero_zero @ nat ) @ P @ X2 @ X2 ) ).
% 0.28/0.47
% 0.28/0.47 % relpowp_0_I
% 0.28/0.47 thf(fact_89_relpowp__0__E,axiom,
% 0.28/0.47 ! [A: $tType,P: A > A > $o,X2: A,Y: A] :
% 0.28/0.47 ( ( compow @ ( A > A > $o ) @ ( zero_zero @ nat ) @ P @ X2 @ Y )
% 0.28/0.47 => ( X2 = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % relpowp_0_E
% 0.28/0.47 thf(fact_90_relpowp_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,R: A > A > $o] :
% 0.28/0.47 ( ( compow @ ( A > A > $o ) @ ( zero_zero @ nat ) @ R )
% 0.28/0.47 = ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % relpowp.simps(1)
% 0.28/0.47 thf(fact_91_fun_Omap__comp,axiom,
% 0.28/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,G2: B > C,F: A > B,V: D > A] :
% 0.28/0.47 ( ( comp @ B @ C @ D @ G2 @ ( comp @ A @ B @ D @ F @ V ) )
% 0.28/0.47 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G2 @ F ) @ V ) ) ).
% 0.28/0.47
% 0.28/0.47 % fun.map_comp
% 0.28/0.47 thf(fact_92_vector__space__over__itself_Oscale__right__imp__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [X2: A,A2: A,B2: A] :
% 0.28/0.47 ( ( X2
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ( times_times @ A @ A2 @ X2 )
% 0.28/0.47 = ( times_times @ A @ B2 @ X2 ) )
% 0.28/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_right_imp_eq
% 0.28/0.47 thf(fact_93_vector__space__over__itself_Oscale__left__imp__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field @ A )
% 0.28/0.47 => ! [A2: A,X2: A,Y: A] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ( times_times @ A @ A2 @ X2 )
% 0.28/0.47 = ( times_times @ A @ A2 @ Y ) )
% 0.28/0.47 => ( X2 = Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % vector_space_over_itself.scale_left_imp_eq
% 0.28/0.47 thf(fact_94_fun_Omap__id0,axiom,
% 0.28/0.47 ! [A: $tType,D: $tType] :
% 0.28/0.47 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.28/0.47 = ( id @ ( D > A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fun.map_id0
% 0.28/0.47 thf(fact_95_complex__derivative__transform__within__open,axiom,
% 0.28/0.47 ! [F: complex > complex,S2: set @ complex,G2: complex > complex,Z: complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S2 )
% 0.28/0.47 => ( ( comple372758642hic_on @ G2 @ S2 )
% 0.28/0.47 => ( ( topolo1751647064n_open @ complex @ S2 )
% 0.28/0.47 => ( ( member @ complex @ Z @ S2 )
% 0.28/0.47 => ( ! [W: complex] :
% 0.28/0.47 ( ( member @ complex @ W @ S2 )
% 0.28/0.47 => ( ( F @ W )
% 0.28/0.47 = ( G2 @ W ) ) )
% 0.28/0.47 => ( ( deriv @ complex @ F @ Z )
% 0.28/0.47 = ( deriv @ complex @ G2 @ Z ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % complex_derivative_transform_within_open
% 0.28/0.47 thf(fact_96_holomorphic__on__id,axiom,
% 0.28/0.47 ! [S2: set @ complex] : ( comple372758642hic_on @ ( id @ complex ) @ S2 ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_on_id
% 0.28/0.47 thf(fact_97_relpowp__code__def,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( transitive_relpowp @ A )
% 0.28/0.47 = ( compow @ ( A > A > $o ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % relpowp_code_def
% 0.28/0.47 thf(fact_98_holomorphic__on__linear,axiom,
% 0.28/0.47 ! [C2: complex,S2: set @ complex] : ( comple372758642hic_on @ ( times_times @ complex @ C2 ) @ S2 ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_on_linear
% 0.28/0.47 thf(fact_99_pointfree__idE,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: B > A,G2: A > B,X2: A] :
% 0.28/0.47 ( ( ( comp @ B @ A @ A @ F @ G2 )
% 0.28/0.47 = ( id @ A ) )
% 0.28/0.47 => ( ( F @ ( G2 @ X2 ) )
% 0.28/0.47 = X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pointfree_idE
% 0.28/0.47 thf(fact_100_isomorphism__expand,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: B > A,G2: A > B] :
% 0.28/0.47 ( ( ( ( comp @ B @ A @ A @ F @ G2 )
% 0.28/0.47 = ( id @ A ) )
% 0.28/0.47 & ( ( comp @ A @ B @ B @ G2 @ F )
% 0.28/0.47 = ( id @ B ) ) )
% 0.28/0.47 = ( ! [X: A] :
% 0.28/0.47 ( ( F @ ( G2 @ X ) )
% 0.28/0.47 = X )
% 0.28/0.47 & ! [X: B] :
% 0.28/0.47 ( ( G2 @ ( F @ X ) )
% 0.28/0.47 = X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % isomorphism_expand
% 0.28/0.47 thf(fact_101_left__right__inverse__eq,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: B > A,G2: A > B,H: B > A] :
% 0.28/0.47 ( ( ( comp @ B @ A @ A @ F @ G2 )
% 0.28/0.47 = ( id @ A ) )
% 0.28/0.47 => ( ( ( comp @ A @ B @ B @ G2 @ H )
% 0.28/0.47 = ( id @ B ) )
% 0.28/0.47 => ( F = H ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % left_right_inverse_eq
% 0.28/0.47 thf(fact_102_rewriteL__comp__comp,axiom,
% 0.28/0.47 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G2: A > C,L: A > B,H: D > A] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ F @ G2 )
% 0.28/0.47 = L )
% 0.28/0.47 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G2 @ H ) )
% 0.28/0.47 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rewriteL_comp_comp
% 0.28/0.47 thf(fact_103_rewriteR__comp__comp,axiom,
% 0.28/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,G2: C > B,H: A > C,R2: A > B,F: B > D] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 0.28/0.47 = R2 )
% 0.28/0.47 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G2 ) @ H )
% 0.28/0.47 = ( comp @ B @ D @ A @ F @ R2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rewriteR_comp_comp
% 0.28/0.47 thf(fact_104_rewriteL__comp__comp2,axiom,
% 0.28/0.47 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G2: A > C,L1: D > B,L2: A > D,H: E > A,R2: E > D] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ F @ G2 )
% 0.28/0.47 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.28/0.47 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 0.28/0.47 = R2 )
% 0.28/0.47 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G2 @ H ) )
% 0.28/0.47 = ( comp @ D @ B @ E @ L1 @ R2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rewriteL_comp_comp2
% 0.28/0.47 thf(fact_105_rewriteR__comp__comp2,axiom,
% 0.28/0.47 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G2: C > B,H: A > C,R1: D > B,R22: A > D,F: B > E,L: D > E] :
% 0.28/0.47 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 0.28/0.47 = ( comp @ D @ B @ A @ R1 @ R22 ) )
% 0.28/0.47 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 0.28/0.47 = L )
% 0.28/0.47 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G2 ) @ H )
% 0.28/0.47 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rewriteR_comp_comp2
% 0.28/0.47 thf(fact_106_holomorphic__cong,axiom,
% 0.28/0.47 ! [S2: set @ complex,T: set @ complex,F: complex > complex,G2: complex > complex] :
% 0.28/0.47 ( ( S2 = T )
% 0.28/0.47 => ( ! [X3: complex] :
% 0.28/0.47 ( ( member @ complex @ X3 @ S2 )
% 0.28/0.47 => ( ( F @ X3 )
% 0.28/0.47 = ( G2 @ X3 ) ) )
% 0.28/0.47 => ( ( comple372758642hic_on @ F @ S2 )
% 0.28/0.47 = ( comple372758642hic_on @ G2 @ T ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_cong
% 0.28/0.47 thf(fact_107_holomorphic__transform,axiom,
% 0.28/0.47 ! [F: complex > complex,S2: set @ complex,G2: complex > complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S2 )
% 0.28/0.47 => ( ! [X3: complex] :
% 0.28/0.47 ( ( member @ complex @ X3 @ S2 )
% 0.28/0.47 => ( ( F @ X3 )
% 0.28/0.47 = ( G2 @ X3 ) ) )
% 0.28/0.47 => ( comple372758642hic_on @ G2 @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_transform
% 0.28/0.47 thf(fact_108_assms_I5_J,axiom,
% 0.28/0.47 ord_less_eq @ ( set @ complex ) @ ( image @ complex @ complex @ f @ s ) @ t ).
% 0.28/0.47
% 0.28/0.47 % assms(5)
% 0.28/0.47 thf(fact_109_nat__mult__eq__cancel__disj,axiom,
% 0.28/0.47 ! [K: nat,M: nat,N: nat] :
% 0.28/0.47 ( ( ( times_times @ nat @ K @ M )
% 0.28/0.47 = ( times_times @ nat @ K @ N ) )
% 0.28/0.47 = ( ( K
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 | ( M = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_mult_eq_cancel_disj
% 0.28/0.47 thf(fact_110_mult__delta__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( mult_zero @ A )
% 0.28/0.47 => ! [B2: $o,X2: A,Y: A] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 => ( ( times_times @ A @ ( if @ A @ B2 @ X2 @ ( zero_zero @ A ) ) @ Y )
% 0.28/0.47 = ( times_times @ A @ X2 @ Y ) ) )
% 0.28/0.47 & ( ~ B2
% 0.28/0.47 => ( ( times_times @ A @ ( if @ A @ B2 @ X2 @ ( zero_zero @ A ) ) @ Y )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_delta_left
% 0.28/0.47 thf(fact_111_mult__delta__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( mult_zero @ A )
% 0.28/0.47 => ! [B2: $o,X2: A,Y: A] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 => ( ( times_times @ A @ X2 @ ( if @ A @ B2 @ Y @ ( zero_zero @ A ) ) )
% 0.28/0.47 = ( times_times @ A @ X2 @ Y ) ) )
% 0.28/0.47 & ( ~ B2
% 0.28/0.47 => ( ( times_times @ A @ X2 @ ( if @ A @ B2 @ Y @ ( zero_zero @ A ) ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_delta_right
% 0.28/0.47 thf(fact_112_arcosh__1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ln @ A )
% 0.28/0.47 => ( ( arcosh @ A @ ( one_one @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % arcosh_1
% 0.28/0.47 thf(fact_113_le__zero__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [N: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.28/0.47 = ( N
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_zero_eq
% 0.28/0.47 thf(fact_114_image__id,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( image @ A @ A @ ( id @ A ) )
% 0.28/0.47 = ( id @ ( set @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_id
% 0.28/0.47 thf(fact_115_set__times__mono2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( times @ A )
% 0.28/0.47 => ! [C3: set @ A,D3: set @ A,E2: set @ A,F3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ E2 @ F3 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ ( times_times @ ( set @ A ) @ C3 @ E2 ) @ ( times_times @ ( set @ A ) @ D3 @ F3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_times_mono2
% 0.28/0.47 thf(fact_116_holomorphic__on__compose__gen,axiom,
% 0.28/0.47 ! [F: complex > complex,S2: set @ complex,G2: complex > complex,T: set @ complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S2 )
% 0.28/0.47 => ( ( comple372758642hic_on @ G2 @ T )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ complex ) @ ( image @ complex @ complex @ F @ S2 ) @ T )
% 0.28/0.47 => ( comple372758642hic_on @ ( comp @ complex @ complex @ complex @ G2 @ F ) @ S2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_on_compose_gen
% 0.28/0.47 thf(fact_117_image__comp,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,C: $tType,F: B > A,G2: C > B,R2: set @ C] :
% 0.28/0.47 ( ( image @ B @ A @ F @ ( image @ C @ B @ G2 @ R2 ) )
% 0.28/0.47 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G2 ) @ R2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_comp
% 0.28/0.47 thf(fact_118_image__eq__imp__comp,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A3: set @ B,G2: C > A,B4: set @ C,H: A > D] :
% 0.28/0.47 ( ( ( image @ B @ A @ F @ A3 )
% 0.28/0.47 = ( image @ C @ A @ G2 @ B4 ) )
% 0.28/0.47 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H @ F ) @ A3 )
% 0.28/0.47 = ( image @ C @ D @ ( comp @ A @ D @ C @ H @ G2 ) @ B4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eq_imp_comp
% 0.28/0.47 thf(fact_119_zero__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [X2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_le
% 0.28/0.47 thf(fact_120_holomorphic__on__subset,axiom,
% 0.28/0.47 ! [F: complex > complex,S2: set @ complex,T: set @ complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S2 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ complex ) @ T @ S2 )
% 0.28/0.47 => ( comple372758642hic_on @ F @ T ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_on_subset
% 0.28/0.47 thf(fact_121_set__times__mono2__b,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( times @ A )
% 0.28/0.47 => ! [C3: set @ A,D3: set @ A,E2: set @ A,F3: set @ A,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ E2 @ F3 )
% 0.28/0.47 => ( ( member @ A @ X2 @ ( times_times @ ( set @ A ) @ C3 @ E2 ) )
% 0.28/0.47 => ( member @ A @ X2 @ ( times_times @ ( set @ A ) @ D3 @ F3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_times_mono2_b
% 0.28/0.47 thf(fact_122_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere1490568538miring @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ C2 @ A2 ) @ ( times_times @ A @ C2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.28/0.47 thf(fact_123_zero__le__mult__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord581940658strict @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 0.28/0.47 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.28/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_le_mult_iff
% 0.28/0.47 thf(fact_124_mult__nonneg__nonpos2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring_0 @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_nonneg_nonpos2
% 0.28/0.47 thf(fact_125_mult__nonpos__nonneg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring_0 @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_nonpos_nonneg
% 0.28/0.47 thf(fact_126_mult__nonneg__nonpos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring_0 @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_nonneg_nonpos
% 0.28/0.47 thf(fact_127_mult__nonneg__nonneg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring_0 @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_nonneg_nonneg
% 0.28/0.47 thf(fact_128_split__mult__neg__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring_0 @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.28/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_mult_neg_le
% 0.28/0.47 thf(fact_129_mult__le__0__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord581940658strict @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.28/0.47 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.28/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_le_0_iff
% 0.28/0.47 thf(fact_130_mult__right__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_right_mono
% 0.28/0.47 thf(fact_131_mult__right__mono__neg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_ring @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_right_mono_neg
% 0.28/0.47 thf(fact_132_mult__left__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ C2 @ A2 ) @ ( times_times @ A @ C2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_left_mono
% 0.28/0.47 thf(fact_133_mult__nonpos__nonpos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_ring @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_nonpos_nonpos
% 0.28/0.47 thf(fact_134_mult__left__mono__neg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_ring @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ C2 @ A2 ) @ ( times_times @ A @ C2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_left_mono_neg
% 0.28/0.47 thf(fact_135_split__mult__pos__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_ring @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.28/0.47 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_mult_pos_le
% 0.28/0.47 thf(fact_136_zero__le__square,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_ring @ A )
% 0.28/0.47 => ! [A2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_le_square
% 0.28/0.47 thf(fact_137_mult__mono_H,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A,D2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C2 @ D2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ D2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_mono'
% 0.28/0.47 thf(fact_138_mult__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_semiring @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A,D2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C2 @ D2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ D2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_mono
% 0.28/0.47 thf(fact_139_zero__le__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_le_one
% 0.28/0.47 thf(fact_140_not__one__le__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_one_le_zero
% 0.28/0.47 thf(fact_141_holomorphic__on__compose,axiom,
% 0.28/0.47 ! [F: complex > complex,S2: set @ complex,G2: complex > complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S2 )
% 0.28/0.47 => ( ( comple372758642hic_on @ G2 @ ( image @ complex @ complex @ F @ S2 ) )
% 0.28/0.47 => ( comple372758642hic_on @ ( comp @ complex @ complex @ complex @ G2 @ F ) @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_on_compose
% 0.28/0.47 thf(fact_142_deriv__left__inverse,axiom,
% 0.28/0.47 ! [F: complex > complex,S: set @ complex,G2: complex > complex,T2: set @ complex,W2: complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S )
% 0.28/0.47 => ( ( comple372758642hic_on @ G2 @ T2 )
% 0.28/0.47 => ( ( topolo1751647064n_open @ complex @ S )
% 0.28/0.47 => ( ( topolo1751647064n_open @ complex @ T2 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ complex ) @ ( image @ complex @ complex @ F @ S ) @ T2 )
% 0.28/0.47 => ( ! [Z5: complex] :
% 0.28/0.47 ( ( member @ complex @ Z5 @ S )
% 0.28/0.47 => ( ( G2 @ ( F @ Z5 ) )
% 0.28/0.47 = Z5 ) )
% 0.28/0.47 => ( ( member @ complex @ W2 @ S )
% 0.28/0.47 => ( ( times_times @ complex @ ( deriv @ complex @ F @ W2 ) @ ( deriv @ complex @ G2 @ ( F @ W2 ) ) )
% 0.28/0.47 = ( one_one @ complex ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % deriv_left_inverse
% 0.28/0.47 thf(fact_143_mult__left__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ! [C2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ C2 @ ( one_one @ A ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_left_le
% 0.28/0.47 thf(fact_144_mult__le__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ ( one_one @ A ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ ( one_one @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( one_one @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_le_one
% 0.28/0.47 thf(fact_145_mult__right__le__one__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_idom @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ X2 @ Y ) @ X2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_right_le_one_le
% 0.28/0.47 thf(fact_146_mult__left__le__one__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_idom @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( times_times @ A @ Y @ X2 ) @ X2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_left_le_one_le
% 0.28/0.47 thf(fact_147_mult__eq__1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ( comm_monoid_mult @ A )
% 0.28/0.47 & ( ordered_semiring @ A ) )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ A2 @ ( one_one @ A ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ ( one_one @ A ) )
% 0.28/0.47 => ( ( ( times_times @ A @ A2 @ B2 )
% 0.28/0.47 = ( one_one @ A ) )
% 0.28/0.47 = ( ( A2
% 0.28/0.47 = ( one_one @ A ) )
% 0.28/0.47 & ( B2
% 0.28/0.47 = ( one_one @ A ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_eq_1
% 0.28/0.47 thf(fact_148_artanh__0,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ( real_V758409581_field @ A )
% 0.28/0.47 & ( ln @ A ) )
% 0.28/0.47 => ( ( artanh @ A @ ( zero_zero @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % artanh_0
% 0.28/0.47 thf(fact_149_arsinh__0,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ln @ A )
% 0.28/0.47 => ( ( arsinh @ A @ ( zero_zero @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % arsinh_0
% 0.28/0.47 thf(fact_150_subset__antisym,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 0.28/0.47 => ( A3 = B4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_151_image__eqI,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A3: set @ B] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( ( member @ B @ X2 @ A3 )
% 0.28/0.47 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_eqI
% 0.28/0.47 thf(fact_152_subsetI,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 => ( member @ A @ X3 @ B4 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_153_le0,axiom,
% 0.28/0.47 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.28/0.47
% 0.28/0.47 % le0
% 0.28/0.47 thf(fact_154_bot__nat__0_Oextremum,axiom,
% 0.28/0.47 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.28/0.47
% 0.28/0.47 % bot_nat_0.extremum
% 0.28/0.47 thf(fact_155_less__eq__nat_Osimps_I1_J,axiom,
% 0.28/0.47 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_nat.simps(1)
% 0.28/0.47 thf(fact_156_le__0__eq,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 0.28/0.47 = ( N
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_0_eq
% 0.28/0.47 thf(fact_157_bot__nat__0_Oextremum__unique,axiom,
% 0.28/0.47 ! [A2: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.28/0.47 = ( A2
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bot_nat_0.extremum_unique
% 0.28/0.47 thf(fact_158_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.28/0.47 ! [A2: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.28/0.47 => ( A2
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bot_nat_0.extremum_uniqueI
% 0.28/0.47 thf(fact_159_mult__le__mono2,axiom,
% 0.28/0.47 ! [I: nat,J: nat,K: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.28/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_le_mono2
% 0.28/0.47 thf(fact_160_mult__le__mono1,axiom,
% 0.28/0.47 ! [I: nat,J: nat,K: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.28/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_le_mono1
% 0.28/0.47 thf(fact_161_mult__le__mono,axiom,
% 0.28/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.28/0.47 => ( ( ord_less_eq @ nat @ K @ L )
% 0.28/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_le_mono
% 0.28/0.47 thf(fact_162_le__square,axiom,
% 0.28/0.47 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_square
% 0.28/0.47 thf(fact_163_le__cube,axiom,
% 0.28/0.47 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_cube
% 0.28/0.47 thf(fact_164_imageI,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,X2: A,A3: set @ A,F: A > B] :
% 0.28/0.47 ( ( member @ A @ X2 @ A3 )
% 0.28/0.47 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % imageI
% 0.28/0.47 thf(fact_165_image__iff,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,Z: A,F: B > A,A3: set @ B] :
% 0.28/0.47 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A3 ) )
% 0.28/0.47 = ( ? [X: B] :
% 0.28/0.47 ( ( member @ B @ X @ A3 )
% 0.28/0.47 & ( Z
% 0.28/0.47 = ( F @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_iff
% 0.28/0.47 thf(fact_166_bex__imageD,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P: A > $o] :
% 0.28/0.47 ( ? [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A3 ) )
% 0.28/0.47 & ( P @ X4 ) )
% 0.28/0.47 => ? [X3: B] :
% 0.28/0.47 ( ( member @ B @ X3 @ A3 )
% 0.28/0.47 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bex_imageD
% 0.28/0.47 thf(fact_167_image__cong,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,M2: set @ A,N2: set @ A,F: A > B,G2: A > B] :
% 0.28/0.47 ( ( M2 = N2 )
% 0.28/0.47 => ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ N2 )
% 0.28/0.47 => ( ( F @ X3 )
% 0.28/0.47 = ( G2 @ X3 ) ) )
% 0.28/0.47 => ( ( image @ A @ B @ F @ M2 )
% 0.28/0.47 = ( image @ A @ B @ G2 @ N2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_cong
% 0.28/0.47 thf(fact_168_ball__imageD,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P: A > $o] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A3 ) )
% 0.28/0.47 => ( P @ X3 ) )
% 0.28/0.47 => ! [X4: B] :
% 0.28/0.47 ( ( member @ B @ X4 @ A3 )
% 0.28/0.47 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ball_imageD
% 0.28/0.47 thf(fact_169_rev__image__eqI,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,X2: A,A3: set @ A,B2: B,F: A > B] :
% 0.28/0.47 ( ( member @ A @ X2 @ A3 )
% 0.28/0.47 => ( ( B2
% 0.28/0.47 = ( F @ X2 ) )
% 0.28/0.47 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_image_eqI
% 0.28/0.47 thf(fact_170_in__mono,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.28/0.47 => ( ( member @ A @ X2 @ A3 )
% 0.28/0.47 => ( member @ A @ X2 @ B4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_171_subsetD,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.28/0.47 => ( ( member @ A @ C2 @ A3 )
% 0.28/0.47 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_172_equalityE,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.28/0.47 ( ( A3 = B4 )
% 0.28/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.28/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_173_subset__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.28/0.47 ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ A6 )
% 0.28/0.47 => ( member @ A @ X @ B6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_174_equalityD1,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.28/0.47 ( ( A3 = B4 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_175_equalityD2,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.28/0.47 ( ( A3 = B4 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_176_subset__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.28/0.47 ! [T3: A] :
% 0.28/0.47 ( ( member @ A @ T3 @ A6 )
% 0.28/0.47 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_177_subset__refl,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_178_Collect__mono,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ( Q @ X3 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_179_subset__trans,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_180_set__eq__subset,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ^ [Y3: set @ A,Z4: set @ A] : ( Y3 = Z4 ) )
% 0.28/0.47 = ( ^ [A6: set @ A,B6: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 0.28/0.47 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_181_Collect__mono__iff,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.28/0.47 = ( ! [X: A] :
% 0.28/0.47 ( ( P @ X )
% 0.28/0.47 => ( Q @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_182_image__mono,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,A3: set @ A,B4: set @ A,F: A > B] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A3 ) @ ( image @ A @ B @ F @ B4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_mono
% 0.28/0.47 thf(fact_183_image__subsetI,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,A3: set @ A,F: A > B,B4: set @ B] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 => ( member @ B @ ( F @ X3 ) @ B4 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A3 ) @ B4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subsetI
% 0.28/0.47 thf(fact_184_subset__imageE,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,B4: set @ A,F: B > A,A3: set @ B] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A3 ) )
% 0.28/0.47 => ~ ! [C4: set @ B] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ B ) @ C4 @ A3 )
% 0.28/0.47 => ( B4
% 0.28/0.47 != ( image @ B @ A @ F @ C4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_imageE
% 0.28/0.47 thf(fact_185_image__subset__iff,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,B4: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ F @ A3 ) @ B4 )
% 0.28/0.47 = ( ! [X: B] :
% 0.28/0.47 ( ( member @ B @ X @ A3 )
% 0.28/0.47 => ( member @ A @ ( F @ X ) @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % image_subset_iff
% 0.28/0.47 thf(fact_186_subset__image__iff,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,B4: set @ A,F: B > A,A3: set @ B] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A3 ) )
% 0.28/0.47 = ( ? [AA: set @ B] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ B ) @ AA @ A3 )
% 0.28/0.47 & ( B4
% 0.28/0.47 = ( image @ B @ A @ F @ AA ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_image_iff
% 0.28/0.47 thf(fact_187_order__refl,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_refl
% 0.28/0.47 thf(fact_188_kuhn__labelling__lemma_H,axiom,
% 0.28/0.47 ! [P: ( nat > real ) > $o,F: ( nat > real ) > nat > real,Q: nat > $o] :
% 0.28/0.47 ( ! [X3: nat > real] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ( P @ ( F @ X3 ) ) )
% 0.28/0.47 => ( ! [X3: nat > real] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ! [I2: nat] :
% 0.28/0.47 ( ( Q @ I2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( X3 @ I2 ) )
% 0.28/0.47 & ( ord_less_eq @ real @ ( X3 @ I2 ) @ ( one_one @ real ) ) ) ) )
% 0.28/0.47 => ? [L3: ( nat > real ) > nat > nat] :
% 0.28/0.47 ( ! [X4: nat > real,I3: nat] : ( ord_less_eq @ nat @ ( L3 @ X4 @ I3 ) @ ( one_one @ nat ) )
% 0.28/0.47 & ! [X4: nat > real,I3: nat] :
% 0.28/0.47 ( ( ( P @ X4 )
% 0.28/0.47 & ( Q @ I3 )
% 0.28/0.47 & ( ( X4 @ I3 )
% 0.28/0.47 = ( zero_zero @ real ) ) )
% 0.28/0.47 => ( ( L3 @ X4 @ I3 )
% 0.28/0.47 = ( zero_zero @ nat ) ) )
% 0.28/0.47 & ! [X4: nat > real,I3: nat] :
% 0.28/0.47 ( ( ( P @ X4 )
% 0.28/0.47 & ( Q @ I3 )
% 0.28/0.47 & ( ( X4 @ I3 )
% 0.28/0.47 = ( one_one @ real ) ) )
% 0.28/0.47 => ( ( L3 @ X4 @ I3 )
% 0.28/0.47 = ( one_one @ nat ) ) )
% 0.28/0.47 & ! [X4: nat > real,I3: nat] :
% 0.28/0.47 ( ( ( P @ X4 )
% 0.28/0.47 & ( Q @ I3 )
% 0.28/0.47 & ( ( L3 @ X4 @ I3 )
% 0.28/0.47 = ( zero_zero @ nat ) ) )
% 0.28/0.47 => ( ord_less_eq @ real @ ( X4 @ I3 ) @ ( F @ X4 @ I3 ) ) )
% 0.28/0.47 & ! [X4: nat > real,I3: nat] :
% 0.28/0.47 ( ( ( P @ X4 )
% 0.28/0.47 & ( Q @ I3 )
% 0.28/0.47 & ( ( L3 @ X4 @ I3 )
% 0.28/0.47 = ( one_one @ nat ) ) )
% 0.28/0.47 => ( ord_less_eq @ real @ ( F @ X4 @ I3 ) @ ( X4 @ I3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % kuhn_labelling_lemma'
% 0.28/0.47 thf(fact_189_Sup_OSUP__id__eq,axiom,
% 0.28/0.47 ! [A: $tType,Sup: ( set @ A ) > A,A3: set @ A] :
% 0.28/0.47 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 0.28/0.47 = ( Sup @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sup.SUP_id_eq
% 0.28/0.47 thf(fact_190_le__refl,axiom,
% 0.28/0.47 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.28/0.47
% 0.28/0.47 % le_refl
% 0.28/0.47 thf(fact_191_le__trans,axiom,
% 0.28/0.47 ! [I: nat,J: nat,K: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.28/0.47 => ( ( ord_less_eq @ nat @ J @ K )
% 0.28/0.47 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_trans
% 0.28/0.47 thf(fact_192_eq__imp__le,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( M = N )
% 0.28/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_imp_le
% 0.28/0.47 thf(fact_193_le__antisym,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.28/0.47 => ( ( ord_less_eq @ nat @ N @ M )
% 0.28/0.47 => ( M = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_antisym
% 0.28/0.47 thf(fact_194_nat__le__linear,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.28/0.47 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_le_linear
% 0.28/0.47 thf(fact_195_Nat_Oex__has__greatest__nat,axiom,
% 0.28/0.47 ! [P: nat > $o,K: nat,B2: nat] :
% 0.28/0.47 ( ( P @ K )
% 0.28/0.47 => ( ! [Y4: nat] :
% 0.28/0.47 ( ( P @ Y4 )
% 0.28/0.47 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 0.28/0.47 => ? [X3: nat] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 & ! [Y2: nat] :
% 0.28/0.47 ( ( P @ Y2 )
% 0.28/0.47 => ( ord_less_eq @ nat @ Y2 @ X3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nat.ex_has_greatest_nat
% 0.28/0.47 thf(fact_196_dual__order_Oantisym,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [B2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.antisym
% 0.28/0.47 thf(fact_197_dual__order_Oeq__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 0.28/0.47 = ( ^ [A4: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.28/0.47 & ( ord_less_eq @ A @ A4 @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.eq_iff
% 0.28/0.47 thf(fact_198_dual__order_Otrans,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.28/0.47 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.trans
% 0.28/0.47 thf(fact_199_linorder__wlog,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.28/0.47 ( ! [A5: A,B5: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.28/0.47 => ( P @ A5 @ B5 ) )
% 0.28/0.47 => ( ! [A5: A,B5: A] :
% 0.28/0.47 ( ( P @ B5 @ A5 )
% 0.28/0.47 => ( P @ A5 @ B5 ) )
% 0.28/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linorder_wlog
% 0.28/0.47 thf(fact_200_dual__order_Orefl,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.refl
% 0.28/0.47 thf(fact_201_order__trans,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: A,Y: A,Z: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.28/0.47 => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_trans
% 0.28/0.47 thf(fact_202_order__class_Oorder_Oantisym,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.antisym
% 0.28/0.47 thf(fact_203_ord__le__eq__trans,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( B2 = C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_trans
% 0.28/0.47 thf(fact_204_ord__eq__le__trans,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( A2 = B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_trans
% 0.28/0.47 thf(fact_205_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 0.28/0.47 = ( ^ [A4: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.28/0.47 & ( ord_less_eq @ A @ B3 @ A4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.eq_iff
% 0.28/0.47 thf(fact_206_antisym__conv,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [Y: A,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ X2 @ Y )
% 0.28/0.47 = ( X2 = Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv
% 0.28/0.47 thf(fact_207_le__cases3,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ! [X2: A,Y: A,Z: A] :
% 0.28/0.47 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 0.28/0.47 => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_cases3
% 0.28/0.47 thf(fact_208_order_Otrans,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.trans
% 0.28/0.47 thf(fact_209_le__cases,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 0.28/0.47 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_cases
% 0.28/0.47 thf(fact_210_eq__refl,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( X2 = Y )
% 0.28/0.47 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_refl
% 0.28/0.47 thf(fact_211_linear,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.28/0.47 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linear
% 0.28/0.47 thf(fact_212_antisym,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Y @ X2 )
% 0.28/0.47 => ( X2 = Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym
% 0.28/0.47 thf(fact_213_eq__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 0.28/0.47 = ( ^ [X: A,Y5: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X @ Y5 )
% 0.28/0.47 & ( ord_less_eq @ A @ Y5 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_iff
% 0.28/0.47 thf(fact_214_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( ord @ B )
% 0.28/0.47 & ( ord @ A ) )
% 0.28/0.47 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ( F @ B2 )
% 0.28/0.47 = C2 )
% 0.28/0.47 => ( ! [X3: A,Y4: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_215_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( ord @ B )
% 0.28/0.47 & ( ord @ A ) )
% 0.28/0.47 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.28/0.47 => ( ! [X3: B,Y4: B] :
% 0.28/0.47 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_216_order__subst2,axiom,
% 0.28/0.47 ! [A: $tType,C: $tType] :
% 0.28/0.47 ( ( ( order @ C )
% 0.28/0.47 & ( order @ A ) )
% 0.28/0.47 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 0.28/0.47 => ( ! [X3: A,Y4: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.28/0.47 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_217_order__subst1,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( order @ B )
% 0.28/0.47 & ( order @ A ) )
% 0.28/0.47 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.28/0.47 => ( ! [X3: B,Y4: B] :
% 0.28/0.47 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_218_le__fun__def,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.28/0.47 = ( ^ [F2: A > B,G: A > B] :
% 0.28/0.47 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_fun_def
% 0.28/0.47 thf(fact_219_le__funI,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ! [F: A > B,G2: A > B] :
% 0.28/0.47 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G2 @ X3 ) )
% 0.28/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_funI
% 0.28/0.47 thf(fact_220_le__funE,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ! [F: A > B,G2: A > B,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_funE
% 0.28/0.47 thf(fact_221_le__funD,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ! [F: A > B,G2: A > B,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_funD
% 0.28/0.47 thf(fact_222_Sup_OSUP__cong,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C3: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 0.28/0.47 ( ( A3 = B4 )
% 0.28/0.47 => ( ! [X3: B] :
% 0.28/0.47 ( ( member @ B @ X3 @ B4 )
% 0.28/0.47 => ( ( C3 @ X3 )
% 0.28/0.47 = ( D3 @ X3 ) ) )
% 0.28/0.47 => ( ( Sup @ ( image @ B @ A @ C3 @ A3 ) )
% 0.28/0.47 = ( Sup @ ( image @ B @ A @ D3 @ B4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sup.SUP_cong
% 0.28/0.47 thf(fact_223_Inf_OINF__cong,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C3: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 0.28/0.47 ( ( A3 = B4 )
% 0.28/0.47 => ( ! [X3: B] :
% 0.28/0.47 ( ( member @ B @ X3 @ B4 )
% 0.28/0.47 => ( ( C3 @ X3 )
% 0.28/0.47 = ( D3 @ X3 ) ) )
% 0.28/0.47 => ( ( Inf @ ( image @ B @ A @ C3 @ A3 ) )
% 0.28/0.47 = ( Inf @ ( image @ B @ A @ D3 @ B4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Inf.INF_cong
% 0.28/0.47 thf(fact_224_Inf_OINF__image,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G2: B > A,F: C > B,A3: set @ C] :
% 0.28/0.47 ( ( Inf @ ( image @ B @ A @ G2 @ ( image @ C @ B @ F @ A3 ) ) )
% 0.28/0.47 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G2 @ F ) @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Inf.INF_image
% 0.28/0.47 thf(fact_225_Sup_OSUP__image,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G2: B > A,F: C > B,A3: set @ C] :
% 0.28/0.47 ( ( Sup @ ( image @ B @ A @ G2 @ ( image @ C @ B @ F @ A3 ) ) )
% 0.28/0.47 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G2 @ F ) @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Sup.SUP_image
% 0.28/0.47 thf(fact_226_Inf_OINF__id__eq,axiom,
% 0.28/0.47 ! [A: $tType,Inf: ( set @ A ) > A,A3: set @ A] :
% 0.28/0.47 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 0.28/0.47 = ( Inf @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Inf.INF_id_eq
% 0.28/0.47 thf(fact_227_topological__space__class_OopenI,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topolo503727757_space @ A )
% 0.28/0.47 => ! [S: set @ A] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ S )
% 0.28/0.47 => ? [T4: set @ A] :
% 0.28/0.47 ( ( topolo1751647064n_open @ A @ T4 )
% 0.28/0.47 & ( member @ A @ X3 @ T4 )
% 0.28/0.47 & ( ord_less_eq @ ( set @ A ) @ T4 @ S ) ) )
% 0.28/0.47 => ( topolo1751647064n_open @ A @ S ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % topological_space_class.openI
% 0.28/0.47 thf(fact_228_open__subopen,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topolo503727757_space @ A )
% 0.28/0.47 => ( ( topolo1751647064n_open @ A )
% 0.28/0.47 = ( ^ [S3: set @ A] :
% 0.28/0.47 ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ S3 )
% 0.28/0.47 => ? [T5: set @ A] :
% 0.28/0.47 ( ( topolo1751647064n_open @ A @ T5 )
% 0.28/0.47 & ( member @ A @ X @ T5 )
% 0.28/0.47 & ( ord_less_eq @ ( set @ A ) @ T5 @ S3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % open_subopen
% 0.28/0.47 thf(fact_229_t0__space,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topological_t0_space @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( X2 != Y )
% 0.28/0.47 => ? [U: set @ A] :
% 0.28/0.47 ( ( topolo1751647064n_open @ A @ U )
% 0.28/0.47 & ( ( member @ A @ X2 @ U )
% 0.28/0.47 != ( member @ A @ Y @ U ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % t0_space
% 0.28/0.47 thf(fact_230_t1__space,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topological_t1_space @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( X2 != Y )
% 0.28/0.47 => ? [U: set @ A] :
% 0.28/0.47 ( ( topolo1751647064n_open @ A @ U )
% 0.28/0.47 & ( member @ A @ X2 @ U )
% 0.28/0.47 & ~ ( member @ A @ Y @ U ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % t1_space
% 0.28/0.47 thf(fact_231_separation__t0,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topological_t0_space @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( X2 != Y )
% 0.28/0.47 = ( ? [U2: set @ A] :
% 0.28/0.47 ( ( topolo1751647064n_open @ A @ U2 )
% 0.28/0.47 & ( ( member @ A @ X2 @ U2 )
% 0.28/0.47 != ( member @ A @ Y @ U2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % separation_t0
% 0.28/0.47 thf(fact_232_separation__t1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topological_t1_space @ A )
% 0.28/0.47 => ! [X2: A,Y: A] :
% 0.28/0.47 ( ( X2 != Y )
% 0.28/0.47 = ( ? [U2: set @ A] :
% 0.28/0.47 ( ( topolo1751647064n_open @ A @ U2 )
% 0.28/0.47 & ( member @ A @ X2 @ U2 )
% 0.28/0.47 & ~ ( member @ A @ Y @ U2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % separation_t1
% 0.28/0.47 thf(fact_233_open__discrete,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topolo2133971006pology @ A )
% 0.28/0.47 => ! [A3: set @ A] : ( topolo1751647064n_open @ A @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % open_discrete
% 0.28/0.47 thf(fact_234_first__countable__basis,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( topolo2135403230pology @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ? [A7: nat > ( set @ A )] :
% 0.28/0.47 ( ! [I3: nat] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( A7 @ I3 ) )
% 0.28/0.47 & ( topolo1751647064n_open @ A @ ( A7 @ I3 ) ) )
% 0.28/0.47 & ! [S4: set @ A] :
% 0.28/0.47 ( ( ( topolo1751647064n_open @ A @ S4 )
% 0.28/0.47 & ( member @ A @ X2 @ S4 ) )
% 0.28/0.47 => ? [I2: nat] : ( ord_less_eq @ ( set @ A ) @ ( A7 @ I2 ) @ S4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % first_countable_basis
% 0.28/0.47 thf(fact_235_landau__omega_OR__mult__right__mono,axiom,
% 0.28/0.47 ! [B2: real,A2: real,C2: real] :
% 0.28/0.47 ( ( ord_less_eq @ real @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ real @ ( times_times @ real @ B2 @ C2 ) @ ( times_times @ real @ A2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_omega.R_mult_right_mono
% 0.28/0.47 thf(fact_236_landau__omega_OR__mult__left__mono,axiom,
% 0.28/0.47 ! [B2: real,A2: real,C2: real] :
% 0.28/0.47 ( ( ord_less_eq @ real @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ real @ ( times_times @ real @ C2 @ B2 ) @ ( times_times @ real @ C2 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_omega.R_mult_left_mono
% 0.28/0.47 thf(fact_237_landau__omega_OR__linear,axiom,
% 0.28/0.47 ! [Y: real,X2: real] :
% 0.28/0.47 ( ~ ( ord_less_eq @ real @ Y @ X2 )
% 0.28/0.47 => ( ord_less_eq @ real @ X2 @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_omega.R_linear
% 0.28/0.47 thf(fact_238_landau__omega_OR__trans,axiom,
% 0.28/0.47 ! [B2: real,A2: real,C2: real] :
% 0.28/0.47 ( ( ord_less_eq @ real @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ C2 @ B2 )
% 0.28/0.47 => ( ord_less_eq @ real @ C2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_omega.R_trans
% 0.28/0.47 thf(fact_239_landau__omega_OR__refl,axiom,
% 0.28/0.47 ! [X2: real] : ( ord_less_eq @ real @ X2 @ X2 ) ).
% 0.28/0.47
% 0.28/0.47 % landau_omega.R_refl
% 0.28/0.47 thf(fact_240_landau__o_OR__linear,axiom,
% 0.28/0.47 ! [X2: real,Y: real] :
% 0.28/0.47 ( ~ ( ord_less_eq @ real @ X2 @ Y )
% 0.28/0.47 => ( ord_less_eq @ real @ Y @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_o.R_linear
% 0.28/0.47 thf(fact_241_landau__o_OR__trans,axiom,
% 0.28/0.47 ! [A2: real,B2: real,C2: real] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ B2 @ C2 )
% 0.28/0.47 => ( ord_less_eq @ real @ A2 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_o.R_trans
% 0.28/0.47 thf(fact_242_landau__o_OR__mult__left__mono,axiom,
% 0.28/0.47 ! [A2: real,B2: real,C2: real] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ real @ ( times_times @ real @ C2 @ A2 ) @ ( times_times @ real @ C2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_o.R_mult_left_mono
% 0.28/0.47 thf(fact_243_landau__o_OR__mult__right__mono,axiom,
% 0.28/0.47 ! [A2: real,B2: real,C2: real] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 0.28/0.47 => ( ord_less_eq @ real @ ( times_times @ real @ A2 @ C2 ) @ ( times_times @ real @ B2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % landau_o.R_mult_right_mono
% 0.28/0.47 thf(fact_244_all__subset__image,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P: ( set @ A ) > $o] :
% 0.28/0.47 ( ( ! [B6: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ B6 @ ( image @ B @ A @ F @ A3 ) )
% 0.28/0.47 => ( P @ B6 ) ) )
% 0.28/0.47 = ( ! [B6: set @ B] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ B ) @ B6 @ A3 )
% 0.28/0.47 => ( P @ ( image @ B @ A @ F @ B6 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_subset_image
% 0.28/0.47 thf(fact_245_le__numeral__extra_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_numeral_extra(4)
% 0.28/0.47 thf(fact_246_le__numeral__extra_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_numeral_extra(3)
% 0.28/0.47 thf(fact_247_dbl__inc__simps_I2_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( neg_numeral @ A )
% 0.28/0.47 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 0.28/0.47 = ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dbl_inc_simps(2)
% 0.28/0.47 thf(fact_248_ln__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ln @ A )
% 0.28/0.47 => ( ( ln_ln @ A @ ( one_one @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ln_one
% 0.28/0.47 thf(fact_249_ln__ge__zero,axiom,
% 0.28/0.47 ! [X2: real] :
% 0.28/0.47 ( ( ord_less_eq @ real @ ( one_one @ real ) @ X2 )
% 0.28/0.47 => ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ln_ge_zero
% 0.28/0.47 thf(fact_250_Ln__1,axiom,
% 0.28/0.47 ( ( ln_ln @ complex @ ( one_one @ complex ) )
% 0.28/0.47 = ( zero_zero @ complex ) ) ).
% 0.28/0.47
% 0.28/0.47 % Ln_1
% 0.28/0.47 thf(fact_251_fps__tan__0,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( field_char_0 @ A )
% 0.28/0.47 => ( ( formal_Power_fps_tan @ A @ ( zero_zero @ A ) )
% 0.28/0.47 = ( zero_zero @ ( formal_Power_fps @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fps_tan_0
% 0.28/0.47 thf(fact_252_holomorphic__fun__eq__0__on__connected,axiom,
% 0.28/0.47 ! [F: complex > complex,S: set @ complex,Z: complex,W2: complex] :
% 0.28/0.47 ( ( comple372758642hic_on @ F @ S )
% 0.28/0.47 => ( ( topolo1751647064n_open @ complex @ S )
% 0.28/0.47 => ( ( topolo1099314120nected @ complex @ S )
% 0.28/0.47 => ( ! [N3: nat] :
% 0.28/0.47 ( ( compow @ ( ( complex > complex ) > complex > complex ) @ N3 @ ( deriv @ complex ) @ F @ Z )
% 0.28/0.47 = ( zero_zero @ complex ) )
% 0.28/0.47 => ( ( member @ complex @ Z @ S )
% 0.28/0.47 => ( ( member @ complex @ W2 @ S )
% 0.28/0.47 => ( ( F @ W2 )
% 0.28/0.47 = ( zero_zero @ complex ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % holomorphic_fun_eq_0_on_connected
% 0.28/0.47
% 0.28/0.47 % Type constructors (163)
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Real__Vector__Spaces_Ometric__space,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( group_add @ A8 )
% 0.28/0.47 => ( real_V2090557954_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Ogroup__add,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( group_add @ A8 )
% 0.28/0.47 => ( group_add @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocancel__semigroup__add,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( cancel_semigroup_add @ A8 )
% 0.28/0.47 => ( cancel_semigroup_add @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Ocomm__semiring__0,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_semiring_0 @ A8 )
% 0.28/0.47 => ( comm_semiring_0 @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__0,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semiring_0 @ A8 )
% 0.28/0.47 => ( semiring_0 @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__1,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semiring_1 @ A8 )
% 0.28/0.47 => ( semiring_1 @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocomm__monoid__add,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A8 )
% 0.28/0.47 => ( comm_monoid_add @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Oring__1,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ring_1 @ A8 )
% 0.28/0.47 => ( ring_1 @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Real__Vector__Spaces_Ometric__space_1,axiom,
% 0.28/0.47 real_V2090557954_space @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Ogroup__add_2,axiom,
% 0.28/0.47 group_add @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Ocancel__semigroup__add_3,axiom,
% 0.28/0.47 cancel_semigroup_add @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Ocomm__semiring__0_4,axiom,
% 0.28/0.47 comm_semiring_0 @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Osemiring__0_5,axiom,
% 0.28/0.47 semiring_0 @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Osemiring__1_6,axiom,
% 0.28/0.47 semiring_1 @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Ocomm__monoid__add_7,axiom,
% 0.28/0.47 comm_monoid_add @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Oring__1_8,axiom,
% 0.28/0.47 ring_1 @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_9,axiom,
% 0.28/0.47 real_V2090557954_space @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ogroup__add_10,axiom,
% 0.28/0.47 group_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_11,axiom,
% 0.28/0.47 cancel_semigroup_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__0_12,axiom,
% 0.28/0.47 comm_semiring_0 @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Osemiring__0_13,axiom,
% 0.28/0.47 semiring_0 @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Osemiring__1_14,axiom,
% 0.28/0.47 semiring_1 @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_15,axiom,
% 0.28/0.47 comm_monoid_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Oring__1_16,axiom,
% 0.28/0.47 ring_1 @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Countable_Ocountable,axiom,
% 0.28/0.47 countable @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Countable_Ocountable_17,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( finite_finite @ A8 )
% 0.28/0.47 => ( countable @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add_18,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A8 )
% 0.28/0.47 => ( comm_monoid_add @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Countable_Ocountable_19,axiom,
% 0.28/0.47 countable @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add_20,axiom,
% 0.28/0.47 cancel_semigroup_add @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0_21,axiom,
% 0.28/0.47 comm_semiring_0 @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Osemiring__0_22,axiom,
% 0.28/0.47 semiring_0 @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Osemiring__1_23,axiom,
% 0.28/0.47 semiring_1 @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_24,axiom,
% 0.28/0.47 comm_monoid_add @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Countable_Ocountable_25,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( finite_finite @ A8 )
% 0.28/0.47 & ( countable @ A9 ) )
% 0.28/0.47 => ( countable @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Real__Vector__Spaces_Ometric__space_26,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( countable @ A8 )
% 0.28/0.47 & ( real_V2090557954_space @ A9 ) )
% 0.28/0.47 => ( real_V2090557954_space @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( finite_finite @ A8 )
% 0.28/0.47 & ( finite_finite @ A9 ) )
% 0.28/0.47 => ( finite_finite @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Finite__Set_Ofinite_27,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( finite_finite @ A8 )
% 0.28/0.47 => ( finite_finite @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Finite__Set_Ofinite_28,axiom,
% 0.28/0.47 finite_finite @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Topological__Spaces_Ofirst__countable__topology,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( countable @ A8 )
% 0.28/0.47 & ( topolo2135403230pology @ A9 ) )
% 0.28/0.47 => ( topolo2135403230pology @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( topolo503727757_space @ A9 )
% 0.28/0.47 => ( topolo503727757_space @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Topological__Spaces_Ot1__space,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( countable @ A8 )
% 0.28/0.47 & ( real_V2090557954_space @ A9 ) )
% 0.28/0.47 => ( topological_t1_space @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Topological__Spaces_Ot0__space,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( countable @ A8 )
% 0.28/0.47 & ( real_V2090557954_space @ A9 ) )
% 0.28/0.47 => ( topological_t0_space @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( preorder @ A9 )
% 0.28/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( order @ A9 )
% 0.28/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ord @ A9 )
% 0.28/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Ofirst__countable__topology_29,axiom,
% 0.28/0.47 topolo2135403230pology @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 0.28/0.47 semiri1923998003cancel @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.28/0.47 canoni770627133id_add @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Otopological__space_30,axiom,
% 0.28/0.47 topolo503727757_space @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Odiscrete__topology,axiom,
% 0.28/0.47 topolo2133971006pology @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.28/0.47 linord1659791738miring @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 0.28/0.47 semiri1193490041visors @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Ot1__space_31,axiom,
% 0.28/0.47 topological_t1_space @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Ot0__space_32,axiom,
% 0.28/0.47 topological_t0_space @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
% 0.28/0.47 ordere1490568538miring @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0,axiom,
% 0.28/0.47 ordered_semiring_0 @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.28/0.47 ab_semigroup_mult @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.28/0.47 comm_monoid_mult @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Oordered__semiring,axiom,
% 0.28/0.47 ordered_semiring @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.28/0.47 comm_semiring_1 @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.28/0.47 semigroup_mult @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.28/0.47 zero_neq_one @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_33,axiom,
% 0.28/0.47 preorder @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.28/0.47 linorder @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.28/0.47 monoid_mult @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 0.28/0.47 mult_zero @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_34,axiom,
% 0.28/0.47 order @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Orderings_Oord_35,axiom,
% 0.28/0.47 ord @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Otimes,axiom,
% 0.28/0.47 times @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.28/0.47 zero @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.28/0.47 one @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Oab__semigroup__mult_36,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ab_semigroup_mult @ A8 )
% 0.28/0.47 => ( ab_semigroup_mult @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Ocomm__monoid__mult_37,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_monoid_mult @ A8 )
% 0.28/0.47 => ( comm_monoid_mult @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Osemigroup__mult_38,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semigroup_mult @ A8 )
% 0.28/0.47 => ( semigroup_mult @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_39,axiom,
% 0.28/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Omonoid__mult_40,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( monoid_mult @ A8 )
% 0.28/0.47 => ( monoid_mult @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Oorder_41,axiom,
% 0.28/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Oord_42,axiom,
% 0.28/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Otimes_43,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( times @ A8 )
% 0.28/0.47 => ( times @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Ozero_44,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( zero @ A8 )
% 0.28/0.47 => ( zero @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Oone_45,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( one @ A8 )
% 0.28/0.47 => ( one @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_46,axiom,
% 0.28/0.47 topolo503727757_space @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology_47,axiom,
% 0.28/0.47 topolo2133971006pology @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Topological__Spaces_Ot1__space_48,axiom,
% 0.28/0.47 topological_t1_space @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Topological__Spaces_Ot0__space_49,axiom,
% 0.28/0.47 topological_t0_space @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_50,axiom,
% 0.28/0.47 preorder @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_51,axiom,
% 0.28/0.47 linorder @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_52,axiom,
% 0.28/0.47 order @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Oord_53,axiom,
% 0.28/0.47 ord @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Topological__Spaces_Ofirst__countable__topology_54,axiom,
% 0.28/0.47 topolo2135403230pology @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors__cancel_55,axiom,
% 0.28/0.47 semiri1923998003cancel @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_56,axiom,
% 0.28/0.47 topolo503727757_space @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__field,axiom,
% 0.28/0.47 real_V758409581_field @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_57,axiom,
% 0.28/0.47 linord1659791738miring @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors_58,axiom,
% 0.28/0.47 semiri1193490041visors @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Oring__1__no__zero__divisors,axiom,
% 0.28/0.47 ring_11004092258visors @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__ring__strict,axiom,
% 0.28/0.47 linord581940658strict @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Topological__Spaces_Ot1__space_59,axiom,
% 0.28/0.47 topological_t1_space @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Topological__Spaces_Ot0__space_60,axiom,
% 0.28/0.47 topological_t0_space @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Oordered__comm__semiring_61,axiom,
% 0.28/0.47 ordere1490568538miring @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Oordered__semiring__0_62,axiom,
% 0.28/0.47 ordered_semiring_0 @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oab__semigroup__mult_63,axiom,
% 0.28/0.47 ab_semigroup_mult @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__mult_64,axiom,
% 0.28/0.47 comm_monoid_mult @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Oordered__semiring_65,axiom,
% 0.28/0.47 ordered_semiring @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__ring,axiom,
% 0.28/0.47 linordered_ring @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.28/0.47 linordered_idom @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_66,axiom,
% 0.28/0.47 comm_semiring_1 @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Osemigroup__mult_67,axiom,
% 0.28/0.47 semigroup_mult @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Fields_Ofield__char__0,axiom,
% 0.28/0.47 field_char_0 @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_68,axiom,
% 0.28/0.47 zero_neq_one @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Oordered__ring,axiom,
% 0.28/0.47 ordered_ring @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Opreorder_69,axiom,
% 0.28/0.47 preorder @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Olinorder_70,axiom,
% 0.28/0.47 linorder @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Omonoid__mult_71,axiom,
% 0.28/0.47 monoid_mult @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Transcendental_Oln,axiom,
% 0.28/0.47 ln @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Omult__zero_72,axiom,
% 0.28/0.47 mult_zero @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Oorder_73,axiom,
% 0.28/0.47 order @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.28/0.47 neg_numeral @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Oord_74,axiom,
% 0.28/0.47 ord @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Otimes_75,axiom,
% 0.28/0.47 times @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Fields_Ofield,axiom,
% 0.28/0.47 field @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ozero_76,axiom,
% 0.28/0.47 zero @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oone_77,axiom,
% 0.28/0.47 one @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ofirst__countable__topology_78,axiom,
% 0.28/0.47 topolo2135403230pology @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Osemiring__no__zero__divisors__cancel_79,axiom,
% 0.28/0.47 semiri1923998003cancel @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Topological__Spaces_Otopological__space_80,axiom,
% 0.28/0.47 topolo503727757_space @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__field_81,axiom,
% 0.28/0.47 real_V758409581_field @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Osemiring__no__zero__divisors_82,axiom,
% 0.28/0.47 semiri1193490041visors @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors_83,axiom,
% 0.28/0.47 ring_11004092258visors @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ot1__space_84,axiom,
% 0.28/0.47 topological_t1_space @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ot0__space_85,axiom,
% 0.28/0.47 topological_t0_space @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Oab__semigroup__mult_86,axiom,
% 0.28/0.47 ab_semigroup_mult @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Ocomm__monoid__mult_87,axiom,
% 0.28/0.47 comm_monoid_mult @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Ocomm__semiring__1_88,axiom,
% 0.28/0.47 comm_semiring_1 @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Osemigroup__mult_89,axiom,
% 0.28/0.47 semigroup_mult @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Fields_Ofield__char__0_90,axiom,
% 0.28/0.47 field_char_0 @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Ozero__neq__one_91,axiom,
% 0.28/0.47 zero_neq_one @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Omonoid__mult_92,axiom,
% 0.28/0.47 monoid_mult @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Transcendental_Oln_93,axiom,
% 0.28/0.47 ln @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Rings_Omult__zero_94,axiom,
% 0.28/0.47 mult_zero @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Num_Oneg__numeral_95,axiom,
% 0.28/0.47 neg_numeral @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Otimes_96,axiom,
% 0.28/0.47 times @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Fields_Ofield_97,axiom,
% 0.28/0.47 field @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Ozero_98,axiom,
% 0.28/0.47 zero @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Complex_Ocomplex___Groups_Oone_99,axiom,
% 0.28/0.47 one @ complex ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ofirst__countable__topology_100,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( group_add @ A8 )
% 0.28/0.47 => ( topolo2135403230pology @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__no__zero__divisors__cancel_101,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ( cancel_semigroup_add @ A8 )
% 0.28/0.47 & ( semiri1923998003cancel @ A8 ) )
% 0.28/0.47 => ( semiri1923998003cancel @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Otopological__space_102,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( group_add @ A8 )
% 0.28/0.47 => ( topolo503727757_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__no__zero__divisors_103,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semiri1193490041visors @ A8 )
% 0.28/0.47 => ( semiri1193490041visors @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Oring__1__no__zero__divisors_104,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ring_11004092258visors @ A8 )
% 0.28/0.47 => ( ring_11004092258visors @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ot1__space_105,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( group_add @ A8 )
% 0.28/0.47 => ( topological_t1_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ot0__space_106,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( group_add @ A8 )
% 0.28/0.47 => ( topological_t0_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Oab__semigroup__mult_107,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_semiring_0 @ A8 )
% 0.28/0.47 => ( ab_semigroup_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocomm__monoid__mult_108,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_semiring_1 @ A8 )
% 0.28/0.47 => ( comm_monoid_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Ocomm__semiring__1_109,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_semiring_1 @ A8 )
% 0.28/0.47 => ( comm_semiring_1 @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Osemigroup__mult_110,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semiring_0 @ A8 )
% 0.28/0.47 => ( semigroup_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Ozero__neq__one_111,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( zero_neq_one @ A8 )
% 0.28/0.47 => ( zero_neq_one @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Omonoid__mult_112,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semiring_1 @ A8 )
% 0.28/0.47 => ( monoid_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Rings_Omult__zero_113,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ( comm_monoid_add @ A8 )
% 0.28/0.47 & ( mult_zero @ A8 ) )
% 0.28/0.47 => ( mult_zero @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Num_Oneg__numeral_114,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ring_1 @ A8 )
% 0.28/0.47 => ( neg_numeral @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Formal__Power__Series_Ofps___Groups_Otimes_115,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ( comm_monoid_add @ A8 )
% 0.28/0.47 & ( times @ A8 ) )
% 0.28/0.48 => ( times @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(tcon_Formal__Power__Series_Ofps___Groups_Ozero_116,axiom,
% 0.28/0.48 ! [A8: $tType] :
% 0.28/0.48 ( ( zero @ A8 )
% 0.28/0.48 => ( zero @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(tcon_Formal__Power__Series_Ofps___Groups_Oone_117,axiom,
% 0.28/0.48 ! [A8: $tType] :
% 0.28/0.48 ( ( ( one @ A8 )
% 0.28/0.48 & ( zero @ A8 ) )
% 0.28/0.48 => ( one @ ( formal_Power_fps @ A8 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % Helper facts (3)
% 0.28/0.48 thf(help_If_3_1_T,axiom,
% 0.28/0.48 ! [P: $o] :
% 0.28/0.48 ( ( P = $true )
% 0.28/0.48 | ( P = $false ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(help_If_2_1_T,axiom,
% 0.28/0.48 ! [A: $tType,X2: A,Y: A] :
% 0.28/0.48 ( ( if @ A @ $false @ X2 @ Y )
% 0.28/0.48 = Y ) ).
% 0.28/0.48
% 0.28/0.48 thf(help_If_1_1_T,axiom,
% 0.28/0.48 ! [A: $tType,X2: A,Y: A] :
% 0.28/0.48 ( ( if @ A @ $true @ X2 @ Y )
% 0.28/0.48 = X2 ) ).
% 0.28/0.48
% 0.28/0.48 % Conjectures (1)
% 0.28/0.48 thf(conj_0,conjecture,
% 0.28/0.48 ( ( deriv @ complex @ ( id @ complex ) @ w )
% 0.28/0.48 = ( one_one @ complex ) ) ).
% 0.28/0.48
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 ------------------------
% 2.66/1.52 ---- Embedded in THF ---
% 2.66/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.66/1.52 %%% Generated on Tue Feb 24 08:24:28 EST 2026
% 2.66/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.66/1.52 %%% Logic specification used:
% 2.66/1.52 %%% thf(spec, logic, $$dhol).
% 2.66/1.52
% 2.66/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.opwukp64f0/DTF2DTF11704.p
% 2.66/1.52 thf(ty_t_Formal__Power__Series_Ofps, type, formal_Power_fps: ($tType > $tType)).
% 2.66/1.52 thf(ty_t_Complex_Ocomplex, type, complex: $tType).
% 2.66/1.52 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.66/1.52 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.66/1.52 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.66/1.52 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Osemiring__1, type, semiring_1: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Osemiring__0, type, semiring_0: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Ocomm__semiring__0, type, comm_semiring_0: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Real__Vector__Spaces_Ometric__space, type, real_V2090557954_space: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Countable_Ocountable, type, countable: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Fields_Ofield, type, field: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Otimes, type, times: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Omult__zero, type, mult_zero: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Transcendental_Oln, type, ln: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Omonoid__mult, type, monoid_mult: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Oordered__ring, type, ordered_ring: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Fields_Ofield__char__0, type, field_char_0: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Olinordered__ring, type, linordered_ring: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Oordered__semiring, type, ordered_semiring: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Ocomm__monoid__mult, type, comm_monoid_mult: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Oordered__semiring__0, type, ordered_semiring_0: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Oordered__comm__semiring, type, ordere1490568538miring: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Topological__Spaces_Ot0__space, type, topological_t0_space: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Topological__Spaces_Ot1__space, type, topological_t1_space: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Olinordered__ring__strict, type, linord581940658strict: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Oring__1__no__zero__divisors, type, ring_11004092258visors: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Osemiring__no__zero__divisors, type, semiri1193490041visors: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__field, type, real_V758409581_field: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Topological__Spaces_Odiscrete__topology, type, topolo2133971006pology: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Topological__Spaces_Otopological__space, type, topolo503727757_space: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel, type, semiri1923998003cancel: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_cl_Topological__Spaces_Ofirst__countable__topology, type, topolo2135403230pology: (!> [A:$tType]: ($o))).
% 2.66/1.52 thf(sy_c_Complex__Analysis__Basics_Oholomorphic__on, type, comple372758642hic_on: ((complex > complex) > ((set @ complex) > $o))).
% 2.66/1.52 thf(sy_c_Derivative_Oderiv, type, deriv: (!> [A:$tType]: (((A > A) > (A > A))))).
% 2.66/1.52 thf(sy_c_Formal__Power__Series_Ofps__tan, type, formal_Power_fps_tan: (!> [A:$tType]: ((A > (formal_Power_fps @ A))))).
% 2.66/1.52 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 2.66/1.52 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 2.66/1.52 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.66/1.52 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 2.66/1.52 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.66/1.53 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.66/1.53 thf(sy_c_Nat_Ocompow, type, compow: (!> [A:$tType]: ((nat > (A > A))))).
% 2.66/1.53 thf(sy_c_Nat_Ofunpow, type, funpow: (!> [A:$tType]: ((nat > ((A > A) > (A > A)))))).
% 2.66/1.53 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc, type, neg_numeral_dbl_inc: (!> [A:$tType]: ((A > A)))).
% 2.66/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.66/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.66/1.53 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 2.66/1.53 thf(sy_c_Topological__Spaces_Oopen__class_Oopen, type, topolo1751647064n_open: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.66/1.53 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconnected, type, topolo1099314120nected: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.66/1.53 thf(sy_c_Transcendental_Oarcosh, type, arcosh: (!> [A:$tType]: ((A > A)))).
% 2.66/1.53 thf(sy_c_Transcendental_Oarsinh, type, arsinh: (!> [A:$tType]: ((A > A)))).
% 2.66/1.53 thf(sy_c_Transcendental_Oartanh, type, artanh: (!> [A:$tType]: ((A > A)))).
% 2.66/1.53 thf(sy_c_Transcendental_Oln__class_Oln, type, ln_ln: (!> [A:$tType]: ((A > A)))).
% 2.66/1.53 thf(sy_c_Transitive__Closure_Orelpowp, type, transitive_relpowp: (!> [A:$tType]: ((nat > ((A > (A > $o)) > (A > (A > $o))))))).
% 2.66/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.66/1.53 thf(sy_v_S, type, s: (set @ complex)).
% 2.66/1.53 thf(sy_v_T, type, t: (set @ complex)).
% 2.66/1.53 thf(sy_v_f, type, f: (complex > complex)).
% 2.66/1.53 thf(sy_v_g, type, g: (complex > complex)).
% 2.66/1.53 thf(sy_v_w, type, w: complex).
% 2.66/1.53 thf(fact_0__092_060open_062_092_060And_062z_O_A_Ideriv_A_094_094_A1_J_Aid_Az_A_061_A_Iif_A1_A_061_A0_Athen_Az_Aelse_Aif_A1_A_061_A1_Athen_A1_058_058_063_Ha_Aelse_A_I0_058_058_063_Ha_J_J_092_060close_062, axiom, (! [A:$tType]: (((real_V758409581_field @ A) => (! [Z:A]: (((((one_one @ nat) = (zero_zero @ nat)) => ((((((compow @ ((A > A) > (A > A))) @ (one_one @ nat)) @ (deriv @ A)) @ (id @ A)) @ Z) = Z)) & (((one_one @ nat) != (zero_zero @ nat)) => ((((((compow @ ((A > A) > (A > A))) @ (one_one @ nat)) @ (deriv @ A)) @ (id @ A)) @ Z) = (one_one @ A)))))))))).
% 2.66/1.53 thf(fact_1_assms_I7_J, axiom, (((member @ complex) @ w) @ s)).
% 2.66/1.53 thf(fact_2_deriv__id, axiom, (! [A:$tType]: (((real_V758409581_field @ A) => (((deriv @ A) @ (id @ A)) = (^ [Z2:A]: ((one_one @ A)))))))).
% 2.66/1.53 thf(fact_3_id__apply, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 2.66/1.53 thf(fact_4_id__def, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 2.66/1.53 thf(fact_5_eq__id__iff, axiom, (! [A:$tType,F:(A > A)]: (((! [X:A]: (((F @ X) = X))) = (F = (id @ A)))))).
% 2.66/1.53 thf(fact_6_higher__deriv__id, axiom, (! [A:$tType]: (((real_V758409581_field @ A) => (! [N:nat,Z:A]: ((((N = (zero_zero @ nat)) => ((((((compow @ ((A > A) > (A > A))) @ N) @ (deriv @ A)) @ (id @ A)) @ Z) = Z)) & ((N != (zero_zero @ nat)) => (((N = (one_one @ nat)) => ((((((compow @ ((A > A) > (A > A))) @ N) @ (deriv @ A)) @ (id @ A)) @ Z) = (one_one @ A))) & ((N != (one_one @ nat)) => ((((((compow @ ((A > A) > (A > A))) @ N) @ (deriv @ A)) @ (id @ A)) @ Z) = (zero_zero @ A)))))))))))).
% 2.66/1.53 thf(fact_7_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X2:A]: ((((one_one @ A) = X2) = (X2 = (one_one @ A))))))))).
% 2.66/1.53 thf(fact_8_id__funpow, axiom, (! [A:$tType,N:nat]: (((((compow @ (A > A)) @ N) @ (id @ A)) = (id @ A))))).
% 2.66/1.53 thf(fact_9_calculation, axiom, ((((times_times @ complex) @ (((deriv @ complex) @ f) @ w)) @ (((deriv @ complex) @ g) @ (f @ w))) = (((deriv @ complex) @ (id @ complex)) @ w))).
% 2.66/1.53 thf(fact_10__092_060open_062deriv_A_Ig_A_092_060circ_062_Af_J_Aw_A_061_Aderiv_Aid_Aw_092_060close_062, axiom, ((((deriv @ complex) @ (((((comp @ complex) @ complex) @ complex) @ g) @ f)) @ w) = (((deriv @ complex) @ (id @ complex)) @ w))).
% 2.66/1.53 thf(fact_11_zero__neq__one, axiom, (! [A:$tType]: (((zero_neq_one @ A) => ((zero_zero @ A) != (one_one @ A)))))).
% 2.66/1.53 thf(fact_12__092_060open_062deriv_Af_Aw_A_K_Aderiv_Ag_A_If_Aw_J_A_061_Aderiv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_092_060close_062, axiom, ((((times_times @ complex) @ (((deriv @ complex) @ f) @ w)) @ (((deriv @ complex) @ g) @ (f @ w))) = (((times_times @ complex) @ (((deriv @ complex) @ g) @ (f @ w))) @ (((deriv @ complex) @ f) @ w)))).
% 2.66/1.53 thf(fact_13_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F2:(B > A),G:(C > B),X:C]: ((F2 @ (G @ X)))))))).
% 2.66/1.53 thf(fact_14_mult__zero__left, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.66/1.53 thf(fact_15_mult__zero__right, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.66/1.53 thf(fact_16_mult__eq__0__iff, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) = (zero_zero @ A)) = ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_17_mult__cancel__left, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C2:A,A2:A,B2:A]: ((((((times_times @ A) @ C2) @ A2) = (((times_times @ A) @ C2) @ B2)) = ((C2 = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.66/1.53 thf(fact_18_mult__cancel__right, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [A2:A,C2:A,B2:A]: ((((((times_times @ A) @ A2) @ C2) = (((times_times @ A) @ B2) @ C2)) = ((C2 = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.66/1.53 thf(fact_19_mult_Oright__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 2.66/1.53 thf(fact_20_mult_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 2.66/1.53 thf(fact_21_id__comp, axiom, (! [B:$tType,A:$tType,G2:(A > B)]: (((((((comp @ B) @ B) @ A) @ (id @ B)) @ G2) = G2)))).
% 2.66/1.53 thf(fact_22_comp__id, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((((comp @ A) @ B) @ A) @ F) @ (id @ A)) = F)))).
% 2.66/1.53 thf(fact_23_funpow__0, axiom, (! [A:$tType,F:(A > A),X2:A]: ((((((compow @ (A > A)) @ (zero_zero @ nat)) @ F) @ X2) = X2)))).
% 2.66/1.53 thf(fact_24_assms_I3_J, axiom, ((topolo1751647064n_open @ complex) @ s)).
% 2.66/1.53 thf(fact_25__092_060open_062deriv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_A_061_Aderiv_A_Ig_A_092_060circ_062_Af_J_Aw_092_060close_062, axiom, ((((times_times @ complex) @ (((deriv @ complex) @ g) @ (f @ w))) @ (((deriv @ complex) @ f) @ w)) = (((deriv @ complex) @ (((((comp @ complex) @ complex) @ complex) @ g) @ f)) @ w))).
% 2.66/1.53 thf(fact_26_mult__cancel__right2, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [A2:A,C2:A]: ((((((times_times @ A) @ A2) @ C2) = C2) = ((C2 = (zero_zero @ A)) | (A2 = (one_one @ A)))))))))).
% 2.66/1.53 thf(fact_27_mult__cancel__right1, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C2:A,B2:A]: (((C2 = (((times_times @ A) @ B2) @ C2)) = ((C2 = (zero_zero @ A)) | (B2 = (one_one @ A)))))))))).
% 2.66/1.53 thf(fact_28_mult__cancel__left2, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C2:A,A2:A]: ((((((times_times @ A) @ C2) @ A2) = C2) = ((C2 = (zero_zero @ A)) | (A2 = (one_one @ A)))))))))).
% 2.66/1.53 thf(fact_29_mult__cancel__left1, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C2:A,B2:A]: (((C2 = (((times_times @ A) @ C2) @ B2)) = ((C2 = (zero_zero @ A)) | (B2 = (one_one @ A)))))))))).
% 2.66/1.53 thf(fact_30_assms_I6_J, axiom, (! [Z:complex]: (((((member @ complex) @ Z) @ s) => ((g @ (f @ Z)) = Z))))).
% 2.66/1.53 thf(fact_31_assms_I1_J, axiom, ((comple372758642hic_on @ f) @ s)).
% 2.66/1.53 thf(fact_32_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [A2:A,B2:A,C2:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C2) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.66/1.53 thf(fact_33_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F2:(B > C),G:(A > B),X:A]: ((F2 @ (G @ X)))))))).
% 2.66/1.53 thf(fact_34_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F:(D > B),G2:(C > D),H:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F) @ G2)) @ H) = (((((comp @ D) @ B) @ A) @ F) @ (((((comp @ C) @ D) @ A) @ G2) @ H)))))).
% 2.66/1.53 thf(fact_35_comp__funpow, axiom, (! [B:$tType,A:$tType,N:nat,F:(A > A)]: (((((compow @ ((B > A) > (B > A))) @ N) @ ((((comp @ A) @ A) @ B) @ F)) = ((((comp @ A) @ A) @ B) @ (((compow @ (A > A)) @ N) @ F)))))).
% 2.66/1.53 thf(fact_36_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(D > B),D2:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => ((A2 @ (B2 @ V)) = (C2 @ (D2 @ V))))))).
% 2.66/1.53 thf(fact_37_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(D > B),D2:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => (! [V2:A]: (((A2 @ (B2 @ V2)) = (C2 @ (D2 @ V2))))))))).
% 2.66/1.53 thf(fact_38_funpow__swap1, axiom, (! [A:$tType,F:(A > A),N:nat,X2:A]: (((F @ ((((compow @ (A > A)) @ N) @ F) @ X2)) = ((((compow @ (A > A)) @ N) @ F) @ (F @ X2)))))).
% 2.66/1.53 thf(fact_39_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = C2) => ((A2 @ (B2 @ V)) = (C2 @ V)))))).
% 2.66/1.53 thf(fact_40_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X2:A]: ((((zero_zero @ A) = X2) = (X2 = (zero_zero @ A))))))))).
% 2.66/1.53 thf(fact_41_mult__not__zero, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) != (zero_zero @ A)) => ((A2 != (zero_zero @ A)) & (B2 != (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_42_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.66/1.53 thf(fact_43_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) = A3)))).
% 2.66/1.53 thf(fact_44_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.66/1.53 thf(fact_45_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X3:A]: (((F @ X3) = (G2 @ X3)))) => (F = G2))))).
% 2.66/1.53 thf(fact_46_mult_Oassoc, axiom, (! [A:$tType]: (((semigroup_mult @ A) => (! [A2:A,B2:A,C2:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C2) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.66/1.53 thf(fact_47_mult_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => ((times_times @ A) = (^ [A4:A,B3:A]: ((((times_times @ A) @ B3) @ A4)))))))).
% 2.66/1.53 thf(fact_48_mult_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [B2:A,A2:A,C2:A]: (((((times_times @ A) @ B2) @ (((times_times @ A) @ A2) @ C2)) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.66/1.53 thf(fact_49_divisors__zero, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) = (zero_zero @ A)) => ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_50_no__zero__divisors, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: (((A2 != (zero_zero @ A)) => ((B2 != (zero_zero @ A)) => ((((times_times @ A) @ A2) @ B2) != (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_51_mult__left__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C2:A,A2:A,B2:A]: (((C2 != (zero_zero @ A)) => (((((times_times @ A) @ C2) @ A2) = (((times_times @ A) @ C2) @ B2)) = (A2 = B2))))))))).
% 2.66/1.53 thf(fact_52_mult__right__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C2:A,A2:A,B2:A]: (((C2 != (zero_zero @ A)) => (((((times_times @ A) @ A2) @ C2) = (((times_times @ A) @ B2) @ C2)) = (A2 = B2))))))))).
% 2.66/1.53 thf(fact_53_comp__eq__id__dest, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ B) @ B) @ A) @ (id @ B)) @ C2)) => ((A2 @ (B2 @ V)) = (C2 @ V)))))).
% 2.66/1.53 thf(fact_54_mult_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 2.66/1.53 thf(fact_55_comm__monoid__mult__class_Omult__1, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 2.66/1.53 thf(fact_56_funpow__simps__right_I1_J, axiom, (! [A:$tType,F:(A > A)]: (((((compow @ (A > A)) @ (zero_zero @ nat)) @ F) = (id @ A))))).
% 2.66/1.53 thf(fact_57_fun_Omap__id, axiom, (! [A:$tType,D:$tType,T:(D > A)]: (((((((comp @ A) @ A) @ D) @ (id @ A)) @ T) = T)))).
% 2.66/1.53 thf(fact_58_vector__space__over__itself_Oscale__one, axiom, (! [A:$tType]: (((field @ A) => (! [X2:A]: (((((times_times @ A) @ (one_one @ A)) @ X2) = X2))))))).
% 2.66/1.53 thf(fact_59_vector__space__over__itself_Oscale__eq__0__iff, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,X2:A]: ((((((times_times @ A) @ A2) @ X2) = (zero_zero @ A)) = ((A2 = (zero_zero @ A)) | (X2 = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_60_vector__space__over__itself_Oscale__zero__left, axiom, (! [A:$tType]: (((field @ A) => (! [X2:A]: (((((times_times @ A) @ (zero_zero @ A)) @ X2) = (zero_zero @ A)))))))).
% 2.66/1.53 thf(fact_61_vector__space__over__itself_Oscale__zero__right, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.66/1.53 thf(fact_62_vector__space__over__itself_Oscale__cancel__left, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,X2:A,Y:A]: ((((((times_times @ A) @ A2) @ X2) = (((times_times @ A) @ A2) @ Y)) = ((X2 = Y) | (A2 = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_63_vector__space__over__itself_Oscale__cancel__right, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,X2:A,B2:A]: ((((((times_times @ A) @ A2) @ X2) = (((times_times @ A) @ B2) @ X2)) = ((A2 = B2) | (X2 = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_64_mult__if__delta, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (! [P:$o,Q2:A]: (((P => ((((times_times @ A) @ ((((if @ A) @ P) @ (one_one @ A)) @ (zero_zero @ A))) @ Q2) = Q2)) & ((~ (P)) => ((((times_times @ A) @ ((((if @ A) @ P) @ (one_one @ A)) @ (zero_zero @ A))) @ Q2) = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_65_relpowp__1, axiom, (! [A:$tType,P:(A > (A > $o))]: (((((compow @ (A > (A > $o))) @ (one_one @ nat)) @ P) = P)))).
% 2.66/1.53 thf(fact_66_set__times__intro, axiom, (! [A:$tType]: (((times @ A) => (! [A2:A,C3:(set @ A),B2:A,D3:(set @ A)]: (((((member @ A) @ A2) @ C3) => ((((member @ A) @ B2) @ D3) => (((member @ A) @ (((times_times @ A) @ A2) @ B2)) @ (((times_times @ (set @ A)) @ C3) @ D3)))))))))).
% 2.66/1.53 thf(fact_67_funpow__code__def, axiom, (! [A:$tType]: (((funpow @ A) = (compow @ (A > A)))))).
% 2.66/1.53 thf(fact_68_assms_I4_J, axiom, ((topolo1751647064n_open @ complex) @ t)).
% 2.66/1.53 thf(fact_69_assms_I2_J, axiom, ((comple372758642hic_on @ g) @ t)).
% 2.66/1.53 thf(fact_70_mult__cancel2, axiom, (! [M:nat,K:nat,N:nat]: ((((((times_times @ nat) @ M) @ K) = (((times_times @ nat) @ N) @ K)) = ((M = N) | (K = (zero_zero @ nat))))))).
% 2.66/1.53 thf(fact_71_mult__cancel1, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = ((M = N) | (K = (zero_zero @ nat))))))).
% 2.66/1.53 thf(fact_72_mult__0__right, axiom, (! [M:nat]: (((((times_times @ nat) @ M) @ (zero_zero @ nat)) = (zero_zero @ nat))))).
% 2.66/1.53 thf(fact_73_mult__is__0, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) | (N = (zero_zero @ nat))))))).
% 2.66/1.53 thf(fact_74_nat__mult__eq__1__iff, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (one_one @ nat)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 2.66/1.53 thf(fact_75_nat__1__eq__mult__iff, axiom, (! [M:nat,N:nat]: ((((one_one @ nat) = (((times_times @ nat) @ M) @ N)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 2.66/1.53 thf(fact_76_relpowp__Suc__D2_H, axiom, (! [A:$tType,N:nat,P:(A > (A > $o)),X4:A,Y2:A,Z3:A]: ((((((((compow @ (A > (A > $o))) @ N) @ P) @ X4) @ Y2) & ((P @ Y2) @ Z3)) => (? [W:A]: ((((P @ X4) @ W) & (((((compow @ (A > (A > $o))) @ N) @ P) @ W) @ Z3)))))))).
% 2.66/1.53 thf(fact_77_higher__deriv__transform__within__open, axiom, (! [F:(complex > complex),S:(set @ complex),G2:(complex > complex),Z:complex,I:nat]: ((((comple372758642hic_on @ F) @ S) => (((comple372758642hic_on @ G2) @ S) => (((topolo1751647064n_open @ complex) @ S) => ((((member @ complex) @ Z) @ S) => ((! [W:complex]: (((((member @ complex) @ W) @ S) => ((F @ W) = (G2 @ W))))) => ((((((compow @ ((complex > complex) > (complex > complex))) @ I) @ (deriv @ complex)) @ F) @ Z) = (((((compow @ ((complex > complex) > (complex > complex))) @ I) @ (deriv @ complex)) @ G2) @ Z)))))))))).
% 2.66/1.53 thf(fact_78_holomorphic__higher__deriv, axiom, (! [F:(complex > complex),S:(set @ complex),N:nat]: ((((comple372758642hic_on @ F) @ S) => (((topolo1751647064n_open @ complex) @ S) => ((comple372758642hic_on @ ((((compow @ ((complex > complex) > (complex > complex))) @ N) @ (deriv @ complex)) @ F)) @ S)))))).
% 2.66/1.53 thf(fact_79_holomorphic__deriv, axiom, (! [F:(complex > complex),S:(set @ complex)]: ((((comple372758642hic_on @ F) @ S) => (((topolo1751647064n_open @ complex) @ S) => ((comple372758642hic_on @ ((deriv @ complex) @ F)) @ S)))))).
% 2.66/1.53 thf(fact_80_mult__0, axiom, (! [N:nat]: (((((times_times @ nat) @ (zero_zero @ nat)) @ N) = (zero_zero @ nat))))).
% 2.66/1.53 thf(fact_81_nat__mult__1__right, axiom, (! [N:nat]: (((((times_times @ nat) @ N) @ (one_one @ nat)) = N)))).
% 2.66/1.53 thf(fact_82_nat__mult__1, axiom, (! [N:nat]: (((((times_times @ nat) @ (one_one @ nat)) @ N) = N)))).
% 2.66/1.53 thf(fact_83_funpow__mult, axiom, (! [A:$tType,N:nat,M:nat,F:(A > A)]: (((((compow @ (A > A)) @ N) @ (((compow @ (A > A)) @ M) @ F)) = (((compow @ (A > A)) @ (((times_times @ nat) @ M) @ N)) @ F))))).
% 2.66/1.53 thf(fact_84_mult__eq__self__implies__10, axiom, (! [M:nat,N:nat]: (((M = (((times_times @ nat) @ M) @ N)) => ((N = (one_one @ nat)) | (M = (zero_zero @ nat))))))).
% 2.66/1.53 thf(fact_85_vector__space__over__itself_Oscale__left__commute, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,B2:A,X2:A]: (((((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ X2)) = (((times_times @ A) @ B2) @ (((times_times @ A) @ A2) @ X2))))))))).
% 2.66/1.53 thf(fact_86_vector__space__over__itself_Oscale__scale, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,B2:A,X2:A]: (((((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ X2)) = (((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ X2)))))))).
% 2.66/1.53 thf(fact_87_set__times__elim, axiom, (! [A:$tType]: (((times @ A) => (! [X2:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ X2) @ (((times_times @ (set @ A)) @ A3) @ B4)) => (~ ((! [A5:A,B5:A]: (((X2 = (((times_times @ A) @ A5) @ B5)) => ((((member @ A) @ A5) @ A3) => (~ ((((member @ A) @ B5) @ B4)))))))))))))))).
% 2.66/1.53 thf(fact_88_relpowp__0__I, axiom, (! [A:$tType,P:(A > (A > $o)),X2:A]: ((((((compow @ (A > (A > $o))) @ (zero_zero @ nat)) @ P) @ X2) @ X2)))).
% 2.66/1.53 thf(fact_89_relpowp__0__E, axiom, (! [A:$tType,P:(A > (A > $o)),X2:A,Y:A]: (((((((compow @ (A > (A > $o))) @ (zero_zero @ nat)) @ P) @ X2) @ Y) => (X2 = Y))))).
% 2.66/1.53 thf(fact_90_relpowp_Osimps_I1_J, axiom, (! [A:$tType,R:(A > (A > $o))]: (((((compow @ (A > (A > $o))) @ (zero_zero @ nat)) @ R) = (^ [Y3:A,Z4:A]: ((Y3 = Z4))))))).
% 2.66/1.53 thf(fact_91_fun_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,G2:(B > C),F:(A > B),V:(D > A)]: (((((((comp @ B) @ C) @ D) @ G2) @ (((((comp @ A) @ B) @ D) @ F) @ V)) = (((((comp @ A) @ C) @ D) @ (((((comp @ B) @ C) @ A) @ G2) @ F)) @ V))))).
% 2.66/1.53 thf(fact_92_vector__space__over__itself_Oscale__right__imp__eq, axiom, (! [A:$tType]: (((field @ A) => (! [X2:A,A2:A,B2:A]: (((X2 != (zero_zero @ A)) => (((((times_times @ A) @ A2) @ X2) = (((times_times @ A) @ B2) @ X2)) => (A2 = B2))))))))).
% 2.66/1.53 thf(fact_93_vector__space__over__itself_Oscale__left__imp__eq, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,X2:A,Y:A]: (((A2 != (zero_zero @ A)) => (((((times_times @ A) @ A2) @ X2) = (((times_times @ A) @ A2) @ Y)) => (X2 = Y))))))))).
% 2.66/1.53 thf(fact_94_fun_Omap__id0, axiom, (! [A:$tType,D:$tType]: ((((((comp @ A) @ A) @ D) @ (id @ A)) = (id @ (D > A)))))).
% 2.66/1.53 thf(fact_95_complex__derivative__transform__within__open, axiom, (! [F:(complex > complex),S2:(set @ complex),G2:(complex > complex),Z:complex]: ((((comple372758642hic_on @ F) @ S2) => (((comple372758642hic_on @ G2) @ S2) => (((topolo1751647064n_open @ complex) @ S2) => ((((member @ complex) @ Z) @ S2) => ((! [W:complex]: (((((member @ complex) @ W) @ S2) => ((F @ W) = (G2 @ W))))) => ((((deriv @ complex) @ F) @ Z) = (((deriv @ complex) @ G2) @ Z)))))))))).
% 2.66/1.53 thf(fact_96_holomorphic__on__id, axiom, (! [S2:(set @ complex)]: (((comple372758642hic_on @ (id @ complex)) @ S2)))).
% 2.66/1.53 thf(fact_97_relpowp__code__def, axiom, (! [A:$tType]: (((transitive_relpowp @ A) = (compow @ (A > (A > $o))))))).
% 2.66/1.53 thf(fact_98_holomorphic__on__linear, axiom, (! [C2:complex,S2:(set @ complex)]: (((comple372758642hic_on @ ((times_times @ complex) @ C2)) @ S2)))).
% 2.66/1.53 thf(fact_99_pointfree__idE, axiom, (! [B:$tType,A:$tType,F:(B > A),G2:(A > B),X2:A]: ((((((((comp @ B) @ A) @ A) @ F) @ G2) = (id @ A)) => ((F @ (G2 @ X2)) = X2))))).
% 2.66/1.53 thf(fact_100_isomorphism__expand, axiom, (! [A:$tType,B:$tType,F:(B > A),G2:(A > B)]: (((((((((comp @ B) @ A) @ A) @ F) @ G2) = (id @ A)) & ((((((comp @ A) @ B) @ B) @ G2) @ F) = (id @ B))) = ((! [X:A]: (((F @ (G2 @ X)) = X))) & (! [X:B]: (((G2 @ (F @ X)) = X)))))))).
% 2.66/1.53 thf(fact_101_left__right__inverse__eq, axiom, (! [A:$tType,B:$tType,F:(B > A),G2:(A > B),H:(B > A)]: ((((((((comp @ B) @ A) @ A) @ F) @ G2) = (id @ A)) => (((((((comp @ A) @ B) @ B) @ G2) @ H) = (id @ B)) => (F = H)))))).
% 2.66/1.53 thf(fact_102_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F:(C > B),G2:(A > C),L:(A > B),H:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F) @ G2) = L) => ((((((comp @ C) @ B) @ D) @ F) @ (((((comp @ A) @ C) @ D) @ G2) @ H)) = (((((comp @ A) @ B) @ D) @ L) @ H)))))).
% 2.66/1.53 thf(fact_103_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G2:(C > B),H:(A > C),R2:(A > B),F:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G2) @ H) = R2) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F) @ G2)) @ H) = (((((comp @ B) @ D) @ A) @ F) @ R2)))))).
% 2.66/1.53 thf(fact_104_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType,F:(C > B),G2:(A > C),L1:(D > B),L2:(A > D),H:(E > A),R2:(E > D)]: ((((((((comp @ C) @ B) @ A) @ F) @ G2) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E) @ L2) @ H) = R2) => ((((((comp @ C) @ B) @ E) @ F) @ (((((comp @ A) @ C) @ E) @ G2) @ H)) = (((((comp @ D) @ B) @ E) @ L1) @ R2))))))).
% 2.66/1.53 thf(fact_105_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E:$tType,D:$tType,A:$tType,G2:(C > B),H:(A > C),R1:(D > B),R22:(A > D),F:(B > E),L:(D > E)]: ((((((((comp @ C) @ B) @ A) @ G2) @ H) = (((((comp @ D) @ B) @ A) @ R1) @ R22)) => (((((((comp @ B) @ E) @ D) @ F) @ R1) = L) => ((((((comp @ C) @ E) @ A) @ (((((comp @ B) @ E) @ C) @ F) @ G2)) @ H) = (((((comp @ D) @ E) @ A) @ L) @ R22))))))).
% 2.66/1.53 thf(fact_106_holomorphic__cong, axiom, (! [S2:(set @ complex),T:(set @ complex),F:(complex > complex),G2:(complex > complex)]: (((S2 = T) => ((! [X3:complex]: (((((member @ complex) @ X3) @ S2) => ((F @ X3) = (G2 @ X3))))) => (((comple372758642hic_on @ F) @ S2) = ((comple372758642hic_on @ G2) @ T))))))).
% 2.66/1.53 thf(fact_107_holomorphic__transform, axiom, (! [F:(complex > complex),S2:(set @ complex),G2:(complex > complex)]: ((((comple372758642hic_on @ F) @ S2) => ((! [X3:complex]: (((((member @ complex) @ X3) @ S2) => ((F @ X3) = (G2 @ X3))))) => ((comple372758642hic_on @ G2) @ S2)))))).
% 2.66/1.53 thf(fact_108_assms_I5_J, axiom, (((ord_less_eq @ (set @ complex)) @ ((((image @ complex) @ complex) @ f) @ s)) @ t)).
% 2.66/1.53 thf(fact_109_nat__mult__eq__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = ((K = (zero_zero @ nat)) | (M = N)))))).
% 2.66/1.53 thf(fact_110_mult__delta__left, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [B2:$o,X2:A,Y:A]: (((B2 => ((((times_times @ A) @ ((((if @ A) @ B2) @ X2) @ (zero_zero @ A))) @ Y) = (((times_times @ A) @ X2) @ Y))) & ((~ (B2)) => ((((times_times @ A) @ ((((if @ A) @ B2) @ X2) @ (zero_zero @ A))) @ Y) = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_111_mult__delta__right, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [B2:$o,X2:A,Y:A]: (((B2 => ((((times_times @ A) @ X2) @ ((((if @ A) @ B2) @ Y) @ (zero_zero @ A))) = (((times_times @ A) @ X2) @ Y))) & ((~ (B2)) => ((((times_times @ A) @ X2) @ ((((if @ A) @ B2) @ Y) @ (zero_zero @ A))) = (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_112_arcosh__1, axiom, (! [A:$tType]: (((ln @ A) => (((arcosh @ A) @ (one_one @ A)) = (zero_zero @ A)))))).
% 2.66/1.53 thf(fact_113_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.66/1.53 thf(fact_114_image__id, axiom, (! [A:$tType]: (((((image @ A) @ A) @ (id @ A)) = (id @ (set @ A)))))).
% 2.66/1.53 thf(fact_115_set__times__mono2, axiom, (! [A:$tType]: (((times @ A) => (! [C3:(set @ A),D3:(set @ A),E2:(set @ A),F3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C3) @ D3) => ((((ord_less_eq @ (set @ A)) @ E2) @ F3) => (((ord_less_eq @ (set @ A)) @ (((times_times @ (set @ A)) @ C3) @ E2)) @ (((times_times @ (set @ A)) @ D3) @ F3)))))))))).
% 2.66/1.53 thf(fact_116_holomorphic__on__compose__gen, axiom, (! [F:(complex > complex),S2:(set @ complex),G2:(complex > complex),T:(set @ complex)]: ((((comple372758642hic_on @ F) @ S2) => (((comple372758642hic_on @ G2) @ T) => ((((ord_less_eq @ (set @ complex)) @ ((((image @ complex) @ complex) @ F) @ S2)) @ T) => ((comple372758642hic_on @ (((((comp @ complex) @ complex) @ complex) @ G2) @ F)) @ S2))))))).
% 2.66/1.53 thf(fact_117_image__comp, axiom, (! [B:$tType,A:$tType,C:$tType,F:(B > A),G2:(C > B),R2:(set @ C)]: ((((((image @ B) @ A) @ F) @ ((((image @ C) @ B) @ G2) @ R2)) = ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ F) @ G2)) @ R2))))).
% 2.66/1.53 thf(fact_118_image__eq__imp__comp, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,F:(B > A),A3:(set @ B),G2:(C > A),B4:(set @ C),H:(A > D)]: (((((((image @ B) @ A) @ F) @ A3) = ((((image @ C) @ A) @ G2) @ B4)) => (((((image @ B) @ D) @ (((((comp @ A) @ D) @ B) @ H) @ F)) @ A3) = ((((image @ C) @ D) @ (((((comp @ A) @ D) @ C) @ H) @ G2)) @ B4)))))).
% 2.66/1.53 thf(fact_119_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X2))))))).
% 2.66/1.53 thf(fact_120_holomorphic__on__subset, axiom, (! [F:(complex > complex),S2:(set @ complex),T:(set @ complex)]: ((((comple372758642hic_on @ F) @ S2) => ((((ord_less_eq @ (set @ complex)) @ T) @ S2) => ((comple372758642hic_on @ F) @ T)))))).
% 2.66/1.53 thf(fact_121_set__times__mono2__b, axiom, (! [A:$tType]: (((times @ A) => (! [C3:(set @ A),D3:(set @ A),E2:(set @ A),F3:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ C3) @ D3) => ((((ord_less_eq @ (set @ A)) @ E2) @ F3) => ((((member @ A) @ X2) @ (((times_times @ (set @ A)) @ C3) @ E2)) => (((member @ A) @ X2) @ (((times_times @ (set @ A)) @ D3) @ F3))))))))))).
% 2.66/1.53 thf(fact_122_ordered__comm__semiring__class_Ocomm__mult__left__mono, axiom, (! [A:$tType]: (((ordere1490568538miring @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C2) => (((ord_less_eq @ A) @ (((times_times @ A) @ C2) @ A2)) @ (((times_times @ A) @ C2) @ B2)))))))))).
% 2.66/1.53 thf(fact_123_zero__le__mult__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.66/1.53 thf(fact_124_mult__nonneg__nonpos2, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ B2) @ A2)) @ (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_125_mult__nonpos__nonneg, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_126_mult__nonneg__nonpos, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.66/1.53 thf(fact_127_mult__nonneg__nonneg, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.66/1.53 thf(fact_128_split__mult__neg__le, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2))) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A))))))))).
% 2.66/1.53 thf(fact_129_mult__le__0__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.66/1.53 thf(fact_130_mult__right__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C2)) @ (((times_times @ A) @ B2) @ C2)))))))))).
% 2.66/1.53 thf(fact_131_mult__right__mono__neg, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C2)) @ (((times_times @ A) @ B2) @ C2)))))))))).
% 2.66/1.53 thf(fact_132_mult__left__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C2) => (((ord_less_eq @ A) @ (((times_times @ A) @ C2) @ A2)) @ (((times_times @ A) @ C2) @ B2)))))))))).
% 2.66/1.53 thf(fact_133_mult__nonpos__nonpos, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.66/1.53 thf(fact_134_mult__left__mono__neg, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ C2) @ A2)) @ (((times_times @ A) @ C2) @ B2)))))))))).
% 2.66/1.53 thf(fact_135_split__mult__pos__le, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,B2:A]: (((((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A)))) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2))))))))).
% 2.66/1.53 thf(fact_136_zero__le__square, axiom, (! [A:$tType]: (((linordered_ring @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ A2)))))))).
% 2.66/1.53 thf(fact_137_mult__mono_H, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C2:A,D2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C2) @ D2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C2)) @ (((times_times @ A) @ B2) @ D2)))))))))))).
% 2.66/1.53 thf(fact_138_mult__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C2:A,D2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C2) @ D2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C2)) @ (((times_times @ A) @ B2) @ D2)))))))))))).
% 2.66/1.53 thf(fact_139_zero__le__one, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.66/1.53 thf(fact_140_not__one__le__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less_eq @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.66/1.53 thf(fact_141_holomorphic__on__compose, axiom, (! [F:(complex > complex),S2:(set @ complex),G2:(complex > complex)]: ((((comple372758642hic_on @ F) @ S2) => (((comple372758642hic_on @ G2) @ ((((image @ complex) @ complex) @ F) @ S2)) => ((comple372758642hic_on @ (((((comp @ complex) @ complex) @ complex) @ G2) @ F)) @ S2)))))).
% 2.66/1.53 thf(fact_142_deriv__left__inverse, axiom, (! [F:(complex > complex),S:(set @ complex),G2:(complex > complex),T2:(set @ complex),W2:complex]: ((((comple372758642hic_on @ F) @ S) => (((comple372758642hic_on @ G2) @ T2) => (((topolo1751647064n_open @ complex) @ S) => (((topolo1751647064n_open @ complex) @ T2) => ((((ord_less_eq @ (set @ complex)) @ ((((image @ complex) @ complex) @ F) @ S)) @ T2) => ((! [Z5:complex]: (((((member @ complex) @ Z5) @ S) => ((G2 @ (F @ Z5)) = Z5)))) => ((((member @ complex) @ W2) @ S) => ((((times_times @ complex) @ (((deriv @ complex) @ F) @ W2)) @ (((deriv @ complex) @ G2) @ (F @ W2))) = (one_one @ complex)))))))))))).
% 2.66/1.53 thf(fact_143_mult__left__le, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [C2:A,A2:A]: (((((ord_less_eq @ A) @ C2) @ (one_one @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C2)) @ A2))))))))).
% 2.66/1.53 thf(fact_144_mult__le__one, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (one_one @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => ((((ord_less_eq @ A) @ B2) @ (one_one @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (one_one @ A))))))))))).
% 2.66/1.53 thf(fact_145_mult__right__le__one__le, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y) => ((((ord_less_eq @ A) @ Y) @ (one_one @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ X2) @ Y)) @ X2)))))))))).
% 2.66/1.53 thf(fact_146_mult__left__le__one__le, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y) => ((((ord_less_eq @ A) @ Y) @ (one_one @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ Y) @ X2)) @ X2)))))))))).
% 2.66/1.53 thf(fact_147_mult__eq__1, axiom, (! [A:$tType]: ((((comm_monoid_mult @ A) & (ordered_semiring @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ A2) @ (one_one @ A)) => ((((ord_less_eq @ A) @ B2) @ (one_one @ A)) => (((((times_times @ A) @ A2) @ B2) = (one_one @ A)) = ((A2 = (one_one @ A)) & (B2 = (one_one @ A))))))))))))).
% 2.66/1.53 thf(fact_148_artanh__0, axiom, (! [A:$tType]: ((((real_V758409581_field @ A) & (ln @ A)) => (((artanh @ A) @ (zero_zero @ A)) = (zero_zero @ A)))))).
% 2.66/1.53 thf(fact_149_arsinh__0, axiom, (! [A:$tType]: (((ln @ A) => (((arsinh @ A) @ (zero_zero @ A)) = (zero_zero @ A)))))).
% 2.66/1.53 thf(fact_150_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A3) => (A3 = B4)))))).
% 2.66/1.53 thf(fact_151_image__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X2:B,A3:(set @ B)]: (((B2 = (F @ X2)) => ((((member @ B) @ X2) @ A3) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ A3))))))).
% 2.66/1.53 thf(fact_152_subsetI, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.66/1.53 thf(fact_153_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.66/1.53 thf(fact_154_bot__nat__0_Oextremum, axiom, (! [A2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A2)))).
% 2.66/1.53 thf(fact_155_less__eq__nat_Osimps_I1_J, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.66/1.53 thf(fact_156_le__0__eq, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ N) @ (zero_zero @ nat)) = (N = (zero_zero @ nat)))))).
% 2.66/1.53 thf(fact_157_bot__nat__0_Oextremum__unique, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) = (A2 = (zero_zero @ nat)))))).
% 2.66/1.53 thf(fact_158_bot__nat__0_Oextremum__uniqueI, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) => (A2 = (zero_zero @ nat)))))).
% 2.66/1.53 thf(fact_159_mult__le__mono2, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ K) @ I)) @ (((times_times @ nat) @ K) @ J)))))).
% 2.66/1.53 thf(fact_160_mult__le__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I) @ K)) @ (((times_times @ nat) @ J) @ K)))))).
% 2.66/1.53 thf(fact_161_mult__le__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ K) @ L) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I) @ K)) @ (((times_times @ nat) @ J) @ L))))))).
% 2.66/1.53 thf(fact_162_le__square, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ M))))).
% 2.66/1.53 thf(fact_163_le__cube, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ (((times_times @ nat) @ M) @ M)))))).
% 2.66/1.53 thf(fact_164_imageI, axiom, (! [B:$tType,A:$tType,X2:A,A3:(set @ A),F:(A > B)]: (((((member @ A) @ X2) @ A3) => (((member @ B) @ (F @ X2)) @ ((((image @ A) @ B) @ F) @ A3)))))).
% 2.66/1.53 thf(fact_165_image__iff, axiom, (! [A:$tType,B:$tType,Z:A,F:(B > A),A3:(set @ B)]: (((((member @ A) @ Z) @ ((((image @ B) @ A) @ F) @ A3)) = (? [X:B]: (((((member @ B) @ X) @ A3) & (Z = (F @ X))))))))).
% 2.66/1.53 thf(fact_166_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((((image @ B) @ A) @ F) @ A3)) & (P @ X4)))) => (? [X3:B]: (((((member @ B) @ X3) @ A3) & (P @ (F @ X3))))))))).
% 2.66/1.53 thf(fact_167_image__cong, axiom, (! [B:$tType,A:$tType,M2:(set @ A),N2:(set @ A),F:(A > B),G2:(A > B)]: (((M2 = N2) => ((! [X3:A]: (((((member @ A) @ X3) @ N2) => ((F @ X3) = (G2 @ X3))))) => (((((image @ A) @ B) @ F) @ M2) = ((((image @ A) @ B) @ G2) @ N2))))))).
% 2.66/1.53 thf(fact_168_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((((image @ B) @ A) @ F) @ A3)) => (P @ X3)))) => (! [X4:B]: (((((member @ B) @ X4) @ A3) => (P @ (F @ X4))))))))).
% 2.66/1.53 thf(fact_169_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X2:A,A3:(set @ A),B2:B,F:(A > B)]: (((((member @ A) @ X2) @ A3) => ((B2 = (F @ X2)) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ A3))))))).
% 2.66/1.53 thf(fact_170_in__mono, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B4)))))).
% 2.66/1.53 thf(fact_171_subsetD, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B4)))))).
% 2.66/1.53 thf(fact_172_equalityE, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (~ ((((ord_less_eq @ (set @ A)) @ B4) @ A3)))))))))).
% 2.66/1.53 thf(fact_173_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A6) => (((member @ A) @ X) @ B6)))))))))).
% 2.66/1.53 thf(fact_174_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (((ord_less_eq @ (set @ A)) @ A3) @ B4))))).
% 2.66/1.53 thf(fact_175_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((A3 = B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A3))))).
% 2.66/1.53 thf(fact_176_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B6:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A6) => (((member @ A) @ T3) @ B6)))))))))).
% 2.66/1.53 thf(fact_177_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 2.66/1.53 thf(fact_178_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.66/1.53 thf(fact_179_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C3) => (((ord_less_eq @ (set @ A)) @ A3) @ C3)))))).
% 2.66/1.53 thf(fact_180_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z4:(set @ A)]: ((Y3 = Z4))) = (^ [A6:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A6)))))))).
% 2.66/1.53 thf(fact_181_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X:A]: (((P @ X) => (Q @ X)))))))).
% 2.66/1.53 thf(fact_182_image__mono, axiom, (! [B:$tType,A:$tType,A3:(set @ A),B4:(set @ A),F:(A > B)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B4) => (((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A3)) @ ((((image @ A) @ B) @ F) @ B4)))))).
% 2.66/1.53 thf(fact_183_image__subsetI, axiom, (! [A:$tType,B:$tType,A3:(set @ A),F:(A > B),B4:(set @ B)]: (((! [X3:A]: (((((member @ A) @ X3) @ A3) => (((member @ B) @ (F @ X3)) @ B4)))) => (((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ F) @ A3)) @ B4))))).
% 2.66/1.53 thf(fact_184_subset__imageE, axiom, (! [A:$tType,B:$tType,B4:(set @ A),F:(B > A),A3:(set @ B)]: (((((ord_less_eq @ (set @ A)) @ B4) @ ((((image @ B) @ A) @ F) @ A3)) => (~ ((! [C4:(set @ B)]: (((((ord_less_eq @ (set @ B)) @ C4) @ A3) => (B4 != ((((image @ B) @ A) @ F) @ C4))))))))))).
% 2.66/1.53 thf(fact_185_image__subset__iff, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((((image @ B) @ A) @ F) @ A3)) @ B4) = (! [X:B]: (((((member @ B) @ X) @ A3) => (((member @ A) @ (F @ X)) @ B4)))))))).
% 2.66/1.53 thf(fact_186_subset__image__iff, axiom, (! [A:$tType,B:$tType,B4:(set @ A),F:(B > A),A3:(set @ B)]: (((((ord_less_eq @ (set @ A)) @ B4) @ ((((image @ B) @ A) @ F) @ A3)) = (? [AA:(set @ B)]: (((((ord_less_eq @ (set @ B)) @ AA) @ A3) & (B4 = ((((image @ B) @ A) @ F) @ AA))))))))).
% 2.66/1.53 thf(fact_187_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 2.66/1.53 thf(fact_188_kuhn__labelling__lemma_H, axiom, (! [P:((nat > real) > $o),F:((nat > real) > (nat > real)),Q:(nat > $o)]: (((! [X3:(nat > real)]: (((P @ X3) => (P @ (F @ X3))))) => ((! [X3:(nat > real)]: (((P @ X3) => (! [I2:nat]: (((Q @ I2) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ (X3 @ I2)) & (((ord_less_eq @ real) @ (X3 @ I2)) @ (one_one @ real))))))))) => (? [L3:((nat > real) > (nat > nat))]: (((! [X4:(nat > real),I3:nat]: ((((ord_less_eq @ nat) @ ((L3 @ X4) @ I3)) @ (one_one @ nat)))) & ((! [X4:(nat > real),I3:nat]: ((((P @ X4) & ((Q @ I3) & ((X4 @ I3) = (zero_zero @ real)))) => (((L3 @ X4) @ I3) = (zero_zero @ nat))))) & ((! [X4:(nat > real),I3:nat]: ((((P @ X4) & ((Q @ I3) & ((X4 @ I3) = (one_one @ real)))) => (((L3 @ X4) @ I3) = (one_one @ nat))))) & ((! [X4:(nat > real),I3:nat]: ((((P @ X4) & ((Q @ I3) & (((L3 @ X4) @ I3) = (zero_zero @ nat)))) => (((ord_less_eq @ real) @ (X4 @ I3)) @ ((F @ X4) @ I3))))) & (! [X4:(nat > real),I3:nat]: ((((P @ X4) & ((Q @ I3) & (((L3 @ X4) @ I3) = (one_one @ nat)))) => (((ord_less_eq @ real) @ ((F @ X4) @ I3)) @ (X4 @ I3)))))))))))))))).
% 2.66/1.53 thf(fact_189_Sup_OSUP__id__eq, axiom, (! [A:$tType,Sup:((set @ A) > A),A3:(set @ A)]: (((Sup @ ((((image @ A) @ A) @ (id @ A)) @ A3)) = (Sup @ A3))))).
% 2.66/1.53 thf(fact_190_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.66/1.53 thf(fact_191_le__trans, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I) @ K)))))).
% 2.66/1.53 thf(fact_192_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.66/1.53 thf(fact_193_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.66/1.53 thf(fact_194_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.66/1.53 thf(fact_195_Nat_Oex__has__greatest__nat, axiom, (! [P:(nat > $o),K:nat,B2:nat]: (((P @ K) => ((! [Y4:nat]: (((P @ Y4) => (((ord_less_eq @ nat) @ Y4) @ B2)))) => (? [X3:nat]: (((P @ X3) & (! [Y2:nat]: (((P @ Y2) => (((ord_less_eq @ nat) @ Y2) @ X3)))))))))))).
% 2.66/1.53 thf(fact_196_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.66/1.53 thf(fact_197_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z4:A]: ((Y3 = Z4))) = (^ [A4:A,B3:A]: (((((ord_less_eq @ A) @ B3) @ A4) & (((ord_less_eq @ A) @ A4) @ B3))))))))).
% 2.66/1.53 thf(fact_198_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.66/1.53 thf(fact_199_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) => ((P @ A5) @ B5)))) => ((! [A5:A,B5:A]: ((((P @ B5) @ A5) => ((P @ A5) @ B5)))) => ((P @ A2) @ B2))))))))).
% 2.66/1.53 thf(fact_200_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.66/1.53 thf(fact_201_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X2) @ Z))))))))).
% 2.66/1.53 thf(fact_202_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.66/1.53 thf(fact_203_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.66/1.53 thf(fact_204_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.66/1.53 thf(fact_205_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z4:A]: ((Y3 = Z4))) = (^ [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) & (((ord_less_eq @ A) @ B3) @ A4))))))))).
% 2.66/1.53 thf(fact_206_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X2:A]: (((((ord_less_eq @ A) @ Y) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y) = (X2 = Y))))))))).
% 2.66/1.53 thf(fact_207_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z)))) => (((((ord_less_eq @ A) @ X2) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X2)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y))))))))))))))))).
% 2.66/1.53 thf(fact_208_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.66/1.53 thf(fact_209_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y))) => (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 2.66/1.53 thf(fact_210_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((X2 = Y) => (((ord_less_eq @ A) @ X2) @ Y)))))))).
% 2.66/1.53 thf(fact_211_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) | (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 2.66/1.53 thf(fact_212_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ X2) => (X2 = Y))))))))).
% 2.66/1.53 thf(fact_213_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z4:A]: ((Y3 = Z4))) = (^ [X:A,Y5:A]: (((((ord_less_eq @ A) @ X) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X))))))))).
% 2.66/1.53 thf(fact_214_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C2) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C2)))))))))).
% 2.66/1.53 thf(fact_215_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.66/1.53 thf(fact_216_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F @ B2)) @ C2) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C2)))))))))).
% 2.66/1.53 thf(fact_217_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.66/1.53 thf(fact_218_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F2 @ X)) @ (G @ X))))))))))).
% 2.66/1.53 thf(fact_219_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G2:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G2 @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G2)))))))).
% 2.66/1.53 thf(fact_220_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G2:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X2)) @ (G2 @ X2))))))))).
% 2.66/1.53 thf(fact_221_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G2:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X2)) @ (G2 @ X2))))))))).
% 2.66/1.53 thf(fact_222_Sup_OSUP__cong, axiom, (! [A:$tType,B:$tType,A3:(set @ B),B4:(set @ B),C3:(B > A),D3:(B > A),Sup:((set @ A) > A)]: (((A3 = B4) => ((! [X3:B]: (((((member @ B) @ X3) @ B4) => ((C3 @ X3) = (D3 @ X3))))) => ((Sup @ ((((image @ B) @ A) @ C3) @ A3)) = (Sup @ ((((image @ B) @ A) @ D3) @ B4)))))))).
% 2.66/1.53 thf(fact_223_Inf_OINF__cong, axiom, (! [A:$tType,B:$tType,A3:(set @ B),B4:(set @ B),C3:(B > A),D3:(B > A),Inf:((set @ A) > A)]: (((A3 = B4) => ((! [X3:B]: (((((member @ B) @ X3) @ B4) => ((C3 @ X3) = (D3 @ X3))))) => ((Inf @ ((((image @ B) @ A) @ C3) @ A3)) = (Inf @ ((((image @ B) @ A) @ D3) @ B4)))))))).
% 2.66/1.53 thf(fact_224_Inf_OINF__image, axiom, (! [B:$tType,A:$tType,C:$tType,Inf:((set @ A) > A),G2:(B > A),F:(C > B),A3:(set @ C)]: (((Inf @ ((((image @ B) @ A) @ G2) @ ((((image @ C) @ B) @ F) @ A3))) = (Inf @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G2) @ F)) @ A3)))))).
% 2.66/1.53 thf(fact_225_Sup_OSUP__image, axiom, (! [B:$tType,A:$tType,C:$tType,Sup:((set @ A) > A),G2:(B > A),F:(C > B),A3:(set @ C)]: (((Sup @ ((((image @ B) @ A) @ G2) @ ((((image @ C) @ B) @ F) @ A3))) = (Sup @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G2) @ F)) @ A3)))))).
% 2.66/1.53 thf(fact_226_Inf_OINF__id__eq, axiom, (! [A:$tType,Inf:((set @ A) > A),A3:(set @ A)]: (((Inf @ ((((image @ A) @ A) @ (id @ A)) @ A3)) = (Inf @ A3))))).
% 2.66/1.53 thf(fact_227_topological__space__class_OopenI, axiom, (! [A:$tType]: (((topolo503727757_space @ A) => (! [S:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ S) => (? [T4:(set @ A)]: ((((topolo1751647064n_open @ A) @ T4) & ((((member @ A) @ X3) @ T4) & (((ord_less_eq @ (set @ A)) @ T4) @ S)))))))) => ((topolo1751647064n_open @ A) @ S)))))))).
% 2.66/1.53 thf(fact_228_open__subopen, axiom, (! [A:$tType]: (((topolo503727757_space @ A) => ((topolo1751647064n_open @ A) = (^ [S3:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ S3) => (? [T5:(set @ A)]: ((((topolo1751647064n_open @ A) @ T5) & ((((member @ A) @ X) @ T5) & (((ord_less_eq @ (set @ A)) @ T5) @ S3))))))))))))))).
% 2.66/1.53 thf(fact_229_t0__space, axiom, (! [A:$tType]: (((topological_t0_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) => (? [U:(set @ A)]: ((((topolo1751647064n_open @ A) @ U) & ((((member @ A) @ X2) @ U) != (((member @ A) @ Y) @ U)))))))))))).
% 2.66/1.53 thf(fact_230_t1__space, axiom, (! [A:$tType]: (((topological_t1_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) => (? [U:(set @ A)]: ((((topolo1751647064n_open @ A) @ U) & ((((member @ A) @ X2) @ U) & (~ ((((member @ A) @ Y) @ U)))))))))))))).
% 2.66/1.53 thf(fact_231_separation__t0, axiom, (! [A:$tType]: (((topological_t0_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) = (? [U2:(set @ A)]: ((((topolo1751647064n_open @ A) @ U2) & ((((member @ A) @ X2) @ U2) != (((member @ A) @ Y) @ U2)))))))))))).
% 2.66/1.53 thf(fact_232_separation__t1, axiom, (! [A:$tType]: (((topological_t1_space @ A) => (! [X2:A,Y:A]: (((X2 != Y) = (? [U2:(set @ A)]: ((((topolo1751647064n_open @ A) @ U2) & ((((member @ A) @ X2) @ U2) & (~ ((((member @ A) @ Y) @ U2)))))))))))))).
% 2.66/1.53 thf(fact_233_open__discrete, axiom, (! [A:$tType]: (((topolo2133971006pology @ A) => (! [A3:(set @ A)]: (((topolo1751647064n_open @ A) @ A3))))))).
% 2.66/1.53 thf(fact_234_first__countable__basis, axiom, (! [A:$tType]: (((topolo2135403230pology @ A) => (! [X2:A]: ((? [A7:(nat > (set @ A))]: (((! [I3:nat]: (((((member @ A) @ X2) @ (A7 @ I3)) & ((topolo1751647064n_open @ A) @ (A7 @ I3))))) & (! [S4:(set @ A)]: (((((topolo1751647064n_open @ A) @ S4) & (((member @ A) @ X2) @ S4)) => (? [I2:nat]: ((((ord_less_eq @ (set @ A)) @ (A7 @ I2)) @ S4))))))))))))))).
% 2.66/1.53 thf(fact_235_landau__omega_OR__mult__right__mono, axiom, (! [B2:real,A2:real,C2:real]: (((((ord_less_eq @ real) @ B2) @ A2) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ C2) => (((ord_less_eq @ real) @ (((times_times @ real) @ B2) @ C2)) @ (((times_times @ real) @ A2) @ C2))))))).
% 2.66/1.53 thf(fact_236_landau__omega_OR__mult__left__mono, axiom, (! [B2:real,A2:real,C2:real]: (((((ord_less_eq @ real) @ B2) @ A2) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ C2) => (((ord_less_eq @ real) @ (((times_times @ real) @ C2) @ B2)) @ (((times_times @ real) @ C2) @ A2))))))).
% 2.66/1.53 thf(fact_237_landau__omega_OR__linear, axiom, (! [Y:real,X2:real]: (((~ ((((ord_less_eq @ real) @ Y) @ X2))) => (((ord_less_eq @ real) @ X2) @ Y))))).
% 2.66/1.53 thf(fact_238_landau__omega_OR__trans, axiom, (! [B2:real,A2:real,C2:real]: (((((ord_less_eq @ real) @ B2) @ A2) => ((((ord_less_eq @ real) @ C2) @ B2) => (((ord_less_eq @ real) @ C2) @ A2)))))).
% 2.66/1.53 thf(fact_239_landau__omega_OR__refl, axiom, (! [X2:real]: ((((ord_less_eq @ real) @ X2) @ X2)))).
% 2.66/1.53 thf(fact_240_landau__o_OR__linear, axiom, (! [X2:real,Y:real]: (((~ ((((ord_less_eq @ real) @ X2) @ Y))) => (((ord_less_eq @ real) @ Y) @ X2))))).
% 2.66/1.53 thf(fact_241_landau__o_OR__trans, axiom, (! [A2:real,B2:real,C2:real]: (((((ord_less_eq @ real) @ A2) @ B2) => ((((ord_less_eq @ real) @ B2) @ C2) => (((ord_less_eq @ real) @ A2) @ C2)))))).
% 2.66/1.53 thf(fact_242_landau__o_OR__mult__left__mono, axiom, (! [A2:real,B2:real,C2:real]: (((((ord_less_eq @ real) @ A2) @ B2) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ C2) => (((ord_less_eq @ real) @ (((times_times @ real) @ C2) @ A2)) @ (((times_times @ real) @ C2) @ B2))))))).
% 2.66/1.53 thf(fact_243_landau__o_OR__mult__right__mono, axiom, (! [A2:real,B2:real,C2:real]: (((((ord_less_eq @ real) @ A2) @ B2) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ C2) => (((ord_less_eq @ real) @ (((times_times @ real) @ A2) @ C2)) @ (((times_times @ real) @ B2) @ C2))))))).
% 2.66/1.53 thf(fact_244_all__subset__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A3:(set @ B),P:((set @ A) > $o)]: (((! [B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B6) @ ((((image @ B) @ A) @ F) @ A3)) => (P @ B6)))) = (! [B6:(set @ B)]: (((((ord_less_eq @ (set @ B)) @ B6) @ A3) => (P @ ((((image @ B) @ A) @ F) @ B6))))))))).
% 2.66/1.53 thf(fact_245_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 2.66/1.53 thf(fact_246_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.66/1.53 thf(fact_247_dbl__inc__simps_I2_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (((neg_numeral_dbl_inc @ A) @ (zero_zero @ A)) = (one_one @ A)))))).
% 2.66/1.53 thf(fact_248_ln__one, axiom, (! [A:$tType]: (((ln @ A) => (((ln_ln @ A) @ (one_one @ A)) = (zero_zero @ A)))))).
% 2.66/1.53 thf(fact_249_ln__ge__zero, axiom, (! [X2:real]: (((((ord_less_eq @ real) @ (one_one @ real)) @ X2) => (((ord_less_eq @ real) @ (zero_zero @ real)) @ ((ln_ln @ real) @ X2)))))).
% 2.66/1.53 thf(fact_250_Ln__1, axiom, (((ln_ln @ complex) @ (one_one @ complex)) = (zero_zero @ complex))).
% 2.66/1.53 thf(fact_251_fps__tan__0, axiom, (! [A:$tType]: (((field_char_0 @ A) => (((formal_Power_fps_tan @ A) @ (zero_zero @ A)) = (zero_zero @ (formal_Power_fps @ A))))))).
% 2.66/1.53 thf(fact_252_holomorphic__fun__eq__0__on__connected, axiom, (! [F:(complex > complex),S:(set @ complex),Z:complex,W2:complex]: ((((comple372758642hic_on @ F) @ S) => (((topolo1751647064n_open @ complex) @ S) => (((topolo1099314120nected @ complex) @ S) => ((! [N3:nat]: (((((((compow @ ((complex > complex) > (complex > complex))) @ N3) @ (deriv @ complex)) @ F) @ Z) = (zero_zero @ complex)))) => ((((member @ complex) @ Z) @ S) => ((((member @ complex) @ W2) @ S) => ((F @ W2) = (zero_zero @ complex))))))))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Real__Vector__Spaces_Ometric__space, axiom, (! [A8:$tType]: (((group_add @ A8) => (real_V2090557954_space @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Ogroup__add, axiom, (! [A8:$tType]: (((group_add @ A8) => (group_add @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocancel__semigroup__add, axiom, (! [A8:$tType]: (((cancel_semigroup_add @ A8) => (cancel_semigroup_add @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Ocomm__semiring__0, axiom, (! [A8:$tType]: (((comm_semiring_0 @ A8) => (comm_semiring_0 @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__0, axiom, (! [A8:$tType]: (((semiring_0 @ A8) => (semiring_0 @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__1, axiom, (! [A8:$tType]: (((semiring_1 @ A8) => (semiring_1 @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocomm__monoid__add, axiom, (! [A8:$tType]: (((comm_monoid_add @ A8) => (comm_monoid_add @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Oring__1, axiom, (! [A8:$tType]: (((ring_1 @ A8) => (ring_1 @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Real__Vector__Spaces_Ometric__space_1, axiom, (real_V2090557954_space @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Ogroup__add_2, axiom, (group_add @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Ocancel__semigroup__add_3, axiom, (cancel_semigroup_add @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Ocomm__semiring__0_4, axiom, (comm_semiring_0 @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Osemiring__0_5, axiom, (semiring_0 @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Osemiring__1_6, axiom, (semiring_1 @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Ocomm__monoid__add_7, axiom, (comm_monoid_add @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Oring__1_8, axiom, (ring_1 @ complex)).
% 2.66/1.53 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_9, axiom, (real_V2090557954_space @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Ogroup__add_10, axiom, (group_add @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_11, axiom, (cancel_semigroup_add @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__0_12, axiom, (comm_semiring_0 @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Osemiring__0_13, axiom, (semiring_0 @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Osemiring__1_14, axiom, (semiring_1 @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_15, axiom, (comm_monoid_add @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Oring__1_16, axiom, (ring_1 @ real)).
% 2.66/1.53 thf(tcon_HOL_Obool___Countable_Ocountable, axiom, (countable @ $o)).
% 2.66/1.53 thf(tcon_Set_Oset___Countable_Ocountable_17, axiom, (! [A8:$tType]: (((finite_finite @ A8) => (countable @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add_18, axiom, (! [A8:$tType]: (((comm_monoid_add @ A8) => (comm_monoid_add @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Nat_Onat___Countable_Ocountable_19, axiom, (countable @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add_20, axiom, (cancel_semigroup_add @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0_21, axiom, (comm_semiring_0 @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Osemiring__0_22, axiom, (semiring_0 @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Osemiring__1_23, axiom, (semiring_1 @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_24, axiom, (comm_monoid_add @ nat)).
% 2.66/1.53 thf(tcon_fun___Countable_Ocountable_25, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (countable @ A9)) => (countable @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Real__Vector__Spaces_Ometric__space_26, axiom, (! [A8:$tType,A9:$tType]: ((((countable @ A8) & (real_V2090557954_space @ A9)) => (real_V2090557954_space @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (finite_finite @ A9)) => (finite_finite @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Finite__Set_Ofinite_27, axiom, (! [A8:$tType]: (((finite_finite @ A8) => (finite_finite @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_HOL_Obool___Finite__Set_Ofinite_28, axiom, (finite_finite @ $o)).
% 2.66/1.53 thf(tcon_fun___Topological__Spaces_Ofirst__countable__topology, axiom, (! [A8:$tType,A9:$tType]: ((((countable @ A8) & (topolo2135403230pology @ A9)) => (topolo2135403230pology @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Topological__Spaces_Otopological__space, axiom, (! [A8:$tType,A9:$tType]: (((topolo503727757_space @ A9) => (topolo503727757_space @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Topological__Spaces_Ot1__space, axiom, (! [A8:$tType,A9:$tType]: ((((countable @ A8) & (real_V2090557954_space @ A9)) => (topological_t1_space @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Topological__Spaces_Ot0__space, axiom, (! [A8:$tType,A9:$tType]: ((((countable @ A8) & (real_V2090557954_space @ A9)) => (topological_t0_space @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 2.66/1.53 thf(tcon_Nat_Onat___Topological__Spaces_Ofirst__countable__topology_29, axiom, (topolo2135403230pology @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, axiom, (semiri1923998003cancel @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Topological__Spaces_Otopological__space_30, axiom, (topolo503727757_space @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Topological__Spaces_Odiscrete__topology, axiom, (topolo2133971006pology @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, axiom, (semiri1193490041visors @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Topological__Spaces_Ot1__space_31, axiom, (topological_t1_space @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Topological__Spaces_Ot0__space_32, axiom, (topological_t0_space @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring, axiom, (ordere1490568538miring @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0, axiom, (ordered_semiring_0 @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult, axiom, (ab_semigroup_mult @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult, axiom, (comm_monoid_mult @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Oordered__semiring, axiom, (ordered_semiring @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, (comm_semiring_1 @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Osemigroup__mult, axiom, (semigroup_mult @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Ozero__neq__one, axiom, (zero_neq_one @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Orderings_Opreorder_33, axiom, (preorder @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Omonoid__mult, axiom, (monoid_mult @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Rings_Omult__zero, axiom, (mult_zero @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Orderings_Oorder_34, axiom, (order @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Orderings_Oord_35, axiom, (ord @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Otimes, axiom, (times @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.66/1.53 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Oab__semigroup__mult_36, axiom, (! [A8:$tType]: (((ab_semigroup_mult @ A8) => (ab_semigroup_mult @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Ocomm__monoid__mult_37, axiom, (! [A8:$tType]: (((comm_monoid_mult @ A8) => (comm_monoid_mult @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Osemigroup__mult_38, axiom, (! [A8:$tType]: (((semigroup_mult @ A8) => (semigroup_mult @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_39, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Omonoid__mult_40, axiom, (! [A8:$tType]: (((monoid_mult @ A8) => (monoid_mult @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Orderings_Oorder_41, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.66/1.53 thf(tcon_Set_Oset___Orderings_Oord_42, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Otimes_43, axiom, (! [A8:$tType]: (((times @ A8) => (times @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Ozero_44, axiom, (! [A8:$tType]: (((zero @ A8) => (zero @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_Set_Oset___Groups_Oone_45, axiom, (! [A8:$tType]: (((one @ A8) => (one @ (set @ A8)))))).
% 2.66/1.53 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_46, axiom, (topolo503727757_space @ $o)).
% 2.66/1.53 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology_47, axiom, (topolo2133971006pology @ $o)).
% 2.66/1.53 thf(tcon_HOL_Obool___Topological__Spaces_Ot1__space_48, axiom, (topological_t1_space @ $o)).
% 2.66/1.53 thf(tcon_HOL_Obool___Topological__Spaces_Ot0__space_49, axiom, (topological_t0_space @ $o)).
% 2.66/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_50, axiom, (preorder @ $o)).
% 2.66/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder_51, axiom, (linorder @ $o)).
% 2.66/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_52, axiom, (order @ $o)).
% 2.66/1.53 thf(tcon_HOL_Obool___Orderings_Oord_53, axiom, (ord @ $o)).
% 2.66/1.53 thf(tcon_Real_Oreal___Topological__Spaces_Ofirst__countable__topology_54, axiom, (topolo2135403230pology @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors__cancel_55, axiom, (semiri1923998003cancel @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_56, axiom, (topolo503727757_space @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__field, axiom, (real_V758409581_field @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_57, axiom, (linord1659791738miring @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors_58, axiom, (semiri1193490041visors @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Oring__1__no__zero__divisors, axiom, (ring_11004092258visors @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Olinordered__ring__strict, axiom, (linord581940658strict @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Topological__Spaces_Ot1__space_59, axiom, (topological_t1_space @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Topological__Spaces_Ot0__space_60, axiom, (topological_t0_space @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Oordered__comm__semiring_61, axiom, (ordere1490568538miring @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Oordered__semiring__0_62, axiom, (ordered_semiring_0 @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Oab__semigroup__mult_63, axiom, (ab_semigroup_mult @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__mult_64, axiom, (comm_monoid_mult @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Oordered__semiring_65, axiom, (ordered_semiring @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Olinordered__ring, axiom, (linordered_ring @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Olinordered__idom, axiom, (linordered_idom @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_66, axiom, (comm_semiring_1 @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Osemigroup__mult_67, axiom, (semigroup_mult @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Fields_Ofield__char__0, axiom, (field_char_0 @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_68, axiom, (zero_neq_one @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Oordered__ring, axiom, (ordered_ring @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Orderings_Opreorder_69, axiom, (preorder @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Orderings_Olinorder_70, axiom, (linorder @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Omonoid__mult_71, axiom, (monoid_mult @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Transcendental_Oln, axiom, (ln @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Rings_Omult__zero_72, axiom, (mult_zero @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Orderings_Oorder_73, axiom, (order @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Num_Oneg__numeral, axiom, (neg_numeral @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Orderings_Oord_74, axiom, (ord @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Otimes_75, axiom, (times @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Fields_Ofield, axiom, (field @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Ozero_76, axiom, (zero @ real)).
% 2.66/1.53 thf(tcon_Real_Oreal___Groups_Oone_77, axiom, (one @ real)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ofirst__countable__topology_78, axiom, (topolo2135403230pology @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Osemiring__no__zero__divisors__cancel_79, axiom, (semiri1923998003cancel @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Topological__Spaces_Otopological__space_80, axiom, (topolo503727757_space @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__field_81, axiom, (real_V758409581_field @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Osemiring__no__zero__divisors_82, axiom, (semiri1193490041visors @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors_83, axiom, (ring_11004092258visors @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ot1__space_84, axiom, (topological_t1_space @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ot0__space_85, axiom, (topological_t0_space @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Oab__semigroup__mult_86, axiom, (ab_semigroup_mult @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Ocomm__monoid__mult_87, axiom, (comm_monoid_mult @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Ocomm__semiring__1_88, axiom, (comm_semiring_1 @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Osemigroup__mult_89, axiom, (semigroup_mult @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Fields_Ofield__char__0_90, axiom, (field_char_0 @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Ozero__neq__one_91, axiom, (zero_neq_one @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Omonoid__mult_92, axiom, (monoid_mult @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Transcendental_Oln_93, axiom, (ln @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Rings_Omult__zero_94, axiom, (mult_zero @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Num_Oneg__numeral_95, axiom, (neg_numeral @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Otimes_96, axiom, (times @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Fields_Ofield_97, axiom, (field @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Ozero_98, axiom, (zero @ complex)).
% 2.66/1.53 thf(tcon_Complex_Ocomplex___Groups_Oone_99, axiom, (one @ complex)).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ofirst__countable__topology_100, axiom, (! [A8:$tType]: (((group_add @ A8) => (topolo2135403230pology @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__no__zero__divisors__cancel_101, axiom, (! [A8:$tType]: ((((cancel_semigroup_add @ A8) & (semiri1923998003cancel @ A8)) => (semiri1923998003cancel @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Otopological__space_102, axiom, (! [A8:$tType]: (((group_add @ A8) => (topolo503727757_space @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__no__zero__divisors_103, axiom, (! [A8:$tType]: (((semiri1193490041visors @ A8) => (semiri1193490041visors @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Oring__1__no__zero__divisors_104, axiom, (! [A8:$tType]: (((ring_11004092258visors @ A8) => (ring_11004092258visors @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ot1__space_105, axiom, (! [A8:$tType]: (((group_add @ A8) => (topological_t1_space @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ot0__space_106, axiom, (! [A8:$tType]: (((group_add @ A8) => (topological_t0_space @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Oab__semigroup__mult_107, axiom, (! [A8:$tType]: (((comm_semiring_0 @ A8) => (ab_semigroup_mult @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocomm__monoid__mult_108, axiom, (! [A8:$tType]: (((comm_semiring_1 @ A8) => (comm_monoid_mult @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Ocomm__semiring__1_109, axiom, (! [A8:$tType]: (((comm_semiring_1 @ A8) => (comm_semiring_1 @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Osemigroup__mult_110, axiom, (! [A8:$tType]: (((semiring_0 @ A8) => (semigroup_mult @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Ozero__neq__one_111, axiom, (! [A8:$tType]: (((zero_neq_one @ A8) => (zero_neq_one @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Omonoid__mult_112, axiom, (! [A8:$tType]: (((semiring_1 @ A8) => (monoid_mult @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Rings_Omult__zero_113, axiom, (! [A8:$tType]: ((((comm_monoid_add @ A8) & (mult_zero @ A8)) => (mult_zero @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Num_Oneg__numeral_114, axiom, (! [A8:$tType]: (((ring_1 @ A8) => (neg_numeral @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Otimes_115, axiom, (! [A8:$tType]: ((((comm_monoid_add @ A8) & (times @ A8)) => (times @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Ozero_116, axiom, (! [A8:$tType]: (((zero @ A8) => (zero @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(tcon_Formal__Power__Series_Ofps___Groups_Oone_117, axiom, (! [A8:$tType]: ((((one @ A8) & (zero @ A8)) => (one @ (formal_Power_fps @ A8)))))).
% 2.66/1.53 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.66/1.53 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 2.66/1.53 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 2.66/1.53 thf(conj_0, conjecture, ((((deriv @ complex) @ (id @ complex)) @ w) = (one_one @ complex))).
% 2.66/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.opwukp64f0/DTF2DTF11704.p
% 2.66/1.53 ------------------------
% 2.66/1.55 ---- Cleaned THF ---
% 2.66/1.55 thf(ty_t_Formal__Power__Series_Ofps,type,
% 2.66/1.55 formal_Power_fps: $tType > $tType ).
% 2.66/1.55
% 2.66/1.55 thf(ty_t_Complex_Ocomplex,type,
% 2.66/1.55 complex: $tType ).
% 2.66/1.55
% 2.66/1.55 thf(ty_t_Real_Oreal,type,
% 2.66/1.55 real: $tType ).
% 2.66/1.55
% 2.66/1.55 thf(ty_t_Set_Oset,type,
% 2.66/1.55 set: $tType > $tType ).
% 2.66/1.55
% 2.66/1.55 thf(ty_t_Nat_Onat,type,
% 2.66/1.55 nat: $tType ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Finite__Set_Ofinite,type,
% 2.66/1.55 finite_finite:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Oring__1,type,
% 2.66/1.55 ring_1:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.66/1.55 comm_monoid_add:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Osemiring__1,type,
% 2.66/1.55 semiring_1:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Osemiring__0,type,
% 2.66/1.55 semiring_0:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Ocomm__semiring__0,type,
% 2.66/1.55 comm_semiring_0:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.66/1.55 cancel_semigroup_add:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Ogroup__add,type,
% 2.66/1.55 group_add:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 2.66/1.55 real_V2090557954_space:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_HOL_Otype,type,
% 2.66/1.55 type:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Countable_Ocountable,type,
% 2.66/1.55 countable:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Oone,type,
% 2.66/1.55 one:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Ozero,type,
% 2.66/1.55 zero:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Fields_Ofield,type,
% 2.66/1.55 field:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Otimes,type,
% 2.66/1.55 times:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Orderings_Oord,type,
% 2.66/1.55 ord:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Num_Oneg__numeral,type,
% 2.66/1.55 neg_numeral:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Orderings_Oorder,type,
% 2.66/1.55 order:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Omult__zero,type,
% 2.66/1.55 mult_zero:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Transcendental_Oln,type,
% 2.66/1.55 ln:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Omonoid__mult,type,
% 2.66/1.55 monoid_mult:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 2.66/1.55 linorder:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 2.66/1.55 preorder:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Oordered__ring,type,
% 2.66/1.55 ordered_ring:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.66/1.55 zero_neq_one:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Fields_Ofield__char__0,type,
% 2.66/1.55 field_char_0:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Osemigroup__mult,type,
% 2.66/1.55 semigroup_mult:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 2.66/1.55 comm_semiring_1:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.66/1.55 linordered_idom:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Olinordered__ring,type,
% 2.66/1.55 linordered_ring:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Oordered__semiring,type,
% 2.66/1.55 ordered_semiring:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 2.66/1.55 comm_monoid_mult:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 2.66/1.55 ab_semigroup_mult:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Oordered__semiring__0,type,
% 2.66/1.55 ordered_semiring_0:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Oordered__comm__semiring,type,
% 2.66/1.55 ordere1490568538miring:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Topological__Spaces_Ot0__space,type,
% 2.66/1.55 topological_t0_space:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Topological__Spaces_Ot1__space,type,
% 2.66/1.55 topological_t1_space:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 2.66/1.55 linord581940658strict:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 2.66/1.55 ring_11004092258visors:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 2.66/1.55 semiri1193490041visors:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.66/1.55 linord1659791738miring:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__field,type,
% 2.66/1.55 real_V758409581_field:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Topological__Spaces_Odiscrete__topology,type,
% 2.66/1.55 topolo2133971006pology:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 2.66/1.55 topolo503727757_space:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.66/1.55 canoni770627133id_add:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 2.66/1.55 semiri1923998003cancel:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_cl_Topological__Spaces_Ofirst__countable__topology,type,
% 2.66/1.55 topolo2135403230pology:
% 2.66/1.55 !>[A: $tType] : $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Complex__Analysis__Basics_Oholomorphic__on,type,
% 2.66/1.55 comple372758642hic_on: ( complex > complex ) > ( set @ complex ) > $o ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Derivative_Oderiv,type,
% 2.66/1.55 deriv:
% 2.66/1.55 !>[A: $tType] : ( ( A > A ) > A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Formal__Power__Series_Ofps__tan,type,
% 2.66/1.55 formal_Power_fps_tan:
% 2.66/1.55 !>[A: $tType] : ( A > ( formal_Power_fps @ A ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Fun_Ocomp,type,
% 2.66/1.55 comp:
% 2.66/1.55 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Fun_Oid,type,
% 2.66/1.55 id:
% 2.66/1.55 !>[A: $tType] : ( A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.66/1.55 one_one:
% 2.66/1.55 !>[A: $tType] : A ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 2.66/1.55 times_times:
% 2.66/1.55 !>[A: $tType] : ( A > A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.66/1.55 zero_zero:
% 2.66/1.55 !>[A: $tType] : A ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_If,type,
% 2.66/1.55 if:
% 2.66/1.55 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Nat_Ocompow,type,
% 2.66/1.55 compow:
% 2.66/1.55 !>[A: $tType] : ( nat > A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Nat_Ofunpow,type,
% 2.66/1.55 funpow:
% 2.66/1.55 !>[A: $tType] : ( nat > ( A > A ) > A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 2.66/1.55 neg_numeral_dbl_inc:
% 2.66/1.55 !>[A: $tType] : ( A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.66/1.55 ord_less_eq:
% 2.66/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Set_OCollect,type,
% 2.66/1.55 collect:
% 2.66/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Set_Oimage,type,
% 2.66/1.55 image:
% 2.66/1.55 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Topological__Spaces_Oopen__class_Oopen,type,
% 2.66/1.55 topolo1751647064n_open:
% 2.66/1.55 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconnected,type,
% 2.66/1.55 topolo1099314120nected:
% 2.66/1.55 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Transcendental_Oarcosh,type,
% 2.66/1.55 arcosh:
% 2.66/1.55 !>[A: $tType] : ( A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Transcendental_Oarsinh,type,
% 2.66/1.55 arsinh:
% 2.66/1.55 !>[A: $tType] : ( A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Transcendental_Oartanh,type,
% 2.66/1.55 artanh:
% 2.66/1.55 !>[A: $tType] : ( A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Transcendental_Oln__class_Oln,type,
% 2.66/1.55 ln_ln:
% 2.66/1.55 !>[A: $tType] : ( A > A ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_Transitive__Closure_Orelpowp,type,
% 2.66/1.55 transitive_relpowp:
% 2.66/1.55 !>[A: $tType] : ( nat > ( A > A > $o ) > A > A > $o ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_c_member,type,
% 2.66/1.55 member:
% 2.66/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.66/1.55
% 2.66/1.55 thf(sy_v_S,type,
% 2.66/1.55 s: set @ complex ).
% 2.66/1.55
% 2.66/1.55 thf(sy_v_T,type,
% 2.66/1.55 t: set @ complex ).
% 2.66/1.55
% 2.66/1.55 thf(sy_v_f,type,
% 2.66/1.55 f: complex > complex ).
% 2.66/1.55
% 2.66/1.55 thf(sy_v_g,type,
% 2.66/1.55 g: complex > complex ).
% 2.66/1.55
% 2.66/1.55 thf(sy_v_w,type,
% 2.66/1.55 w: complex ).
% 2.66/1.55
% 2.66/1.55 thf(fact_0__092_060open_062_092_060And_062z_O_A_Ideriv_A_094_094_A1_J_Aid_Az_A_061_A_Iif_A1_A_061_A0_Athen_Az_Aelse_Aif_A1_A_061_A1_Athen_A1_058_058_063_Ha_Aelse_A_I0_058_058_063_Ha_J_J_092_060close_062,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( real_V758409581_field @ A )
% 2.66/1.55 => ! [Z: A] :
% 2.66/1.55 ( ( ( ( one_one @ nat )
% 2.66/1.55 = ( zero_zero @ nat ) )
% 2.66/1.55 => ( ( compow @ ( ( A > A ) > A > A ) @ ( one_one @ nat ) @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 2.66/1.55 = Z ) )
% 2.66/1.55 & ( ( ( one_one @ nat )
% 2.66/1.55 != ( zero_zero @ nat ) )
% 2.66/1.55 => ( ( compow @ ( ( A > A ) > A > A ) @ ( one_one @ nat ) @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 2.66/1.55 = ( one_one @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_1_assms_I7_J,axiom,
% 2.66/1.55 member @ complex @ w @ s ).
% 2.66/1.55
% 2.66/1.55 thf(fact_2_deriv__id,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( real_V758409581_field @ A )
% 2.66/1.55 => ( ( deriv @ A @ ( id @ A ) )
% 2.66/1.55 = ( ^ [Z2: A] : ( one_one @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_3_id__apply,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( id @ A )
% 2.66/1.55 = ( ^ [X: A] : X ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_4_id__def,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( id @ A )
% 2.66/1.55 = ( ^ [X: A] : X ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_5_eq__id__iff,axiom,
% 2.66/1.55 ! [A: $tType,F: A > A] :
% 2.66/1.55 ( ( ! [X: A] :
% 2.66/1.55 ( ( F @ X )
% 2.66/1.55 = X ) )
% 2.66/1.55 = ( F
% 2.66/1.55 = ( id @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_6_higher__deriv__id,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( real_V758409581_field @ A )
% 2.66/1.55 => ! [N: nat,Z: A] :
% 2.66/1.55 ( ( ( N
% 2.66/1.55 = ( zero_zero @ nat ) )
% 2.66/1.55 => ( ( compow @ ( ( A > A ) > A > A ) @ N @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 2.66/1.55 = Z ) )
% 2.66/1.55 & ( ( N
% 2.66/1.55 != ( zero_zero @ nat ) )
% 2.66/1.55 => ( ( ( N
% 2.66/1.55 = ( one_one @ nat ) )
% 2.66/1.55 => ( ( compow @ ( ( A > A ) > A > A ) @ N @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 2.66/1.55 = ( one_one @ A ) ) )
% 2.66/1.55 & ( ( N
% 2.66/1.55 != ( one_one @ nat ) )
% 2.66/1.55 => ( ( compow @ ( ( A > A ) > A > A ) @ N @ ( deriv @ A ) @ ( id @ A ) @ Z )
% 2.66/1.55 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_7_one__reorient,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( one @ A )
% 2.66/1.55 => ! [X2: A] :
% 2.66/1.55 ( ( ( one_one @ A )
% 2.66/1.55 = X2 )
% 2.66/1.55 = ( X2
% 2.66/1.55 = ( one_one @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_8_id__funpow,axiom,
% 2.66/1.55 ! [A: $tType,N: nat] :
% 2.66/1.55 ( ( compow @ ( A > A ) @ N @ ( id @ A ) )
% 2.66/1.55 = ( id @ A ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_9_calculation,axiom,
% 2.66/1.55 ( ( times_times @ complex @ ( deriv @ complex @ f @ w ) @ ( deriv @ complex @ g @ ( f @ w ) ) )
% 2.66/1.55 = ( deriv @ complex @ ( id @ complex ) @ w ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_10__092_060open_062deriv_A_Ig_A_092_060circ_062_Af_J_Aw_A_061_Aderiv_Aid_Aw_092_060close_062,axiom,
% 2.66/1.55 ( ( deriv @ complex @ ( comp @ complex @ complex @ complex @ g @ f ) @ w )
% 2.66/1.55 = ( deriv @ complex @ ( id @ complex ) @ w ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_11_zero__neq__one,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( zero_neq_one @ A )
% 2.66/1.55 => ( ( zero_zero @ A )
% 2.66/1.55 != ( one_one @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_12__092_060open_062deriv_Af_Aw_A_K_Aderiv_Ag_A_If_Aw_J_A_061_Aderiv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_092_060close_062,axiom,
% 2.66/1.55 ( ( times_times @ complex @ ( deriv @ complex @ f @ w ) @ ( deriv @ complex @ g @ ( f @ w ) ) )
% 2.66/1.55 = ( times_times @ complex @ ( deriv @ complex @ g @ ( f @ w ) ) @ ( deriv @ complex @ f @ w ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_13_comp__apply,axiom,
% 2.66/1.55 ! [C: $tType,A: $tType,B: $tType] :
% 2.66/1.55 ( ( comp @ B @ A @ C )
% 2.66/1.55 = ( ^ [F2: B > A,G: C > B,X: C] : ( F2 @ ( G @ X ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_14_mult__zero__left,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( mult_zero @ A )
% 2.66/1.55 => ! [A2: A] :
% 2.66/1.55 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.55 = ( zero_zero @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_15_mult__zero__right,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( mult_zero @ A )
% 2.66/1.55 => ! [A2: A] :
% 2.66/1.55 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.55 = ( zero_zero @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_16_mult__eq__0__iff,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semiri1193490041visors @ A )
% 2.66/1.55 => ! [A2: A,B2: A] :
% 2.66/1.55 ( ( ( times_times @ A @ A2 @ B2 )
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 = ( ( A2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( B2
% 2.66/1.55 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_17_mult__cancel__left,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semiri1923998003cancel @ A )
% 2.66/1.55 => ! [C2: A,A2: A,B2: A] :
% 2.66/1.55 ( ( ( times_times @ A @ C2 @ A2 )
% 2.66/1.55 = ( times_times @ A @ C2 @ B2 ) )
% 2.66/1.55 = ( ( C2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( A2 = B2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_18_mult__cancel__right,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semiri1923998003cancel @ A )
% 2.66/1.55 => ! [A2: A,C2: A,B2: A] :
% 2.66/1.55 ( ( ( times_times @ A @ A2 @ C2 )
% 2.66/1.55 = ( times_times @ A @ B2 @ C2 ) )
% 2.66/1.55 = ( ( C2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( A2 = B2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_19_mult_Oright__neutral,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( monoid_mult @ A )
% 2.66/1.55 => ! [A2: A] :
% 2.66/1.55 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 2.66/1.55 = A2 ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_20_mult_Oleft__neutral,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( monoid_mult @ A )
% 2.66/1.55 => ! [A2: A] :
% 2.66/1.55 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 2.66/1.55 = A2 ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_21_id__comp,axiom,
% 2.66/1.55 ! [B: $tType,A: $tType,G2: A > B] :
% 2.66/1.55 ( ( comp @ B @ B @ A @ ( id @ B ) @ G2 )
% 2.66/1.55 = G2 ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_22_comp__id,axiom,
% 2.66/1.55 ! [B: $tType,A: $tType,F: A > B] :
% 2.66/1.55 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 2.66/1.55 = F ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_23_funpow__0,axiom,
% 2.66/1.55 ! [A: $tType,F: A > A,X2: A] :
% 2.66/1.55 ( ( compow @ ( A > A ) @ ( zero_zero @ nat ) @ F @ X2 )
% 2.66/1.55 = X2 ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_24_assms_I3_J,axiom,
% 2.66/1.55 topolo1751647064n_open @ complex @ s ).
% 2.66/1.55
% 2.66/1.55 thf(fact_25__092_060open_062deriv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_A_061_Aderiv_A_Ig_A_092_060circ_062_Af_J_Aw_092_060close_062,axiom,
% 2.66/1.55 ( ( times_times @ complex @ ( deriv @ complex @ g @ ( f @ w ) ) @ ( deriv @ complex @ f @ w ) )
% 2.66/1.55 = ( deriv @ complex @ ( comp @ complex @ complex @ complex @ g @ f ) @ w ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_26_mult__cancel__right2,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( ring_11004092258visors @ A )
% 2.66/1.55 => ! [A2: A,C2: A] :
% 2.66/1.55 ( ( ( times_times @ A @ A2 @ C2 )
% 2.66/1.55 = C2 )
% 2.66/1.55 = ( ( C2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( A2
% 2.66/1.55 = ( one_one @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_27_mult__cancel__right1,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( ring_11004092258visors @ A )
% 2.66/1.55 => ! [C2: A,B2: A] :
% 2.66/1.55 ( ( C2
% 2.66/1.55 = ( times_times @ A @ B2 @ C2 ) )
% 2.66/1.55 = ( ( C2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( B2
% 2.66/1.55 = ( one_one @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_28_mult__cancel__left2,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( ring_11004092258visors @ A )
% 2.66/1.55 => ! [C2: A,A2: A] :
% 2.66/1.55 ( ( ( times_times @ A @ C2 @ A2 )
% 2.66/1.55 = C2 )
% 2.66/1.55 = ( ( C2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( A2
% 2.66/1.55 = ( one_one @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_29_mult__cancel__left1,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( ring_11004092258visors @ A )
% 2.66/1.55 => ! [C2: A,B2: A] :
% 2.66/1.55 ( ( C2
% 2.66/1.55 = ( times_times @ A @ C2 @ B2 ) )
% 2.66/1.55 = ( ( C2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( B2
% 2.66/1.55 = ( one_one @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_30_assms_I6_J,axiom,
% 2.66/1.55 ! [Z: complex] :
% 2.66/1.55 ( ( member @ complex @ Z @ s )
% 2.66/1.55 => ( ( g @ ( f @ Z ) )
% 2.66/1.55 = Z ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_31_assms_I1_J,axiom,
% 2.66/1.55 comple372758642hic_on @ f @ s ).
% 2.66/1.55
% 2.66/1.55 thf(fact_32_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( ab_semigroup_mult @ A )
% 2.66/1.55 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.55 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C2 )
% 2.66/1.55 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_33_comp__def,axiom,
% 2.66/1.55 ! [A: $tType,C: $tType,B: $tType] :
% 2.66/1.55 ( ( comp @ B @ C @ A )
% 2.66/1.55 = ( ^ [F2: B > C,G: A > B,X: A] : ( F2 @ ( G @ X ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_34_comp__assoc,axiom,
% 2.66/1.55 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G2: C > D,H: A > C] :
% 2.66/1.55 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G2 ) @ H )
% 2.66/1.55 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G2 @ H ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_35_comp__funpow,axiom,
% 2.66/1.55 ! [B: $tType,A: $tType,N: nat,F: A > A] :
% 2.66/1.55 ( ( compow @ ( ( B > A ) > B > A ) @ N @ ( comp @ A @ A @ B @ F ) )
% 2.66/1.55 = ( comp @ A @ A @ B @ ( compow @ ( A > A ) @ N @ F ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_36_comp__eq__dest,axiom,
% 2.66/1.55 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 2.66/1.55 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 2.66/1.55 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 2.66/1.55 => ( ( A2 @ ( B2 @ V ) )
% 2.66/1.55 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_37_comp__eq__elim,axiom,
% 2.66/1.55 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 2.66/1.55 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 2.66/1.55 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 2.66/1.55 => ! [V2: A] :
% 2.66/1.55 ( ( A2 @ ( B2 @ V2 ) )
% 2.66/1.55 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_38_funpow__swap1,axiom,
% 2.66/1.55 ! [A: $tType,F: A > A,N: nat,X2: A] :
% 2.66/1.55 ( ( F @ ( compow @ ( A > A ) @ N @ F @ X2 ) )
% 2.66/1.55 = ( compow @ ( A > A ) @ N @ F @ ( F @ X2 ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_39_comp__eq__dest__lhs,axiom,
% 2.66/1.55 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 2.66/1.55 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 2.66/1.55 = C2 )
% 2.66/1.55 => ( ( A2 @ ( B2 @ V ) )
% 2.66/1.55 = ( C2 @ V ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_40_zero__reorient,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( zero @ A )
% 2.66/1.55 => ! [X2: A] :
% 2.66/1.55 ( ( ( zero_zero @ A )
% 2.66/1.55 = X2 )
% 2.66/1.55 = ( X2
% 2.66/1.55 = ( zero_zero @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_41_mult__not__zero,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( mult_zero @ A )
% 2.66/1.55 => ! [A2: A,B2: A] :
% 2.66/1.55 ( ( ( times_times @ A @ A2 @ B2 )
% 2.66/1.55 != ( zero_zero @ A ) )
% 2.66/1.55 => ( ( A2
% 2.66/1.55 != ( zero_zero @ A ) )
% 2.66/1.55 & ( B2
% 2.66/1.55 != ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_42_mem__Collect__eq,axiom,
% 2.66/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 2.66/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.66/1.55 = ( P @ A2 ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_43_Collect__mem__eq,axiom,
% 2.66/1.55 ! [A: $tType,A3: set @ A] :
% 2.66/1.55 ( ( collect @ A
% 2.66/1.55 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 2.66/1.55 = A3 ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_44_Collect__cong,axiom,
% 2.66/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.66/1.55 ( ! [X3: A] :
% 2.66/1.55 ( ( P @ X3 )
% 2.66/1.55 = ( Q @ X3 ) )
% 2.66/1.55 => ( ( collect @ A @ P )
% 2.66/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_45_ext,axiom,
% 2.66/1.55 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 2.66/1.55 ( ! [X3: A] :
% 2.66/1.55 ( ( F @ X3 )
% 2.66/1.55 = ( G2 @ X3 ) )
% 2.66/1.55 => ( F = G2 ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_46_mult_Oassoc,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semigroup_mult @ A )
% 2.66/1.55 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.55 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C2 )
% 2.66/1.55 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_47_mult_Ocommute,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( ab_semigroup_mult @ A )
% 2.66/1.55 => ( ( times_times @ A )
% 2.66/1.55 = ( ^ [A4: A,B3: A] : ( times_times @ A @ B3 @ A4 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_48_mult_Oleft__commute,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( ab_semigroup_mult @ A )
% 2.66/1.55 => ! [B2: A,A2: A,C2: A] :
% 2.66/1.55 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C2 ) )
% 2.66/1.55 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_49_divisors__zero,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semiri1193490041visors @ A )
% 2.66/1.55 => ! [A2: A,B2: A] :
% 2.66/1.55 ( ( ( times_times @ A @ A2 @ B2 )
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 => ( ( A2
% 2.66/1.55 = ( zero_zero @ A ) )
% 2.66/1.55 | ( B2
% 2.66/1.55 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_50_no__zero__divisors,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semiri1193490041visors @ A )
% 2.66/1.55 => ! [A2: A,B2: A] :
% 2.66/1.55 ( ( A2
% 2.66/1.55 != ( zero_zero @ A ) )
% 2.66/1.55 => ( ( B2
% 2.66/1.55 != ( zero_zero @ A ) )
% 2.66/1.55 => ( ( times_times @ A @ A2 @ B2 )
% 2.66/1.55 != ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_51_mult__left__cancel,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semiri1923998003cancel @ A )
% 2.66/1.55 => ! [C2: A,A2: A,B2: A] :
% 2.66/1.55 ( ( C2
% 2.66/1.55 != ( zero_zero @ A ) )
% 2.66/1.55 => ( ( ( times_times @ A @ C2 @ A2 )
% 2.66/1.55 = ( times_times @ A @ C2 @ B2 ) )
% 2.66/1.55 = ( A2 = B2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_52_mult__right__cancel,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( semiri1923998003cancel @ A )
% 2.66/1.55 => ! [C2: A,A2: A,B2: A] :
% 2.66/1.55 ( ( C2
% 2.66/1.55 != ( zero_zero @ A ) )
% 2.66/1.55 => ( ( ( times_times @ A @ A2 @ C2 )
% 2.66/1.55 = ( times_times @ A @ B2 @ C2 ) )
% 2.66/1.55 = ( A2 = B2 ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_53_comp__eq__id__dest,axiom,
% 2.66/1.55 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 2.66/1.55 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 2.66/1.55 = ( comp @ B @ B @ A @ ( id @ B ) @ C2 ) )
% 2.66/1.55 => ( ( A2 @ ( B2 @ V ) )
% 2.66/1.55 = ( C2 @ V ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_54_mult_Ocomm__neutral,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( comm_monoid_mult @ A )
% 2.66/1.55 => ! [A2: A] :
% 2.66/1.55 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 2.66/1.55 = A2 ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_55_comm__monoid__mult__class_Omult__1,axiom,
% 2.66/1.55 ! [A: $tType] :
% 2.66/1.55 ( ( comm_monoid_mult @ A )
% 2.66/1.55 => ! [A2: A] :
% 2.66/1.55 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 2.66/1.55 = A2 ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_56_funpow__simps__right_I1_J,axiom,
% 2.66/1.55 ! [A: $tType,F: A > A] :
% 2.66/1.55 ( ( compow @ ( A > A ) @ ( zero_zero @ nat ) @ F )
% 2.66/1.55 = ( id @ A ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(fact_57_fun_Omap__id,axiom,
% 2.66/1.55 ! [A: $tType,D: $tType,T: D > A] :
% 2.66/1.55 ( ( comp @ A @ A @ D @ ( id @ A ) @ T )
% 2.66/1.56 = T ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_58_vector__space__over__itself_Oscale__one,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [X2: A] :
% 2.66/1.56 ( ( times_times @ A @ ( one_one @ A ) @ X2 )
% 2.66/1.56 = X2 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_59_vector__space__over__itself_Oscale__eq__0__iff,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [A2: A,X2: A] :
% 2.66/1.56 ( ( ( times_times @ A @ A2 @ X2 )
% 2.66/1.56 = ( zero_zero @ A ) )
% 2.66/1.56 = ( ( A2
% 2.66/1.56 = ( zero_zero @ A ) )
% 2.66/1.56 | ( X2
% 2.66/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_60_vector__space__over__itself_Oscale__zero__left,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [X2: A] :
% 2.66/1.56 ( ( times_times @ A @ ( zero_zero @ A ) @ X2 )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_61_vector__space__over__itself_Oscale__zero__right,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [A2: A] :
% 2.66/1.56 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_62_vector__space__over__itself_Oscale__cancel__left,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [A2: A,X2: A,Y: A] :
% 2.66/1.56 ( ( ( times_times @ A @ A2 @ X2 )
% 2.66/1.56 = ( times_times @ A @ A2 @ Y ) )
% 2.66/1.56 = ( ( X2 = Y )
% 2.66/1.56 | ( A2
% 2.66/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_63_vector__space__over__itself_Oscale__cancel__right,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [A2: A,X2: A,B2: A] :
% 2.66/1.56 ( ( ( times_times @ A @ A2 @ X2 )
% 2.66/1.56 = ( times_times @ A @ B2 @ X2 ) )
% 2.66/1.56 = ( ( A2 = B2 )
% 2.66/1.56 | ( X2
% 2.66/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_64_mult__if__delta,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( comm_semiring_1 @ A )
% 2.66/1.56 => ! [P: $o,Q2: A] :
% 2.66/1.56 ( ( P
% 2.66/1.56 => ( ( times_times @ A @ ( if @ A @ P @ ( one_one @ A ) @ ( zero_zero @ A ) ) @ Q2 )
% 2.66/1.56 = Q2 ) )
% 2.66/1.56 & ( ~ P
% 2.66/1.56 => ( ( times_times @ A @ ( if @ A @ P @ ( one_one @ A ) @ ( zero_zero @ A ) ) @ Q2 )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_65_relpowp__1,axiom,
% 2.66/1.56 ! [A: $tType,P: A > A > $o] :
% 2.66/1.56 ( ( compow @ ( A > A > $o ) @ ( one_one @ nat ) @ P )
% 2.66/1.56 = P ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_66_set__times__intro,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( times @ A )
% 2.66/1.56 => ! [A2: A,C3: set @ A,B2: A,D3: set @ A] :
% 2.66/1.56 ( ( member @ A @ A2 @ C3 )
% 2.66/1.56 => ( ( member @ A @ B2 @ D3 )
% 2.66/1.56 => ( member @ A @ ( times_times @ A @ A2 @ B2 ) @ ( times_times @ ( set @ A ) @ C3 @ D3 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_67_funpow__code__def,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( funpow @ A )
% 2.66/1.56 = ( compow @ ( A > A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_68_assms_I4_J,axiom,
% 2.66/1.56 topolo1751647064n_open @ complex @ t ).
% 2.66/1.56
% 2.66/1.56 thf(fact_69_assms_I2_J,axiom,
% 2.66/1.56 comple372758642hic_on @ g @ t ).
% 2.66/1.56
% 2.66/1.56 thf(fact_70_mult__cancel2,axiom,
% 2.66/1.56 ! [M: nat,K: nat,N: nat] :
% 2.66/1.56 ( ( ( times_times @ nat @ M @ K )
% 2.66/1.56 = ( times_times @ nat @ N @ K ) )
% 2.66/1.56 = ( ( M = N )
% 2.66/1.56 | ( K
% 2.66/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_71_mult__cancel1,axiom,
% 2.66/1.56 ! [K: nat,M: nat,N: nat] :
% 2.66/1.56 ( ( ( times_times @ nat @ K @ M )
% 2.66/1.56 = ( times_times @ nat @ K @ N ) )
% 2.66/1.56 = ( ( M = N )
% 2.66/1.56 | ( K
% 2.66/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_72_mult__0__right,axiom,
% 2.66/1.56 ! [M: nat] :
% 2.66/1.56 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 2.66/1.56 = ( zero_zero @ nat ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_73_mult__is__0,axiom,
% 2.66/1.56 ! [M: nat,N: nat] :
% 2.66/1.56 ( ( ( times_times @ nat @ M @ N )
% 2.66/1.56 = ( zero_zero @ nat ) )
% 2.66/1.56 = ( ( M
% 2.66/1.56 = ( zero_zero @ nat ) )
% 2.66/1.56 | ( N
% 2.66/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_74_nat__mult__eq__1__iff,axiom,
% 2.66/1.56 ! [M: nat,N: nat] :
% 2.66/1.56 ( ( ( times_times @ nat @ M @ N )
% 2.66/1.56 = ( one_one @ nat ) )
% 2.66/1.56 = ( ( M
% 2.66/1.56 = ( one_one @ nat ) )
% 2.66/1.56 & ( N
% 2.66/1.56 = ( one_one @ nat ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_75_nat__1__eq__mult__iff,axiom,
% 2.66/1.56 ! [M: nat,N: nat] :
% 2.66/1.56 ( ( ( one_one @ nat )
% 2.66/1.56 = ( times_times @ nat @ M @ N ) )
% 2.66/1.56 = ( ( M
% 2.66/1.56 = ( one_one @ nat ) )
% 2.66/1.56 & ( N
% 2.66/1.56 = ( one_one @ nat ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_76_relpowp__Suc__D2_H,axiom,
% 2.66/1.56 ! [A: $tType,N: nat,P: A > A > $o,X4: A,Y2: A,Z3: A] :
% 2.66/1.56 ( ( ( compow @ ( A > A > $o ) @ N @ P @ X4 @ Y2 )
% 2.66/1.56 & ( P @ Y2 @ Z3 ) )
% 2.66/1.56 => ? [W: A] :
% 2.66/1.56 ( ( P @ X4 @ W )
% 2.66/1.56 & ( compow @ ( A > A > $o ) @ N @ P @ W @ Z3 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_77_higher__deriv__transform__within__open,axiom,
% 2.66/1.56 ! [F: complex > complex,S: set @ complex,G2: complex > complex,Z: complex,I: nat] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S )
% 2.66/1.56 => ( ( comple372758642hic_on @ G2 @ S )
% 2.66/1.56 => ( ( topolo1751647064n_open @ complex @ S )
% 2.66/1.56 => ( ( member @ complex @ Z @ S )
% 2.66/1.56 => ( ! [W: complex] :
% 2.66/1.56 ( ( member @ complex @ W @ S )
% 2.66/1.56 => ( ( F @ W )
% 2.66/1.56 = ( G2 @ W ) ) )
% 2.66/1.56 => ( ( compow @ ( ( complex > complex ) > complex > complex ) @ I @ ( deriv @ complex ) @ F @ Z )
% 2.66/1.56 = ( compow @ ( ( complex > complex ) > complex > complex ) @ I @ ( deriv @ complex ) @ G2 @ Z ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_78_holomorphic__higher__deriv,axiom,
% 2.66/1.56 ! [F: complex > complex,S: set @ complex,N: nat] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S )
% 2.66/1.56 => ( ( topolo1751647064n_open @ complex @ S )
% 2.66/1.56 => ( comple372758642hic_on @ ( compow @ ( ( complex > complex ) > complex > complex ) @ N @ ( deriv @ complex ) @ F ) @ S ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_79_holomorphic__deriv,axiom,
% 2.66/1.56 ! [F: complex > complex,S: set @ complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S )
% 2.66/1.56 => ( ( topolo1751647064n_open @ complex @ S )
% 2.66/1.56 => ( comple372758642hic_on @ ( deriv @ complex @ F ) @ S ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_80_mult__0,axiom,
% 2.66/1.56 ! [N: nat] :
% 2.66/1.56 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 2.66/1.56 = ( zero_zero @ nat ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_81_nat__mult__1__right,axiom,
% 2.66/1.56 ! [N: nat] :
% 2.66/1.56 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 2.66/1.56 = N ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_82_nat__mult__1,axiom,
% 2.66/1.56 ! [N: nat] :
% 2.66/1.56 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 2.66/1.56 = N ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_83_funpow__mult,axiom,
% 2.66/1.56 ! [A: $tType,N: nat,M: nat,F: A > A] :
% 2.66/1.56 ( ( compow @ ( A > A ) @ N @ ( compow @ ( A > A ) @ M @ F ) )
% 2.66/1.56 = ( compow @ ( A > A ) @ ( times_times @ nat @ M @ N ) @ F ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_84_mult__eq__self__implies__10,axiom,
% 2.66/1.56 ! [M: nat,N: nat] :
% 2.66/1.56 ( ( M
% 2.66/1.56 = ( times_times @ nat @ M @ N ) )
% 2.66/1.56 => ( ( N
% 2.66/1.56 = ( one_one @ nat ) )
% 2.66/1.56 | ( M
% 2.66/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_85_vector__space__over__itself_Oscale__left__commute,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [A2: A,B2: A,X2: A] :
% 2.66/1.56 ( ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ X2 ) )
% 2.66/1.56 = ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ X2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_86_vector__space__over__itself_Oscale__scale,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [A2: A,B2: A,X2: A] :
% 2.66/1.56 ( ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ X2 ) )
% 2.66/1.56 = ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ X2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_87_set__times__elim,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( times @ A )
% 2.66/1.56 => ! [X2: A,A3: set @ A,B4: set @ A] :
% 2.66/1.56 ( ( member @ A @ X2 @ ( times_times @ ( set @ A ) @ A3 @ B4 ) )
% 2.66/1.56 => ~ ! [A5: A,B5: A] :
% 2.66/1.56 ( ( X2
% 2.66/1.56 = ( times_times @ A @ A5 @ B5 ) )
% 2.66/1.56 => ( ( member @ A @ A5 @ A3 )
% 2.66/1.56 => ~ ( member @ A @ B5 @ B4 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_88_relpowp__0__I,axiom,
% 2.66/1.56 ! [A: $tType,P: A > A > $o,X2: A] : ( compow @ ( A > A > $o ) @ ( zero_zero @ nat ) @ P @ X2 @ X2 ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_89_relpowp__0__E,axiom,
% 2.66/1.56 ! [A: $tType,P: A > A > $o,X2: A,Y: A] :
% 2.66/1.56 ( ( compow @ ( A > A > $o ) @ ( zero_zero @ nat ) @ P @ X2 @ Y )
% 2.66/1.56 => ( X2 = Y ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_90_relpowp_Osimps_I1_J,axiom,
% 2.66/1.56 ! [A: $tType,R: A > A > $o] :
% 2.66/1.56 ( ( compow @ ( A > A > $o ) @ ( zero_zero @ nat ) @ R )
% 2.66/1.56 = ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_91_fun_Omap__comp,axiom,
% 2.66/1.56 ! [B: $tType,C: $tType,A: $tType,D: $tType,G2: B > C,F: A > B,V: D > A] :
% 2.66/1.56 ( ( comp @ B @ C @ D @ G2 @ ( comp @ A @ B @ D @ F @ V ) )
% 2.66/1.56 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G2 @ F ) @ V ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_92_vector__space__over__itself_Oscale__right__imp__eq,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [X2: A,A2: A,B2: A] :
% 2.66/1.56 ( ( X2
% 2.66/1.56 != ( zero_zero @ A ) )
% 2.66/1.56 => ( ( ( times_times @ A @ A2 @ X2 )
% 2.66/1.56 = ( times_times @ A @ B2 @ X2 ) )
% 2.66/1.56 => ( A2 = B2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_93_vector__space__over__itself_Oscale__left__imp__eq,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field @ A )
% 2.66/1.56 => ! [A2: A,X2: A,Y: A] :
% 2.66/1.56 ( ( A2
% 2.66/1.56 != ( zero_zero @ A ) )
% 2.66/1.56 => ( ( ( times_times @ A @ A2 @ X2 )
% 2.66/1.56 = ( times_times @ A @ A2 @ Y ) )
% 2.66/1.56 => ( X2 = Y ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_94_fun_Omap__id0,axiom,
% 2.66/1.56 ! [A: $tType,D: $tType] :
% 2.66/1.56 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 2.66/1.56 = ( id @ ( D > A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_95_complex__derivative__transform__within__open,axiom,
% 2.66/1.56 ! [F: complex > complex,S2: set @ complex,G2: complex > complex,Z: complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S2 )
% 2.66/1.56 => ( ( comple372758642hic_on @ G2 @ S2 )
% 2.66/1.56 => ( ( topolo1751647064n_open @ complex @ S2 )
% 2.66/1.56 => ( ( member @ complex @ Z @ S2 )
% 2.66/1.56 => ( ! [W: complex] :
% 2.66/1.56 ( ( member @ complex @ W @ S2 )
% 2.66/1.56 => ( ( F @ W )
% 2.66/1.56 = ( G2 @ W ) ) )
% 2.66/1.56 => ( ( deriv @ complex @ F @ Z )
% 2.66/1.56 = ( deriv @ complex @ G2 @ Z ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_96_holomorphic__on__id,axiom,
% 2.66/1.56 ! [S2: set @ complex] : ( comple372758642hic_on @ ( id @ complex ) @ S2 ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_97_relpowp__code__def,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( transitive_relpowp @ A )
% 2.66/1.56 = ( compow @ ( A > A > $o ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_98_holomorphic__on__linear,axiom,
% 2.66/1.56 ! [C2: complex,S2: set @ complex] : ( comple372758642hic_on @ ( times_times @ complex @ C2 ) @ S2 ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_99_pointfree__idE,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,F: B > A,G2: A > B,X2: A] :
% 2.66/1.56 ( ( ( comp @ B @ A @ A @ F @ G2 )
% 2.66/1.56 = ( id @ A ) )
% 2.66/1.56 => ( ( F @ ( G2 @ X2 ) )
% 2.66/1.56 = X2 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_100_isomorphism__expand,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,F: B > A,G2: A > B] :
% 2.66/1.56 ( ( ( ( comp @ B @ A @ A @ F @ G2 )
% 2.66/1.56 = ( id @ A ) )
% 2.66/1.56 & ( ( comp @ A @ B @ B @ G2 @ F )
% 2.66/1.56 = ( id @ B ) ) )
% 2.66/1.56 = ( ! [X: A] :
% 2.66/1.56 ( ( F @ ( G2 @ X ) )
% 2.66/1.56 = X )
% 2.66/1.56 & ! [X: B] :
% 2.66/1.56 ( ( G2 @ ( F @ X ) )
% 2.66/1.56 = X ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_101_left__right__inverse__eq,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,F: B > A,G2: A > B,H: B > A] :
% 2.66/1.56 ( ( ( comp @ B @ A @ A @ F @ G2 )
% 2.66/1.56 = ( id @ A ) )
% 2.66/1.56 => ( ( ( comp @ A @ B @ B @ G2 @ H )
% 2.66/1.56 = ( id @ B ) )
% 2.66/1.56 => ( F = H ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_102_rewriteL__comp__comp,axiom,
% 2.66/1.56 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G2: A > C,L: A > B,H: D > A] :
% 2.66/1.56 ( ( ( comp @ C @ B @ A @ F @ G2 )
% 2.66/1.56 = L )
% 2.66/1.56 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G2 @ H ) )
% 2.66/1.56 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_103_rewriteR__comp__comp,axiom,
% 2.66/1.56 ! [C: $tType,D: $tType,B: $tType,A: $tType,G2: C > B,H: A > C,R2: A > B,F: B > D] :
% 2.66/1.56 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 2.66/1.56 = R2 )
% 2.66/1.56 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G2 ) @ H )
% 2.66/1.56 = ( comp @ B @ D @ A @ F @ R2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_104_rewriteL__comp__comp2,axiom,
% 2.66/1.56 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G2: A > C,L1: D > B,L2: A > D,H: E > A,R2: E > D] :
% 2.66/1.56 ( ( ( comp @ C @ B @ A @ F @ G2 )
% 2.66/1.56 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 2.66/1.56 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 2.66/1.56 = R2 )
% 2.66/1.56 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G2 @ H ) )
% 2.66/1.56 = ( comp @ D @ B @ E @ L1 @ R2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_105_rewriteR__comp__comp2,axiom,
% 2.66/1.56 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G2: C > B,H: A > C,R1: D > B,R22: A > D,F: B > E,L: D > E] :
% 2.66/1.56 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 2.66/1.56 = ( comp @ D @ B @ A @ R1 @ R22 ) )
% 2.66/1.56 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 2.66/1.56 = L )
% 2.66/1.56 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G2 ) @ H )
% 2.66/1.56 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_106_holomorphic__cong,axiom,
% 2.66/1.56 ! [S2: set @ complex,T: set @ complex,F: complex > complex,G2: complex > complex] :
% 2.66/1.56 ( ( S2 = T )
% 2.66/1.56 => ( ! [X3: complex] :
% 2.66/1.56 ( ( member @ complex @ X3 @ S2 )
% 2.66/1.56 => ( ( F @ X3 )
% 2.66/1.56 = ( G2 @ X3 ) ) )
% 2.66/1.56 => ( ( comple372758642hic_on @ F @ S2 )
% 2.66/1.56 = ( comple372758642hic_on @ G2 @ T ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_107_holomorphic__transform,axiom,
% 2.66/1.56 ! [F: complex > complex,S2: set @ complex,G2: complex > complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S2 )
% 2.66/1.56 => ( ! [X3: complex] :
% 2.66/1.56 ( ( member @ complex @ X3 @ S2 )
% 2.66/1.56 => ( ( F @ X3 )
% 2.66/1.56 = ( G2 @ X3 ) ) )
% 2.66/1.56 => ( comple372758642hic_on @ G2 @ S2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_108_assms_I5_J,axiom,
% 2.66/1.56 ord_less_eq @ ( set @ complex ) @ ( image @ complex @ complex @ f @ s ) @ t ).
% 2.66/1.56
% 2.66/1.56 thf(fact_109_nat__mult__eq__cancel__disj,axiom,
% 2.66/1.56 ! [K: nat,M: nat,N: nat] :
% 2.66/1.56 ( ( ( times_times @ nat @ K @ M )
% 2.66/1.56 = ( times_times @ nat @ K @ N ) )
% 2.66/1.56 = ( ( K
% 2.66/1.56 = ( zero_zero @ nat ) )
% 2.66/1.56 | ( M = N ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_110_mult__delta__left,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( mult_zero @ A )
% 2.66/1.56 => ! [B2: $o,X2: A,Y: A] :
% 2.66/1.56 ( ( B2
% 2.66/1.56 => ( ( times_times @ A @ ( if @ A @ B2 @ X2 @ ( zero_zero @ A ) ) @ Y )
% 2.66/1.56 = ( times_times @ A @ X2 @ Y ) ) )
% 2.66/1.56 & ( ~ B2
% 2.66/1.56 => ( ( times_times @ A @ ( if @ A @ B2 @ X2 @ ( zero_zero @ A ) ) @ Y )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_111_mult__delta__right,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( mult_zero @ A )
% 2.66/1.56 => ! [B2: $o,X2: A,Y: A] :
% 2.66/1.56 ( ( B2
% 2.66/1.56 => ( ( times_times @ A @ X2 @ ( if @ A @ B2 @ Y @ ( zero_zero @ A ) ) )
% 2.66/1.56 = ( times_times @ A @ X2 @ Y ) ) )
% 2.66/1.56 & ( ~ B2
% 2.66/1.56 => ( ( times_times @ A @ X2 @ ( if @ A @ B2 @ Y @ ( zero_zero @ A ) ) )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_112_arcosh__1,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ln @ A )
% 2.66/1.56 => ( ( arcosh @ A @ ( one_one @ A ) )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_113_le__zero__eq,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( canoni770627133id_add @ A )
% 2.66/1.56 => ! [N: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.66/1.56 = ( N
% 2.66/1.56 = ( zero_zero @ A ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_114_image__id,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( image @ A @ A @ ( id @ A ) )
% 2.66/1.56 = ( id @ ( set @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_115_set__times__mono2,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( times @ A )
% 2.66/1.56 => ! [C3: set @ A,D3: set @ A,E2: set @ A,F3: set @ A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 2.66/1.56 => ( ( ord_less_eq @ ( set @ A ) @ E2 @ F3 )
% 2.66/1.56 => ( ord_less_eq @ ( set @ A ) @ ( times_times @ ( set @ A ) @ C3 @ E2 ) @ ( times_times @ ( set @ A ) @ D3 @ F3 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_116_holomorphic__on__compose__gen,axiom,
% 2.66/1.56 ! [F: complex > complex,S2: set @ complex,G2: complex > complex,T: set @ complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S2 )
% 2.66/1.56 => ( ( comple372758642hic_on @ G2 @ T )
% 2.66/1.56 => ( ( ord_less_eq @ ( set @ complex ) @ ( image @ complex @ complex @ F @ S2 ) @ T )
% 2.66/1.56 => ( comple372758642hic_on @ ( comp @ complex @ complex @ complex @ G2 @ F ) @ S2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_117_image__comp,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,C: $tType,F: B > A,G2: C > B,R2: set @ C] :
% 2.66/1.56 ( ( image @ B @ A @ F @ ( image @ C @ B @ G2 @ R2 ) )
% 2.66/1.56 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G2 ) @ R2 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_118_image__eq__imp__comp,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A3: set @ B,G2: C > A,B4: set @ C,H: A > D] :
% 2.66/1.56 ( ( ( image @ B @ A @ F @ A3 )
% 2.66/1.56 = ( image @ C @ A @ G2 @ B4 ) )
% 2.66/1.56 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H @ F ) @ A3 )
% 2.66/1.56 = ( image @ C @ D @ ( comp @ A @ D @ C @ H @ G2 ) @ B4 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_119_zero__le,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( canoni770627133id_add @ A )
% 2.66/1.56 => ! [X2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_120_holomorphic__on__subset,axiom,
% 2.66/1.56 ! [F: complex > complex,S2: set @ complex,T: set @ complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S2 )
% 2.66/1.56 => ( ( ord_less_eq @ ( set @ complex ) @ T @ S2 )
% 2.66/1.56 => ( comple372758642hic_on @ F @ T ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_121_set__times__mono2__b,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( times @ A )
% 2.66/1.56 => ! [C3: set @ A,D3: set @ A,E2: set @ A,F3: set @ A,X2: A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 2.66/1.56 => ( ( ord_less_eq @ ( set @ A ) @ E2 @ F3 )
% 2.66/1.56 => ( ( member @ A @ X2 @ ( times_times @ ( set @ A ) @ C3 @ E2 ) )
% 2.66/1.56 => ( member @ A @ X2 @ ( times_times @ ( set @ A ) @ D3 @ F3 ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_122_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordere1490568538miring @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ C2 @ A2 ) @ ( times_times @ A @ C2 @ B2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_123_zero__le__mult__iff,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord581940658strict @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 2.66/1.56 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.66/1.56 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.56 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_124_mult__nonneg__nonpos2,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring_0 @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_125_mult__nonpos__nonneg,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring_0 @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_126_mult__nonneg__nonpos,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring_0 @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_127_mult__nonneg__nonneg,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring_0 @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_128_split__mult__neg__le,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring_0 @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.66/1.56 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_129_mult__le__0__iff,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord581940658strict @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 2.66/1.56 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.66/1.56 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_130_mult__right__mono,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_131_mult__right__mono__neg,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_ring @ A )
% 2.66/1.56 => ! [B2: A,A2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_132_mult__left__mono,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ C2 @ A2 ) @ ( times_times @ A @ C2 @ B2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_133_mult__nonpos__nonpos,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_ring @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_134_mult__left__mono__neg,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_ring @ A )
% 2.66/1.56 => ! [B2: A,A2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ C2 @ ( zero_zero @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ C2 @ A2 ) @ ( times_times @ A @ C2 @ B2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_135_split__mult__pos__le,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_ring @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.66/1.56 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.66/1.56 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_136_zero__le__square,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linordered_ring @ A )
% 2.66/1.56 => ! [A2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ A2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_137_mult__mono_H,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A,D2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ C2 @ D2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ D2 ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_138_mult__mono,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ordered_semiring @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A,D2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ C2 @ D2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ ( times_times @ A @ B2 @ D2 ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_139_zero__le__one,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord1659791738miring @ A )
% 2.66/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_140_not__one__le__zero,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord1659791738miring @ A )
% 2.66/1.56 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_141_holomorphic__on__compose,axiom,
% 2.66/1.56 ! [F: complex > complex,S2: set @ complex,G2: complex > complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S2 )
% 2.66/1.56 => ( ( comple372758642hic_on @ G2 @ ( image @ complex @ complex @ F @ S2 ) )
% 2.66/1.56 => ( comple372758642hic_on @ ( comp @ complex @ complex @ complex @ G2 @ F ) @ S2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_142_deriv__left__inverse,axiom,
% 2.66/1.56 ! [F: complex > complex,S: set @ complex,G2: complex > complex,T2: set @ complex,W2: complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S )
% 2.66/1.56 => ( ( comple372758642hic_on @ G2 @ T2 )
% 2.66/1.56 => ( ( topolo1751647064n_open @ complex @ S )
% 2.66/1.56 => ( ( topolo1751647064n_open @ complex @ T2 )
% 2.66/1.56 => ( ( ord_less_eq @ ( set @ complex ) @ ( image @ complex @ complex @ F @ S ) @ T2 )
% 2.66/1.56 => ( ! [Z5: complex] :
% 2.66/1.56 ( ( member @ complex @ Z5 @ S )
% 2.66/1.56 => ( ( G2 @ ( F @ Z5 ) )
% 2.66/1.56 = Z5 ) )
% 2.66/1.56 => ( ( member @ complex @ W2 @ S )
% 2.66/1.56 => ( ( times_times @ complex @ ( deriv @ complex @ F @ W2 ) @ ( deriv @ complex @ G2 @ ( F @ W2 ) ) )
% 2.66/1.56 = ( one_one @ complex ) ) ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_143_mult__left__le,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord1659791738miring @ A )
% 2.66/1.56 => ! [C2: A,A2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ C2 @ ( one_one @ A ) )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C2 ) @ A2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_144_mult__le__one,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord1659791738miring @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ ( one_one @ A ) )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ ( one_one @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( one_one @ A ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_145_mult__right__le__one__le,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linordered_idom @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 2.66/1.56 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ X2 @ Y ) @ X2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_146_mult__left__le__one__le,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linordered_idom @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 2.66/1.56 => ( ( ord_less_eq @ A @ Y @ ( one_one @ A ) )
% 2.66/1.56 => ( ord_less_eq @ A @ ( times_times @ A @ Y @ X2 ) @ X2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_147_mult__eq__1,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ( comm_monoid_mult @ A )
% 2.66/1.56 & ( ordered_semiring @ A ) )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ A2 @ ( one_one @ A ) )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ ( one_one @ A ) )
% 2.66/1.56 => ( ( ( times_times @ A @ A2 @ B2 )
% 2.66/1.56 = ( one_one @ A ) )
% 2.66/1.56 = ( ( A2
% 2.66/1.56 = ( one_one @ A ) )
% 2.66/1.56 & ( B2
% 2.66/1.56 = ( one_one @ A ) ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_148_artanh__0,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ( real_V758409581_field @ A )
% 2.66/1.56 & ( ln @ A ) )
% 2.66/1.56 => ( ( artanh @ A @ ( zero_zero @ A ) )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_149_arsinh__0,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ln @ A )
% 2.66/1.56 => ( ( arsinh @ A @ ( zero_zero @ A ) )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_150_subset__antisym,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.66/1.56 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A3 )
% 2.66/1.56 => ( A3 = B4 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_151_image__eqI,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A3: set @ B] :
% 2.66/1.56 ( ( B2
% 2.66/1.56 = ( F @ X2 ) )
% 2.66/1.56 => ( ( member @ B @ X2 @ A3 )
% 2.66/1.56 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A3 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_152_subsetI,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.66/1.56 ( ! [X3: A] :
% 2.66/1.56 ( ( member @ A @ X3 @ A3 )
% 2.66/1.56 => ( member @ A @ X3 @ B4 ) )
% 2.66/1.56 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_153_le0,axiom,
% 2.66/1.56 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_154_bot__nat__0_Oextremum,axiom,
% 2.66/1.56 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_155_less__eq__nat_Osimps_I1_J,axiom,
% 2.66/1.56 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_156_le__0__eq,axiom,
% 2.66/1.56 ! [N: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 2.66/1.56 = ( N
% 2.66/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_157_bot__nat__0_Oextremum__unique,axiom,
% 2.66/1.56 ! [A2: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.66/1.56 = ( A2
% 2.66/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_158_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.66/1.56 ! [A2: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.66/1.56 => ( A2
% 2.66/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_159_mult__le__mono2,axiom,
% 2.66/1.56 ! [I: nat,J: nat,K: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ I @ J )
% 2.66/1.56 => ( ord_less_eq @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_160_mult__le__mono1,axiom,
% 2.66/1.56 ! [I: nat,J: nat,K: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ I @ J )
% 2.66/1.56 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_161_mult__le__mono,axiom,
% 2.66/1.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ I @ J )
% 2.66/1.56 => ( ( ord_less_eq @ nat @ K @ L )
% 2.66/1.56 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_162_le__square,axiom,
% 2.66/1.56 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_163_le__cube,axiom,
% 2.66/1.56 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_164_imageI,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,X2: A,A3: set @ A,F: A > B] :
% 2.66/1.56 ( ( member @ A @ X2 @ A3 )
% 2.66/1.56 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A3 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_165_image__iff,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,Z: A,F: B > A,A3: set @ B] :
% 2.66/1.56 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A3 ) )
% 2.66/1.56 = ( ? [X: B] :
% 2.66/1.56 ( ( member @ B @ X @ A3 )
% 2.66/1.56 & ( Z
% 2.66/1.56 = ( F @ X ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_166_bex__imageD,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P: A > $o] :
% 2.66/1.56 ( ? [X4: A] :
% 2.66/1.56 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A3 ) )
% 2.66/1.56 & ( P @ X4 ) )
% 2.66/1.56 => ? [X3: B] :
% 2.66/1.56 ( ( member @ B @ X3 @ A3 )
% 2.66/1.56 & ( P @ ( F @ X3 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_167_image__cong,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,M2: set @ A,N2: set @ A,F: A > B,G2: A > B] :
% 2.66/1.56 ( ( M2 = N2 )
% 2.66/1.56 => ( ! [X3: A] :
% 2.66/1.56 ( ( member @ A @ X3 @ N2 )
% 2.66/1.56 => ( ( F @ X3 )
% 2.66/1.56 = ( G2 @ X3 ) ) )
% 2.66/1.56 => ( ( image @ A @ B @ F @ M2 )
% 2.66/1.56 = ( image @ A @ B @ G2 @ N2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_168_ball__imageD,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P: A > $o] :
% 2.66/1.56 ( ! [X3: A] :
% 2.66/1.56 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A3 ) )
% 2.66/1.56 => ( P @ X3 ) )
% 2.66/1.56 => ! [X4: B] :
% 2.66/1.56 ( ( member @ B @ X4 @ A3 )
% 2.66/1.56 => ( P @ ( F @ X4 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_169_rev__image__eqI,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,X2: A,A3: set @ A,B2: B,F: A > B] :
% 2.66/1.56 ( ( member @ A @ X2 @ A3 )
% 2.66/1.56 => ( ( B2
% 2.66/1.56 = ( F @ X2 ) )
% 2.66/1.56 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A3 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_170_in__mono,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A,X2: A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.66/1.56 => ( ( member @ A @ X2 @ A3 )
% 2.66/1.56 => ( member @ A @ X2 @ B4 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_171_subsetD,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.66/1.56 => ( ( member @ A @ C2 @ A3 )
% 2.66/1.56 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_172_equalityE,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.66/1.56 ( ( A3 = B4 )
% 2.66/1.56 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.66/1.56 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_173_subset__eq,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) )
% 2.66/1.56 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.66/1.56 ! [X: A] :
% 2.66/1.56 ( ( member @ A @ X @ A6 )
% 2.66/1.56 => ( member @ A @ X @ B6 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_174_equalityD1,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.66/1.56 ( ( A3 = B4 )
% 2.66/1.56 => ( ord_less_eq @ ( set @ A ) @ A3 @ B4 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_175_equalityD2,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 2.66/1.56 ( ( A3 = B4 )
% 2.66/1.56 => ( ord_less_eq @ ( set @ A ) @ B4 @ A3 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_176_subset__iff,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) )
% 2.66/1.56 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.66/1.56 ! [T3: A] :
% 2.66/1.56 ( ( member @ A @ T3 @ A6 )
% 2.66/1.56 => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_177_subset__refl,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_178_Collect__mono,axiom,
% 2.66/1.56 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.66/1.56 ( ! [X3: A] :
% 2.66/1.56 ( ( P @ X3 )
% 2.66/1.56 => ( Q @ X3 ) )
% 2.66/1.56 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_179_subset__trans,axiom,
% 2.66/1.56 ! [A: $tType,A3: set @ A,B4: set @ A,C3: set @ A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.66/1.56 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 2.66/1.56 => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_180_set__eq__subset,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ^ [Y3: set @ A,Z4: set @ A] : ( Y3 = Z4 ) )
% 2.66/1.56 = ( ^ [A6: set @ A,B6: set @ A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B6 )
% 2.66/1.56 & ( ord_less_eq @ ( set @ A ) @ B6 @ A6 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_181_Collect__mono__iff,axiom,
% 2.66/1.56 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.66/1.56 = ( ! [X: A] :
% 2.66/1.56 ( ( P @ X )
% 2.66/1.56 => ( Q @ X ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_182_image__mono,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,A3: set @ A,B4: set @ A,F: A > B] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B4 )
% 2.66/1.56 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A3 ) @ ( image @ A @ B @ F @ B4 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_183_image__subsetI,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,A3: set @ A,F: A > B,B4: set @ B] :
% 2.66/1.56 ( ! [X3: A] :
% 2.66/1.56 ( ( member @ A @ X3 @ A3 )
% 2.66/1.56 => ( member @ B @ ( F @ X3 ) @ B4 ) )
% 2.66/1.56 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ F @ A3 ) @ B4 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_184_subset__imageE,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,B4: set @ A,F: B > A,A3: set @ B] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A3 ) )
% 2.66/1.56 => ~ ! [C4: set @ B] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ B ) @ C4 @ A3 )
% 2.66/1.56 => ( B4
% 2.66/1.56 != ( image @ B @ A @ F @ C4 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_185_image__subset__iff,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,B4: set @ A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ ( image @ B @ A @ F @ A3 ) @ B4 )
% 2.66/1.56 = ( ! [X: B] :
% 2.66/1.56 ( ( member @ B @ X @ A3 )
% 2.66/1.56 => ( member @ A @ ( F @ X ) @ B4 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_186_subset__image__iff,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,B4: set @ A,F: B > A,A3: set @ B] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ B4 @ ( image @ B @ A @ F @ A3 ) )
% 2.66/1.56 = ( ? [AA: set @ B] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ B ) @ AA @ A3 )
% 2.66/1.56 & ( B4
% 2.66/1.56 = ( image @ B @ A @ F @ AA ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_187_order__refl,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( preorder @ A )
% 2.66/1.56 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_188_kuhn__labelling__lemma_H,axiom,
% 2.66/1.56 ! [P: ( nat > real ) > $o,F: ( nat > real ) > nat > real,Q: nat > $o] :
% 2.66/1.56 ( ! [X3: nat > real] :
% 2.66/1.56 ( ( P @ X3 )
% 2.66/1.56 => ( P @ ( F @ X3 ) ) )
% 2.66/1.56 => ( ! [X3: nat > real] :
% 2.66/1.56 ( ( P @ X3 )
% 2.66/1.56 => ! [I2: nat] :
% 2.66/1.56 ( ( Q @ I2 )
% 2.66/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( X3 @ I2 ) )
% 2.66/1.56 & ( ord_less_eq @ real @ ( X3 @ I2 ) @ ( one_one @ real ) ) ) ) )
% 2.66/1.56 => ? [L3: ( nat > real ) > nat > nat] :
% 2.66/1.56 ( ! [X4: nat > real,I3: nat] : ( ord_less_eq @ nat @ ( L3 @ X4 @ I3 ) @ ( one_one @ nat ) )
% 2.66/1.56 & ! [X4: nat > real,I3: nat] :
% 2.66/1.56 ( ( ( P @ X4 )
% 2.66/1.56 & ( Q @ I3 )
% 2.66/1.56 & ( ( X4 @ I3 )
% 2.66/1.56 = ( zero_zero @ real ) ) )
% 2.66/1.56 => ( ( L3 @ X4 @ I3 )
% 2.66/1.56 = ( zero_zero @ nat ) ) )
% 2.66/1.56 & ! [X4: nat > real,I3: nat] :
% 2.66/1.56 ( ( ( P @ X4 )
% 2.66/1.56 & ( Q @ I3 )
% 2.66/1.56 & ( ( X4 @ I3 )
% 2.66/1.56 = ( one_one @ real ) ) )
% 2.66/1.56 => ( ( L3 @ X4 @ I3 )
% 2.66/1.56 = ( one_one @ nat ) ) )
% 2.66/1.56 & ! [X4: nat > real,I3: nat] :
% 2.66/1.56 ( ( ( P @ X4 )
% 2.66/1.56 & ( Q @ I3 )
% 2.66/1.56 & ( ( L3 @ X4 @ I3 )
% 2.66/1.56 = ( zero_zero @ nat ) ) )
% 2.66/1.56 => ( ord_less_eq @ real @ ( X4 @ I3 ) @ ( F @ X4 @ I3 ) ) )
% 2.66/1.56 & ! [X4: nat > real,I3: nat] :
% 2.66/1.56 ( ( ( P @ X4 )
% 2.66/1.56 & ( Q @ I3 )
% 2.66/1.56 & ( ( L3 @ X4 @ I3 )
% 2.66/1.56 = ( one_one @ nat ) ) )
% 2.66/1.56 => ( ord_less_eq @ real @ ( F @ X4 @ I3 ) @ ( X4 @ I3 ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_189_Sup_OSUP__id__eq,axiom,
% 2.66/1.56 ! [A: $tType,Sup: ( set @ A ) > A,A3: set @ A] :
% 2.66/1.56 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 2.66/1.56 = ( Sup @ A3 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_190_le__refl,axiom,
% 2.66/1.56 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_191_le__trans,axiom,
% 2.66/1.56 ! [I: nat,J: nat,K: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ I @ J )
% 2.66/1.56 => ( ( ord_less_eq @ nat @ J @ K )
% 2.66/1.56 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_192_eq__imp__le,axiom,
% 2.66/1.56 ! [M: nat,N: nat] :
% 2.66/1.56 ( ( M = N )
% 2.66/1.56 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_193_le__antisym,axiom,
% 2.66/1.56 ! [M: nat,N: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ M @ N )
% 2.66/1.56 => ( ( ord_less_eq @ nat @ N @ M )
% 2.66/1.56 => ( M = N ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_194_nat__le__linear,axiom,
% 2.66/1.56 ! [M: nat,N: nat] :
% 2.66/1.56 ( ( ord_less_eq @ nat @ M @ N )
% 2.66/1.56 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_195_Nat_Oex__has__greatest__nat,axiom,
% 2.66/1.56 ! [P: nat > $o,K: nat,B2: nat] :
% 2.66/1.56 ( ( P @ K )
% 2.66/1.56 => ( ! [Y4: nat] :
% 2.66/1.56 ( ( P @ Y4 )
% 2.66/1.56 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 2.66/1.56 => ? [X3: nat] :
% 2.66/1.56 ( ( P @ X3 )
% 2.66/1.56 & ! [Y2: nat] :
% 2.66/1.56 ( ( P @ Y2 )
% 2.66/1.56 => ( ord_less_eq @ nat @ Y2 @ X3 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_196_dual__order_Oantisym,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ! [B2: A,A2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( A2 = B2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_197_dual__order_Oeq__iff,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 2.66/1.56 = ( ^ [A4: A,B3: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ B3 @ A4 )
% 2.66/1.56 & ( ord_less_eq @ A @ A4 @ B3 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_198_dual__order_Otrans,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ! [B2: A,A2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.66/1.56 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_199_linorder__wlog,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linorder @ A )
% 2.66/1.56 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.66/1.56 ( ! [A5: A,B5: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A5 @ B5 )
% 2.66/1.56 => ( P @ A5 @ B5 ) )
% 2.66/1.56 => ( ! [A5: A,B5: A] :
% 2.66/1.56 ( ( P @ B5 @ A5 )
% 2.66/1.56 => ( P @ A5 @ B5 ) )
% 2.66/1.56 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_200_dual__order_Orefl,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_201_order__trans,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( preorder @ A )
% 2.66/1.56 => ! [X2: A,Y: A,Z: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.66/1.56 => ( ( ord_less_eq @ A @ Y @ Z )
% 2.66/1.56 => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_202_order__class_Oorder_Oantisym,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ! [A2: A,B2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.66/1.56 => ( A2 = B2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_203_ord__le__eq__trans,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ord @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( B2 = C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_204_ord__eq__le__trans,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ord @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.56 ( ( A2 = B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_205_order__class_Oorder_Oeq__iff,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 2.66/1.56 = ( ^ [A4: A,B3: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.66/1.56 & ( ord_less_eq @ A @ B3 @ A4 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_206_antisym__conv,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ! [Y: A,X2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ Y @ X2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ X2 @ Y )
% 2.66/1.56 = ( X2 = Y ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_207_le__cases3,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linorder @ A )
% 2.66/1.56 => ! [X2: A,Y: A,Z: A] :
% 2.66/1.56 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 2.66/1.56 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 2.66/1.56 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 2.66/1.56 => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 2.66/1.56 => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 2.66/1.56 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 2.66/1.56 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 2.66/1.56 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 2.66/1.56 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 2.66/1.56 => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 2.66/1.56 => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 2.66/1.56 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_208_order_Otrans,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ! [A2: A,B2: A,C2: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 2.66/1.56 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_209_le__cases,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linorder @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 2.66/1.56 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_210_eq__refl,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( preorder @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( X2 = Y )
% 2.66/1.56 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_211_linear,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linorder @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.66/1.56 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_212_antisym,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.66/1.56 => ( ( ord_less_eq @ A @ Y @ X2 )
% 2.66/1.56 => ( X2 = Y ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_213_eq__iff,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( order @ A )
% 2.66/1.56 => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 2.66/1.56 = ( ^ [X: A,Y5: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ X @ Y5 )
% 2.66/1.56 & ( ord_less_eq @ A @ Y5 @ X ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_214_ord__le__eq__subst,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType] :
% 2.66/1.56 ( ( ( ord @ B )
% 2.66/1.56 & ( ord @ A ) )
% 2.66/1.56 => ! [A2: A,B2: A,F: A > B,C2: B] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ( F @ B2 )
% 2.66/1.56 = C2 )
% 2.66/1.56 => ( ! [X3: A,Y4: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 2.66/1.56 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.66/1.56 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_215_ord__eq__le__subst,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType] :
% 2.66/1.56 ( ( ( ord @ B )
% 2.66/1.56 & ( ord @ A ) )
% 2.66/1.56 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.66/1.56 ( ( A2
% 2.66/1.56 = ( F @ B2 ) )
% 2.66/1.56 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.66/1.56 => ( ! [X3: B,Y4: B] :
% 2.66/1.56 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.66/1.56 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_216_order__subst2,axiom,
% 2.66/1.56 ! [A: $tType,C: $tType] :
% 2.66/1.56 ( ( ( order @ C )
% 2.66/1.56 & ( order @ A ) )
% 2.66/1.56 => ! [A2: A,B2: A,F: A > C,C2: C] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C2 )
% 2.66/1.56 => ( ! [X3: A,Y4: A] :
% 2.66/1.56 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 2.66/1.56 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.66/1.56 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_217_order__subst1,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType] :
% 2.66/1.56 ( ( ( order @ B )
% 2.66/1.56 & ( order @ A ) )
% 2.66/1.56 => ! [A2: A,F: B > A,B2: B,C2: B] :
% 2.66/1.56 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.66/1.56 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 2.66/1.56 => ( ! [X3: B,Y4: B] :
% 2.66/1.56 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 2.66/1.56 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 2.66/1.56 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_218_le__fun__def,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType] :
% 2.66/1.56 ( ( ord @ B )
% 2.66/1.56 => ( ( ord_less_eq @ ( A > B ) )
% 2.66/1.56 = ( ^ [F2: A > B,G: A > B] :
% 2.66/1.56 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G @ X ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_219_le__funI,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType] :
% 2.66/1.56 ( ( ord @ B )
% 2.66/1.56 => ! [F: A > B,G2: A > B] :
% 2.66/1.56 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G2 @ X3 ) )
% 2.66/1.56 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_220_le__funE,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType] :
% 2.66/1.56 ( ( ord @ B )
% 2.66/1.56 => ! [F: A > B,G2: A > B,X2: A] :
% 2.66/1.56 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 2.66/1.56 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_221_le__funD,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType] :
% 2.66/1.56 ( ( ord @ B )
% 2.66/1.56 => ! [F: A > B,G2: A > B,X2: A] :
% 2.66/1.56 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 2.66/1.56 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_222_Sup_OSUP__cong,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C3: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 2.66/1.56 ( ( A3 = B4 )
% 2.66/1.56 => ( ! [X3: B] :
% 2.66/1.56 ( ( member @ B @ X3 @ B4 )
% 2.66/1.56 => ( ( C3 @ X3 )
% 2.66/1.56 = ( D3 @ X3 ) ) )
% 2.66/1.56 => ( ( Sup @ ( image @ B @ A @ C3 @ A3 ) )
% 2.66/1.56 = ( Sup @ ( image @ B @ A @ D3 @ B4 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_223_Inf_OINF__cong,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,A3: set @ B,B4: set @ B,C3: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 2.66/1.56 ( ( A3 = B4 )
% 2.66/1.56 => ( ! [X3: B] :
% 2.66/1.56 ( ( member @ B @ X3 @ B4 )
% 2.66/1.56 => ( ( C3 @ X3 )
% 2.66/1.56 = ( D3 @ X3 ) ) )
% 2.66/1.56 => ( ( Inf @ ( image @ B @ A @ C3 @ A3 ) )
% 2.66/1.56 = ( Inf @ ( image @ B @ A @ D3 @ B4 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_224_Inf_OINF__image,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G2: B > A,F: C > B,A3: set @ C] :
% 2.66/1.56 ( ( Inf @ ( image @ B @ A @ G2 @ ( image @ C @ B @ F @ A3 ) ) )
% 2.66/1.56 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G2 @ F ) @ A3 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_225_Sup_OSUP__image,axiom,
% 2.66/1.56 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G2: B > A,F: C > B,A3: set @ C] :
% 2.66/1.56 ( ( Sup @ ( image @ B @ A @ G2 @ ( image @ C @ B @ F @ A3 ) ) )
% 2.66/1.56 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G2 @ F ) @ A3 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_226_Inf_OINF__id__eq,axiom,
% 2.66/1.56 ! [A: $tType,Inf: ( set @ A ) > A,A3: set @ A] :
% 2.66/1.56 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A3 ) )
% 2.66/1.56 = ( Inf @ A3 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_227_topological__space__class_OopenI,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topolo503727757_space @ A )
% 2.66/1.56 => ! [S: set @ A] :
% 2.66/1.56 ( ! [X3: A] :
% 2.66/1.56 ( ( member @ A @ X3 @ S )
% 2.66/1.56 => ? [T4: set @ A] :
% 2.66/1.56 ( ( topolo1751647064n_open @ A @ T4 )
% 2.66/1.56 & ( member @ A @ X3 @ T4 )
% 2.66/1.56 & ( ord_less_eq @ ( set @ A ) @ T4 @ S ) ) )
% 2.66/1.56 => ( topolo1751647064n_open @ A @ S ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_228_open__subopen,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topolo503727757_space @ A )
% 2.66/1.56 => ( ( topolo1751647064n_open @ A )
% 2.66/1.56 = ( ^ [S3: set @ A] :
% 2.66/1.56 ! [X: A] :
% 2.66/1.56 ( ( member @ A @ X @ S3 )
% 2.66/1.56 => ? [T5: set @ A] :
% 2.66/1.56 ( ( topolo1751647064n_open @ A @ T5 )
% 2.66/1.56 & ( member @ A @ X @ T5 )
% 2.66/1.56 & ( ord_less_eq @ ( set @ A ) @ T5 @ S3 ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_229_t0__space,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topological_t0_space @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( X2 != Y )
% 2.66/1.56 => ? [U: set @ A] :
% 2.66/1.56 ( ( topolo1751647064n_open @ A @ U )
% 2.66/1.56 & ( ( member @ A @ X2 @ U )
% 2.66/1.56 != ( member @ A @ Y @ U ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_230_t1__space,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topological_t1_space @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( X2 != Y )
% 2.66/1.56 => ? [U: set @ A] :
% 2.66/1.56 ( ( topolo1751647064n_open @ A @ U )
% 2.66/1.56 & ( member @ A @ X2 @ U )
% 2.66/1.56 & ~ ( member @ A @ Y @ U ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_231_separation__t0,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topological_t0_space @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( X2 != Y )
% 2.66/1.56 = ( ? [U2: set @ A] :
% 2.66/1.56 ( ( topolo1751647064n_open @ A @ U2 )
% 2.66/1.56 & ( ( member @ A @ X2 @ U2 )
% 2.66/1.56 != ( member @ A @ Y @ U2 ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_232_separation__t1,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topological_t1_space @ A )
% 2.66/1.56 => ! [X2: A,Y: A] :
% 2.66/1.56 ( ( X2 != Y )
% 2.66/1.56 = ( ? [U2: set @ A] :
% 2.66/1.56 ( ( topolo1751647064n_open @ A @ U2 )
% 2.66/1.56 & ( member @ A @ X2 @ U2 )
% 2.66/1.56 & ~ ( member @ A @ Y @ U2 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_233_open__discrete,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topolo2133971006pology @ A )
% 2.66/1.56 => ! [A3: set @ A] : ( topolo1751647064n_open @ A @ A3 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_234_first__countable__basis,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( topolo2135403230pology @ A )
% 2.66/1.56 => ! [X2: A] :
% 2.66/1.56 ? [A7: nat > ( set @ A )] :
% 2.66/1.56 ( ! [I3: nat] :
% 2.66/1.56 ( ( member @ A @ X2 @ ( A7 @ I3 ) )
% 2.66/1.56 & ( topolo1751647064n_open @ A @ ( A7 @ I3 ) ) )
% 2.66/1.56 & ! [S4: set @ A] :
% 2.66/1.56 ( ( ( topolo1751647064n_open @ A @ S4 )
% 2.66/1.56 & ( member @ A @ X2 @ S4 ) )
% 2.66/1.56 => ? [I2: nat] : ( ord_less_eq @ ( set @ A ) @ ( A7 @ I2 ) @ S4 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_235_landau__omega_OR__mult__right__mono,axiom,
% 2.66/1.56 ! [B2: real,A2: real,C2: real] :
% 2.66/1.56 ( ( ord_less_eq @ real @ B2 @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ real @ ( times_times @ real @ B2 @ C2 ) @ ( times_times @ real @ A2 @ C2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_236_landau__omega_OR__mult__left__mono,axiom,
% 2.66/1.56 ! [B2: real,A2: real,C2: real] :
% 2.66/1.56 ( ( ord_less_eq @ real @ B2 @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ real @ ( times_times @ real @ C2 @ B2 ) @ ( times_times @ real @ C2 @ A2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_237_landau__omega_OR__linear,axiom,
% 2.66/1.56 ! [Y: real,X2: real] :
% 2.66/1.56 ( ~ ( ord_less_eq @ real @ Y @ X2 )
% 2.66/1.56 => ( ord_less_eq @ real @ X2 @ Y ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_238_landau__omega_OR__trans,axiom,
% 2.66/1.56 ! [B2: real,A2: real,C2: real] :
% 2.66/1.56 ( ( ord_less_eq @ real @ B2 @ A2 )
% 2.66/1.56 => ( ( ord_less_eq @ real @ C2 @ B2 )
% 2.66/1.56 => ( ord_less_eq @ real @ C2 @ A2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_239_landau__omega_OR__refl,axiom,
% 2.66/1.56 ! [X2: real] : ( ord_less_eq @ real @ X2 @ X2 ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_240_landau__o_OR__linear,axiom,
% 2.66/1.56 ! [X2: real,Y: real] :
% 2.66/1.56 ( ~ ( ord_less_eq @ real @ X2 @ Y )
% 2.66/1.56 => ( ord_less_eq @ real @ Y @ X2 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_241_landau__o_OR__trans,axiom,
% 2.66/1.56 ! [A2: real,B2: real,C2: real] :
% 2.66/1.56 ( ( ord_less_eq @ real @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ real @ B2 @ C2 )
% 2.66/1.56 => ( ord_less_eq @ real @ A2 @ C2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_242_landau__o_OR__mult__left__mono,axiom,
% 2.66/1.56 ! [A2: real,B2: real,C2: real] :
% 2.66/1.56 ( ( ord_less_eq @ real @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ real @ ( times_times @ real @ C2 @ A2 ) @ ( times_times @ real @ C2 @ B2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_243_landau__o_OR__mult__right__mono,axiom,
% 2.66/1.56 ! [A2: real,B2: real,C2: real] :
% 2.66/1.56 ( ( ord_less_eq @ real @ A2 @ B2 )
% 2.66/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ C2 )
% 2.66/1.56 => ( ord_less_eq @ real @ ( times_times @ real @ A2 @ C2 ) @ ( times_times @ real @ B2 @ C2 ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_244_all__subset__image,axiom,
% 2.66/1.56 ! [A: $tType,B: $tType,F: B > A,A3: set @ B,P: ( set @ A ) > $o] :
% 2.66/1.56 ( ( ! [B6: set @ A] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ A ) @ B6 @ ( image @ B @ A @ F @ A3 ) )
% 2.66/1.56 => ( P @ B6 ) ) )
% 2.66/1.56 = ( ! [B6: set @ B] :
% 2.66/1.56 ( ( ord_less_eq @ ( set @ B ) @ B6 @ A3 )
% 2.66/1.56 => ( P @ ( image @ B @ A @ F @ B6 ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_245_le__numeral__extra_I4_J,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord1659791738miring @ A )
% 2.66/1.56 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_246_le__numeral__extra_I3_J,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( linord1659791738miring @ A )
% 2.66/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_247_dbl__inc__simps_I2_J,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( neg_numeral @ A )
% 2.66/1.56 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 2.66/1.56 = ( one_one @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_248_ln__one,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( ln @ A )
% 2.66/1.56 => ( ( ln_ln @ A @ ( one_one @ A ) )
% 2.66/1.56 = ( zero_zero @ A ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_249_ln__ge__zero,axiom,
% 2.66/1.56 ! [X2: real] :
% 2.66/1.56 ( ( ord_less_eq @ real @ ( one_one @ real ) @ X2 )
% 2.66/1.56 => ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X2 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_250_Ln__1,axiom,
% 2.66/1.56 ( ( ln_ln @ complex @ ( one_one @ complex ) )
% 2.66/1.56 = ( zero_zero @ complex ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_251_fps__tan__0,axiom,
% 2.66/1.56 ! [A: $tType] :
% 2.66/1.56 ( ( field_char_0 @ A )
% 2.66/1.56 => ( ( formal_Power_fps_tan @ A @ ( zero_zero @ A ) )
% 2.66/1.56 = ( zero_zero @ ( formal_Power_fps @ A ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(fact_252_holomorphic__fun__eq__0__on__connected,axiom,
% 2.66/1.56 ! [F: complex > complex,S: set @ complex,Z: complex,W2: complex] :
% 2.66/1.56 ( ( comple372758642hic_on @ F @ S )
% 2.66/1.56 => ( ( topolo1751647064n_open @ complex @ S )
% 2.66/1.56 => ( ( topolo1099314120nected @ complex @ S )
% 2.66/1.56 => ( ! [N3: nat] :
% 2.66/1.56 ( ( compow @ ( ( complex > complex ) > complex > complex ) @ N3 @ ( deriv @ complex ) @ F @ Z )
% 2.66/1.56 = ( zero_zero @ complex ) )
% 2.66/1.56 => ( ( member @ complex @ Z @ S )
% 2.66/1.56 => ( ( member @ complex @ W2 @ S )
% 2.66/1.56 => ( ( F @ W2 )
% 2.66/1.56 = ( zero_zero @ complex ) ) ) ) ) ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Real__Vector__Spaces_Ometric__space,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( group_add @ A8 )
% 2.66/1.56 => ( real_V2090557954_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Ogroup__add,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( group_add @ A8 )
% 2.66/1.56 => ( group_add @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocancel__semigroup__add,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( cancel_semigroup_add @ A8 )
% 2.66/1.56 => ( cancel_semigroup_add @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Ocomm__semiring__0,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( comm_semiring_0 @ A8 )
% 2.66/1.56 => ( comm_semiring_0 @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__0,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( semiring_0 @ A8 )
% 2.66/1.56 => ( semiring_0 @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__1,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( semiring_1 @ A8 )
% 2.66/1.56 => ( semiring_1 @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocomm__monoid__add,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( comm_monoid_add @ A8 )
% 2.66/1.56 => ( comm_monoid_add @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Oring__1,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ring_1 @ A8 )
% 2.66/1.56 => ( ring_1 @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Real__Vector__Spaces_Ometric__space_1,axiom,
% 2.66/1.56 real_V2090557954_space @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Ogroup__add_2,axiom,
% 2.66/1.56 group_add @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Ocancel__semigroup__add_3,axiom,
% 2.66/1.56 cancel_semigroup_add @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Ocomm__semiring__0_4,axiom,
% 2.66/1.56 comm_semiring_0 @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Osemiring__0_5,axiom,
% 2.66/1.56 semiring_0 @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Osemiring__1_6,axiom,
% 2.66/1.56 semiring_1 @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Ocomm__monoid__add_7,axiom,
% 2.66/1.56 comm_monoid_add @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Oring__1_8,axiom,
% 2.66/1.56 ring_1 @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_9,axiom,
% 2.66/1.56 real_V2090557954_space @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Ogroup__add_10,axiom,
% 2.66/1.56 group_add @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_11,axiom,
% 2.66/1.56 cancel_semigroup_add @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__0_12,axiom,
% 2.66/1.56 comm_semiring_0 @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Osemiring__0_13,axiom,
% 2.66/1.56 semiring_0 @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Osemiring__1_14,axiom,
% 2.66/1.56 semiring_1 @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_15,axiom,
% 2.66/1.56 comm_monoid_add @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Oring__1_16,axiom,
% 2.66/1.56 ring_1 @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Countable_Ocountable,axiom,
% 2.66/1.56 countable @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Countable_Ocountable_17,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( finite_finite @ A8 )
% 2.66/1.56 => ( countable @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add_18,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( comm_monoid_add @ A8 )
% 2.66/1.56 => ( comm_monoid_add @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Countable_Ocountable_19,axiom,
% 2.66/1.56 countable @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add_20,axiom,
% 2.66/1.56 cancel_semigroup_add @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0_21,axiom,
% 2.66/1.56 comm_semiring_0 @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Osemiring__0_22,axiom,
% 2.66/1.56 semiring_0 @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Osemiring__1_23,axiom,
% 2.66/1.56 semiring_1 @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_24,axiom,
% 2.66/1.56 comm_monoid_add @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Countable_Ocountable_25,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( ( finite_finite @ A8 )
% 2.66/1.56 & ( countable @ A9 ) )
% 2.66/1.56 => ( countable @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Real__Vector__Spaces_Ometric__space_26,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( ( countable @ A8 )
% 2.66/1.56 & ( real_V2090557954_space @ A9 ) )
% 2.66/1.56 => ( real_V2090557954_space @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( ( finite_finite @ A8 )
% 2.66/1.56 & ( finite_finite @ A9 ) )
% 2.66/1.56 => ( finite_finite @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Finite__Set_Ofinite_27,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( finite_finite @ A8 )
% 2.66/1.56 => ( finite_finite @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Finite__Set_Ofinite_28,axiom,
% 2.66/1.56 finite_finite @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Topological__Spaces_Ofirst__countable__topology,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( ( countable @ A8 )
% 2.66/1.56 & ( topolo2135403230pology @ A9 ) )
% 2.66/1.56 => ( topolo2135403230pology @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( topolo503727757_space @ A9 )
% 2.66/1.56 => ( topolo503727757_space @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Topological__Spaces_Ot1__space,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( ( countable @ A8 )
% 2.66/1.56 & ( real_V2090557954_space @ A9 ) )
% 2.66/1.56 => ( topological_t1_space @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Topological__Spaces_Ot0__space,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( ( countable @ A8 )
% 2.66/1.56 & ( real_V2090557954_space @ A9 ) )
% 2.66/1.56 => ( topological_t0_space @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( preorder @ A9 )
% 2.66/1.56 => ( preorder @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( order @ A9 )
% 2.66/1.56 => ( order @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_fun___Orderings_Oord,axiom,
% 2.66/1.56 ! [A8: $tType,A9: $tType] :
% 2.66/1.56 ( ( ord @ A9 )
% 2.66/1.56 => ( ord @ ( A8 > A9 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Topological__Spaces_Ofirst__countable__topology_29,axiom,
% 2.66/1.56 topolo2135403230pology @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 2.66/1.56 semiri1923998003cancel @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.66/1.56 canoni770627133id_add @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Topological__Spaces_Otopological__space_30,axiom,
% 2.66/1.56 topolo503727757_space @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Topological__Spaces_Odiscrete__topology,axiom,
% 2.66/1.56 topolo2133971006pology @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.66/1.56 linord1659791738miring @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 2.66/1.56 semiri1193490041visors @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Topological__Spaces_Ot1__space_31,axiom,
% 2.66/1.56 topological_t1_space @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Topological__Spaces_Ot0__space_32,axiom,
% 2.66/1.56 topological_t0_space @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
% 2.66/1.56 ordere1490568538miring @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0,axiom,
% 2.66/1.56 ordered_semiring_0 @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 2.66/1.56 ab_semigroup_mult @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 2.66/1.56 comm_monoid_mult @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Oordered__semiring,axiom,
% 2.66/1.56 ordered_semiring @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 2.66/1.56 comm_semiring_1 @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 2.66/1.56 semigroup_mult @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 2.66/1.56 zero_neq_one @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Orderings_Opreorder_33,axiom,
% 2.66/1.56 preorder @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.66/1.56 linorder @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 2.66/1.56 monoid_mult @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 2.66/1.56 mult_zero @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Orderings_Oorder_34,axiom,
% 2.66/1.56 order @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Orderings_Oord_35,axiom,
% 2.66/1.56 ord @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Otimes,axiom,
% 2.66/1.56 times @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.66/1.56 zero @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.66/1.56 one @ nat ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Oab__semigroup__mult_36,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ab_semigroup_mult @ A8 )
% 2.66/1.56 => ( ab_semigroup_mult @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Ocomm__monoid__mult_37,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( comm_monoid_mult @ A8 )
% 2.66/1.56 => ( comm_monoid_mult @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Osemigroup__mult_38,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( semigroup_mult @ A8 )
% 2.66/1.56 => ( semigroup_mult @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Orderings_Opreorder_39,axiom,
% 2.66/1.56 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Omonoid__mult_40,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( monoid_mult @ A8 )
% 2.66/1.56 => ( monoid_mult @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Orderings_Oorder_41,axiom,
% 2.66/1.56 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Orderings_Oord_42,axiom,
% 2.66/1.56 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Otimes_43,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( times @ A8 )
% 2.66/1.56 => ( times @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Ozero_44,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( zero @ A8 )
% 2.66/1.56 => ( zero @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Set_Oset___Groups_Oone_45,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( one @ A8 )
% 2.66/1.56 => ( one @ ( set @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_46,axiom,
% 2.66/1.56 topolo503727757_space @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology_47,axiom,
% 2.66/1.56 topolo2133971006pology @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Topological__Spaces_Ot1__space_48,axiom,
% 2.66/1.56 topological_t1_space @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Topological__Spaces_Ot0__space_49,axiom,
% 2.66/1.56 topological_t0_space @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_50,axiom,
% 2.66/1.56 preorder @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder_51,axiom,
% 2.66/1.56 linorder @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_52,axiom,
% 2.66/1.56 order @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_HOL_Obool___Orderings_Oord_53,axiom,
% 2.66/1.56 ord @ $o ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Topological__Spaces_Ofirst__countable__topology_54,axiom,
% 2.66/1.56 topolo2135403230pology @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors__cancel_55,axiom,
% 2.66/1.56 semiri1923998003cancel @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_56,axiom,
% 2.66/1.56 topolo503727757_space @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__field,axiom,
% 2.66/1.56 real_V758409581_field @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_57,axiom,
% 2.66/1.56 linord1659791738miring @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors_58,axiom,
% 2.66/1.56 semiri1193490041visors @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Oring__1__no__zero__divisors,axiom,
% 2.66/1.56 ring_11004092258visors @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__ring__strict,axiom,
% 2.66/1.56 linord581940658strict @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Topological__Spaces_Ot1__space_59,axiom,
% 2.66/1.56 topological_t1_space @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Topological__Spaces_Ot0__space_60,axiom,
% 2.66/1.56 topological_t0_space @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Oordered__comm__semiring_61,axiom,
% 2.66/1.56 ordere1490568538miring @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Oordered__semiring__0_62,axiom,
% 2.66/1.56 ordered_semiring_0 @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Oab__semigroup__mult_63,axiom,
% 2.66/1.56 ab_semigroup_mult @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__mult_64,axiom,
% 2.66/1.56 comm_monoid_mult @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Oordered__semiring_65,axiom,
% 2.66/1.56 ordered_semiring @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__ring,axiom,
% 2.66/1.56 linordered_ring @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 2.66/1.56 linordered_idom @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_66,axiom,
% 2.66/1.56 comm_semiring_1 @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Osemigroup__mult_67,axiom,
% 2.66/1.56 semigroup_mult @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Fields_Ofield__char__0,axiom,
% 2.66/1.56 field_char_0 @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_68,axiom,
% 2.66/1.56 zero_neq_one @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Oordered__ring,axiom,
% 2.66/1.56 ordered_ring @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Orderings_Opreorder_69,axiom,
% 2.66/1.56 preorder @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Orderings_Olinorder_70,axiom,
% 2.66/1.56 linorder @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Omonoid__mult_71,axiom,
% 2.66/1.56 monoid_mult @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Transcendental_Oln,axiom,
% 2.66/1.56 ln @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Rings_Omult__zero_72,axiom,
% 2.66/1.56 mult_zero @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Orderings_Oorder_73,axiom,
% 2.66/1.56 order @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 2.66/1.56 neg_numeral @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Orderings_Oord_74,axiom,
% 2.66/1.56 ord @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Otimes_75,axiom,
% 2.66/1.56 times @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Fields_Ofield,axiom,
% 2.66/1.56 field @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Ozero_76,axiom,
% 2.66/1.56 zero @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Real_Oreal___Groups_Oone_77,axiom,
% 2.66/1.56 one @ real ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ofirst__countable__topology_78,axiom,
% 2.66/1.56 topolo2135403230pology @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Osemiring__no__zero__divisors__cancel_79,axiom,
% 2.66/1.56 semiri1923998003cancel @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Topological__Spaces_Otopological__space_80,axiom,
% 2.66/1.56 topolo503727757_space @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__field_81,axiom,
% 2.66/1.56 real_V758409581_field @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Osemiring__no__zero__divisors_82,axiom,
% 2.66/1.56 semiri1193490041visors @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors_83,axiom,
% 2.66/1.56 ring_11004092258visors @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ot1__space_84,axiom,
% 2.66/1.56 topological_t1_space @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Topological__Spaces_Ot0__space_85,axiom,
% 2.66/1.56 topological_t0_space @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Oab__semigroup__mult_86,axiom,
% 2.66/1.56 ab_semigroup_mult @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Ocomm__monoid__mult_87,axiom,
% 2.66/1.56 comm_monoid_mult @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Ocomm__semiring__1_88,axiom,
% 2.66/1.56 comm_semiring_1 @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Osemigroup__mult_89,axiom,
% 2.66/1.56 semigroup_mult @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Fields_Ofield__char__0_90,axiom,
% 2.66/1.56 field_char_0 @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Ozero__neq__one_91,axiom,
% 2.66/1.56 zero_neq_one @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Omonoid__mult_92,axiom,
% 2.66/1.56 monoid_mult @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Transcendental_Oln_93,axiom,
% 2.66/1.56 ln @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Rings_Omult__zero_94,axiom,
% 2.66/1.56 mult_zero @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Num_Oneg__numeral_95,axiom,
% 2.66/1.56 neg_numeral @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Otimes_96,axiom,
% 2.66/1.56 times @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Fields_Ofield_97,axiom,
% 2.66/1.56 field @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Ozero_98,axiom,
% 2.66/1.56 zero @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Complex_Ocomplex___Groups_Oone_99,axiom,
% 2.66/1.56 one @ complex ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ofirst__countable__topology_100,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( group_add @ A8 )
% 2.66/1.56 => ( topolo2135403230pology @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__no__zero__divisors__cancel_101,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ( cancel_semigroup_add @ A8 )
% 2.66/1.56 & ( semiri1923998003cancel @ A8 ) )
% 2.66/1.56 => ( semiri1923998003cancel @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Otopological__space_102,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( group_add @ A8 )
% 2.66/1.56 => ( topolo503727757_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Osemiring__no__zero__divisors_103,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( semiri1193490041visors @ A8 )
% 2.66/1.56 => ( semiri1193490041visors @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Oring__1__no__zero__divisors_104,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ring_11004092258visors @ A8 )
% 2.66/1.56 => ( ring_11004092258visors @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ot1__space_105,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( group_add @ A8 )
% 2.66/1.56 => ( topological_t1_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Topological__Spaces_Ot0__space_106,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( group_add @ A8 )
% 2.66/1.56 => ( topological_t0_space @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Oab__semigroup__mult_107,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( comm_semiring_0 @ A8 )
% 2.66/1.56 => ( ab_semigroup_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Ocomm__monoid__mult_108,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( comm_semiring_1 @ A8 )
% 2.66/1.56 => ( comm_monoid_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Ocomm__semiring__1_109,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( comm_semiring_1 @ A8 )
% 2.66/1.56 => ( comm_semiring_1 @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Osemigroup__mult_110,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( semiring_0 @ A8 )
% 2.66/1.56 => ( semigroup_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Ozero__neq__one_111,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( zero_neq_one @ A8 )
% 2.66/1.56 => ( zero_neq_one @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Omonoid__mult_112,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( semiring_1 @ A8 )
% 2.66/1.56 => ( monoid_mult @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Rings_Omult__zero_113,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ( comm_monoid_add @ A8 )
% 2.66/1.56 & ( mult_zero @ A8 ) )
% 2.66/1.56 => ( mult_zero @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Num_Oneg__numeral_114,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ring_1 @ A8 )
% 2.66/1.56 => ( neg_numeral @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Otimes_115,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ( comm_monoid_add @ A8 )
% 2.66/1.56 & ( times @ A8 ) )
% 2.66/1.56 => ( times @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Ozero_116,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( zero @ A8 )
% 2.66/1.56 => ( zero @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(tcon_Formal__Power__Series_Ofps___Groups_Oone_117,axiom,
% 2.66/1.56 ! [A8: $tType] :
% 2.66/1.56 ( ( ( one @ A8 )
% 2.66/1.56 & ( zero @ A8 ) )
% 2.66/1.56 => ( one @ ( formal_Power_fps @ A8 ) ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(help_If_3_1_T,axiom,
% 2.66/1.56 ! [P: $o] :
% 2.66/1.56 ( ( P = $true )
% 2.66/1.56 | ( P = $false ) ) ).
% 2.66/1.56
% 2.66/1.56 thf(help_If_2_1_T,axiom,
% 2.66/1.56 ! [A: $tType,X2: A,Y: A] :
% 2.66/1.56 ( ( if @ A @ $false @ X2 @ Y )
% 2.66/1.56 = Y ) ).
% 2.66/1.56
% 2.66/1.56 thf(help_If_1_1_T,axiom,
% 2.66/1.56 ! [A: $tType,X2: A,Y: A] :
% 2.66/1.56 ( ( if @ A @ $true @ X2 @ Y )
% 2.66/1.56 = X2 ) ).
% 2.66/1.56
% 2.66/1.56 thf(conj_0,conjecture,
% 2.66/1.56 ( ( deriv @ complex @ ( id @ complex ) @ w )
% 2.66/1.56 = ( one_one @ complex ) ) ).
% 2.66/1.56 ------------------------
% 2.66/1.59 % (12029)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/4Mi)
% 2.66/1.59 % (12032)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/2Mi)
% 2.66/1.59 % (12028)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/183Mi)
% 2.66/1.59 % (12032)Instruction limit reached!
% 2.66/1.59 % (12032)------------------------------
% 2.66/1.59 % (12032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.59 % (12032)Termination reason: Unknown
% 2.66/1.59 % (12032)Termination phase: shuffling
% 2.66/1.59
% 2.66/1.59 % (12032)Memory used [KB]: 1407
% 2.66/1.59 % (12032)Time elapsed: 0.002 s
% 2.66/1.59 % (12032)Instructions burned: 2 (million)
% 2.66/1.59 % (12032)------------------------------
% 2.66/1.59 % (12032)------------------------------
% 2.66/1.59 % (12029)Instruction limit reached!
% 2.66/1.59 % (12029)------------------------------
% 2.66/1.59 % (12029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.59 % (12029)Termination reason: Unknown
% 2.66/1.59 % (12029)Termination phase: shuffling
% 2.66/1.59
% 2.66/1.59 % (12029)Memory used [KB]: 1535
% 2.66/1.59 % (12029)Time elapsed: 0.003 s
% 2.66/1.59 % (12029)Instructions burned: 4 (million)
% 2.66/1.59 % (12029)------------------------------
% 2.66/1.59 % (12029)------------------------------
% 2.74/1.60 % (12030)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/27Mi)
% 2.74/1.60 % (12031)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/2Mi)
% 2.74/1.60 % (12033)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/275Mi)
% 2.74/1.60 % (12034)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/18Mi)
% 2.74/1.60 % (12031)Instruction limit reached!
% 2.74/1.60 % (12031)------------------------------
% 2.74/1.60 % (12031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.60 % (12031)Termination reason: Unknown
% 2.74/1.60 % (12031)Termination phase: shuffling
% 2.74/1.60
% 2.74/1.60 % (12031)Memory used [KB]: 1407
% 2.74/1.60 % (12031)Time elapsed: 0.004 s
% 2.74/1.60 % (12031)Instructions burned: 3 (million)
% 2.74/1.60 % (12031)------------------------------
% 2.74/1.60 % (12031)------------------------------
% 2.74/1.60 % (12035)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/3Mi)
% 2.74/1.60 % (12036)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/37Mi)
% 2.74/1.60 % (12035)Instruction limit reached!
% 2.74/1.60 % (12035)------------------------------
% 2.74/1.60 % (12035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.60 % (12035)Termination reason: Unknown
% 2.74/1.60 % (12035)Termination phase: shuffling
% 2.74/1.60
% 2.74/1.60 % (12035)Memory used [KB]: 1535
% 2.74/1.60 % (12035)Time elapsed: 0.003 s
% 2.74/1.60 % (12035)Instructions burned: 5 (million)
% 2.74/1.60 % (12035)------------------------------
% 2.74/1.60 % (12035)------------------------------
% 2.74/1.61 % (12034)Instruction limit reached!
% 2.74/1.61 % (12034)------------------------------
% 2.74/1.61 % (12034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (12034)Termination reason: Unknown
% 2.74/1.61 % (12034)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (12034)Memory used [KB]: 1791
% 2.74/1.61 % (12034)Time elapsed: 0.014 s
% 2.74/1.61 % (12034)Instructions burned: 18 (million)
% 2.74/1.61 % (12034)------------------------------
% 2.74/1.61 % (12034)------------------------------
% 2.74/1.61 % (12038)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/3Mi)
% 2.74/1.61 % (12036)Instruction limit reached!
% 2.74/1.61 % (12036)------------------------------
% 2.74/1.61 % (12036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (12036)Termination reason: Unknown
% 2.74/1.61 % (12036)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (12036)Memory used [KB]: 2174
% 2.74/1.61 % (12036)Time elapsed: 0.012 s
% 2.74/1.61 % (12036)Instructions burned: 38 (million)
% 2.74/1.61 % (12036)------------------------------
% 2.74/1.61 % (12036)------------------------------
% 2.74/1.61 % (12038)Instruction limit reached!
% 2.74/1.61 % (12038)------------------------------
% 2.74/1.61 % (12038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (12038)Termination reason: Unknown
% 2.74/1.61 % (12038)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (12038)Memory used [KB]: 1407
% 2.74/1.61 % (12038)Time elapsed: 0.002 s
% 2.74/1.61 % (12038)Instructions burned: 3 (million)
% 2.74/1.61 % (12038)------------------------------
% 2.74/1.61 % (12038)------------------------------
% 2.74/1.61 % (12030)Instruction limit reached!
% 2.74/1.61 % (12030)------------------------------
% 2.74/1.61 % (12030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (12030)Termination reason: Unknown
% 2.74/1.61 % (12030)Termination phase: Property scanning
% 2.74/1.61
% 2.74/1.61 % (12030)Memory used [KB]: 1918
% 2.74/1.61 % (12030)Time elapsed: 0.019 s
% 2.74/1.61 % (12030)Instructions burned: 28 (million)
% 2.74/1.61 % (12030)------------------------------
% 2.74/1.61 % (12030)------------------------------
% 2.74/1.62 % (12037)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/15Mi)
% 2.74/1.62 % (12040)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/7Mi)
% 2.74/1.62 % (12041)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/16Mi)
% 2.74/1.62 % (12040)Instruction limit reached!
% 2.74/1.62 % (12040)------------------------------
% 2.74/1.62 % (12040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (12040)Termination reason: Unknown
% 2.74/1.62 % (12040)Termination phase: shuffling
% 2.74/1.62
% 2.74/1.62 % (12040)Memory used [KB]: 1535
% 2.74/1.62 % (12040)Time elapsed: 0.004 s
% 2.74/1.62 % (12040)Instructions burned: 9 (million)
% 2.74/1.62 % (12040)------------------------------
% 2.74/1.62 % (12040)------------------------------
% 2.74/1.63 % (12037)Instruction limit reached!
% 2.74/1.63 % (12037)------------------------------
% 2.74/1.63 % (12037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (12037)Termination reason: Unknown
% 2.74/1.63 % (12037)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (12037)Memory used [KB]: 1791
% 2.74/1.63 % (12037)Time elapsed: 0.012 s
% 2.74/1.63 % (12037)Instructions burned: 16 (million)
% 2.74/1.63 % (12037)------------------------------
% 2.74/1.63 % (12037)------------------------------
% 2.74/1.63 % (12039)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/1041Mi)
% 2.74/1.63 % (12041)Instruction limit reached!
% 2.74/1.63 % (12041)------------------------------
% 2.74/1.63 % (12041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (12041)Termination reason: Unknown
% 2.74/1.63 % (12041)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (12041)Memory used [KB]: 1918
% 2.74/1.63 % (12041)Time elapsed: 0.007 s
% 2.74/1.63 % (12041)Instructions burned: 18 (million)
% 2.74/1.63 % (12041)------------------------------
% 2.74/1.63 % (12041)------------------------------
% 2.74/1.63 % (12042)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/3Mi)
% 2.74/1.63 % (12043)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/3Mi)
% 2.74/1.63 % (12042)Instruction limit reached!
% 2.74/1.63 % (12042)------------------------------
% 2.74/1.63 % (12042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (12042)Termination reason: Unknown
% 2.74/1.63 % (12042)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (12042)Memory used [KB]: 1407
% 2.74/1.63 % (12042)Time elapsed: 0.004 s
% 2.74/1.63 % (12042)Instructions burned: 3 (million)
% 2.74/1.63 % (12042)------------------------------
% 2.74/1.63 % (12042)------------------------------
% 2.74/1.63 % (12043)Instruction limit reached!
% 2.74/1.63 % (12043)------------------------------
% 2.74/1.63 % (12043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (12043)Termination reason: Unknown
% 2.74/1.63 % (12043)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (12043)Memory used [KB]: 1407
% 2.74/1.63 % (12043)Time elapsed: 0.002 s
% 2.74/1.63 % (12043)Instructions burned: 3 (million)
% 2.74/1.63 % (12043)------------------------------
% 2.74/1.63 % (12043)------------------------------
% 2.74/1.64 % (12045)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/3Mi)
% 2.74/1.64 % (12045)Instruction limit reached!
% 2.74/1.64 % (12045)------------------------------
% 2.74/1.64 % (12045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (12045)Termination reason: Unknown
% 2.74/1.64 % (12045)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (12045)Memory used [KB]: 1407
% 2.74/1.64 % (12045)Time elapsed: 0.002 s
% 2.74/1.64 % (12045)Instructions burned: 4 (million)
% 2.74/1.64 % (12045)------------------------------
% 2.74/1.64 % (12045)------------------------------
% 2.74/1.64 % (12047)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/18Mi)
% 2.74/1.64 % (12044)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/7Mi)
% 2.74/1.65 % (12048)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/710Mi)
% 2.74/1.65 % (12044)Instruction limit reached!
% 2.74/1.65 % (12044)------------------------------
% 2.74/1.65 % (12044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (12044)Termination reason: Unknown
% 2.74/1.65 % (12044)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (12044)Memory used [KB]: 1535
% 2.74/1.65 % (12044)Time elapsed: 0.007 s
% 2.74/1.65 % (12044)Instructions burned: 8 (million)
% 2.74/1.65 % (12044)------------------------------
% 2.74/1.65 % (12044)------------------------------
% 2.74/1.65 % (12047)Instruction limit reached!
% 2.74/1.65 % (12047)------------------------------
% 2.74/1.65 % (12047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (12047)Termination reason: Unknown
% 2.74/1.65 % (12047)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (12047)Memory used [KB]: 1918
% 2.74/1.65 % (12047)Time elapsed: 0.007 s
% 2.74/1.65 % (12047)Instructions burned: 18 (million)
% 2.74/1.65 % (12047)------------------------------
% 2.74/1.65 % (12047)------------------------------
% 2.74/1.65 % (12028)Instruction limit reached!
% 2.74/1.65 % (12028)------------------------------
% 2.74/1.65 % (12028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (12028)Termination reason: Unknown
% 2.74/1.65 % (12028)Termination phase: Saturation
% 2.74/1.65
% 2.74/1.65 % (12028)Memory used [KB]: 7419
% 2.74/1.65 % (12028)Time elapsed: 0.062 s
% 2.74/1.65 % (12028)Instructions burned: 183 (million)
% 2.74/1.65 % (12028)------------------------------
% 2.74/1.65 % (12028)------------------------------
% 2.74/1.65 % (12046)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/4Mi)
% 2.74/1.65 % (12046)Instruction limit reached!
% 2.74/1.65 % (12046)------------------------------
% 2.74/1.65 % (12046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (12046)Termination reason: Unknown
% 2.74/1.65 % (12046)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (12046)Memory used [KB]: 1535
% 2.74/1.65 % (12046)Time elapsed: 0.004 s
% 2.74/1.65 % (12046)Instructions burned: 4 (million)
% 2.74/1.65 % (12046)------------------------------
% 2.74/1.65 % (12046)------------------------------
% 2.74/1.66 % (12050)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/902Mi)
% 2.74/1.66 % (12051)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/21Mi)
% 2.74/1.67 % (12052)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/5Mi)
% 2.74/1.67 % (12049)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/6Mi)
% 2.74/1.67 % (12052)Instruction limit reached!
% 2.74/1.67 % (12052)------------------------------
% 2.74/1.67 % (12052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.67 % (12052)Termination reason: Unknown
% 2.74/1.67 % (12052)Termination phase: shuffling
% 2.74/1.67
% 2.74/1.67 % (12052)Memory used [KB]: 1535
% 2.74/1.67 % (12052)Time elapsed: 0.004 s
% 2.74/1.67 % (12052)Instructions burned: 7 (million)
% 2.74/1.67 % (12052)------------------------------
% 2.74/1.67 % (12052)------------------------------
% 2.74/1.67 % (12051)Instruction limit reached!
% 2.74/1.67 % (12051)------------------------------
% 2.74/1.67 % (12051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.67 % (12051)Termination reason: Unknown
% 2.74/1.67 % (12051)Termination phase: shuffling
% 2.74/1.67
% 2.74/1.67 % (12051)Memory used [KB]: 2046
% 2.74/1.67 % (12051)Time elapsed: 0.010 s
% 2.74/1.67 % (12051)Instructions burned: 23 (million)
% 2.74/1.67 % (12051)------------------------------
% 2.74/1.67 % (12051)------------------------------
% 2.74/1.67 % (12049)Instruction limit reached!
% 2.74/1.67 % (12049)------------------------------
% 2.74/1.67 % (12049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.67 % (12049)Termination reason: Unknown
% 2.74/1.67 % (12049)Termination phase: shuffling
% 2.74/1.67
% 2.74/1.67 % (12049)Memory used [KB]: 1535
% 2.74/1.67 % (12049)Time elapsed: 0.006 s
% 2.74/1.67 % (12049)Instructions burned: 6 (million)
% 2.74/1.67 % (12049)------------------------------
% 2.74/1.67 % (12049)------------------------------
% 2.74/1.68 % (12053)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/6Mi)
% 2.74/1.68 % (12054)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11704 for (2999ds/377Mi)
% 2.74/1.68 % (12053)Instruction limit reached!
% 2.74/1.68 % (12053)------------------------------
% 2.74/1.68 % (12053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.68 % (12053)Termination reason: Unknown
% 2.74/1.68 % (12053)Termination phase: shuffling
% 2.74/1.68
% 2.74/1.68 % (12053)Memory used [KB]: 1535
% 2.74/1.68 % (12053)Time elapsed: 0.004 s
% 2.74/1.68 % (12053)Instructions burned: 7 (million)
% 2.74/1.68 % (12053)------------------------------
% 2.74/1.68 % (12053)------------------------------
% 2.74/1.69 % (12055)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_11704 for (2998ds/779Mi)
% 2.74/1.69 % (12056)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_11704 for (2998ds/19Mi)
% 2.74/1.70 % (12056)Instruction limit reached!
% 2.74/1.70 % (12056)------------------------------
% 2.74/1.70 % (12056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.70 % (12056)Termination reason: Unknown
% 2.74/1.70 % (12056)Termination phase: shuffling
% 2.74/1.70
% 2.74/1.70 % (12056)Memory used [KB]: 1791
% 2.74/1.70 % (12056)Time elapsed: 0.008 s
% 2.74/1.70 % (12056)Instructions burned: 20 (million)
% 2.74/1.70 % (12056)------------------------------
% 2.74/1.70 % (12056)------------------------------
% 2.74/1.71 % (12057)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11704 for (2998ds/879Mi)
% 2.74/1.71 % (12033)Instruction limit reached!
% 2.74/1.71 % (12033)------------------------------
% 2.74/1.71 % (12033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.71 % (12033)Termination reason: Unknown
% 2.74/1.71 % (12033)Termination phase: Saturation
% 2.74/1.71
% 2.74/1.71 % (12033)Memory used [KB]: 7291
% 2.74/1.71 % (12033)Time elapsed: 0.113 s
% 2.74/1.71 % (12033)Instructions burned: 275 (million)
% 2.74/1.71 % (12033)------------------------------
% 2.74/1.71 % (12033)------------------------------
% 2.74/1.72 % (12058)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11704 for (2998ds/17Mi)
% 2.74/1.72 % (12058)Instruction limit reached!
% 2.74/1.72 % (12058)------------------------------
% 2.74/1.72 % (12058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.72 % (12058)Termination reason: Unknown
% 2.74/1.72 % (12058)Termination phase: shuffling
% 2.74/1.72
% 2.74/1.72 % (12058)Memory used [KB]: 1918
% 2.74/1.72 % (12058)Time elapsed: 0.007 s
% 2.74/1.72 % (12058)Instructions burned: 18 (million)
% 2.74/1.72 % (12058)------------------------------
% 2.74/1.72 % (12058)------------------------------
% 2.74/1.73 % (12059)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11704 for (2998ds/3Mi)
% 2.74/1.73 % (12059)Instruction limit reached!
% 2.74/1.73 % (12059)------------------------------
% 2.74/1.73 % (12059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.73 % (12059)Termination reason: Unknown
% 2.74/1.73 % (12059)Termination phase: shuffling
% 2.74/1.73
% 2.74/1.73 % (12059)Memory used [KB]: 1407
% 2.74/1.73 % (12059)Time elapsed: 0.002 s
% 2.74/1.73 % (12059)Instructions burned: 3 (million)
% 2.74/1.73 % (12059)------------------------------
% 2.74/1.73 % (12059)------------------------------
% 2.74/1.74 % (12060)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11704 for (2998ds/30Mi)
% 2.74/1.75 % (12060)Instruction limit reached!
% 2.74/1.75 % (12060)------------------------------
% 2.74/1.75 % (12060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.75 % (12060)Termination reason: Unknown
% 2.74/1.75 % (12060)Termination phase: Property scanning
% 2.74/1.75
% 2.74/1.75 % (12060)Memory used [KB]: 2046
% 2.74/1.75 % (12060)Time elapsed: 0.011 s
% 2.74/1.75 % (12060)Instructions burned: 32 (million)
% 2.74/1.75 % (12060)------------------------------
% 2.74/1.75 % (12060)------------------------------
% 2.74/1.76 % (12061)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11704 for (2998ds/127Mi)
% 2.74/1.80 % (12061)Instruction limit reached!
% 2.74/1.80 % (12061)------------------------------
% 2.74/1.80 % (12061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.80 % (12061)Termination reason: Unknown
% 2.74/1.80 % (12061)Termination phase: Saturation
% 2.74/1.80
% 2.74/1.80 % (12061)Memory used [KB]: 7291
% 2.74/1.80 % (12061)Time elapsed: 0.040 s
% 2.74/1.80 % (12061)Instructions burned: 129 (million)
% 2.74/1.80 % (12061)------------------------------
% 2.74/1.80 % (12061)------------------------------
% 2.74/1.81 % (12062)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11704 for (2997ds/100Mi)
% 2.74/1.81 % (12054)Instruction limit reached!
% 2.74/1.81 % (12054)------------------------------
% 2.74/1.81 % (12054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.81 % (12054)Termination reason: Unknown
% 2.74/1.81 % (12054)Termination phase: Saturation
% 2.74/1.81
% 2.74/1.81 % (12054)Memory used [KB]: 8059
% 2.74/1.81 % (12054)Time elapsed: 0.134 s
% 2.74/1.81 % (12054)Instructions burned: 379 (million)
% 2.74/1.81 % (12054)------------------------------
% 2.74/1.81 % (12054)------------------------------
% 2.74/1.82 % (12063)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_11704 for (2997ds/3Mi)
% 2.74/1.82 % (12063)Instruction limit reached!
% 2.74/1.82 % (12063)------------------------------
% 2.74/1.82 % (12063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.82 % (12063)Termination reason: Unknown
% 2.74/1.82 % (12063)Termination phase: shuffling
% 2.74/1.82
% 2.74/1.82 % (12063)Memory used [KB]: 1407
% 2.74/1.82 % (12063)Time elapsed: 0.003 s
% 2.74/1.82 % (12063)Instructions burned: 4 (million)
% 2.74/1.82 % (12063)------------------------------
% 2.74/1.82 % (12063)------------------------------
% 2.74/1.83 % (12064)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_11704 for (2997ds/20Mi)
% 2.74/1.84 % (12062)Instruction limit reached!
% 2.74/1.84 % (12062)------------------------------
% 2.74/1.84 % (12062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.84 % (12062)Termination reason: Unknown
% 2.74/1.84 % (12062)Termination phase: Property scanning
% 2.74/1.84
% 2.74/1.84 % (12062)Memory used [KB]: 2430
% 2.74/1.84 % (12062)Time elapsed: 0.028 s
% 2.74/1.84 % (12062)Instructions burned: 101 (million)
% 2.74/1.84 % (12062)------------------------------
% 2.74/1.84 % (12062)------------------------------
% 2.74/1.84 % (12064)Instruction limit reached!
% 2.74/1.84 % (12064)------------------------------
% 2.74/1.84 % (12064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.84 % (12064)Termination reason: Unknown
% 2.74/1.84 % (12064)Termination phase: Property scanning
% 2.74/1.84
% 2.74/1.84 % (12064)Memory used [KB]: 1918
% 2.74/1.84 % (12064)Time elapsed: 0.009 s
% 2.74/1.84 % (12064)Instructions burned: 20 (million)
% 2.74/1.84 % (12064)------------------------------
% 2.74/1.84 % (12064)------------------------------
% 2.74/1.85 % (12065)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_11704 for (2997ds/86Mi)
% 2.74/1.85 % (12066)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_11704 for (2997ds/107Mi)
% 2.74/1.87 % (12048)Instruction limit reached!
% 2.74/1.87 % (12048)------------------------------
% 2.74/1.87 % (12048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.87 % (12048)Termination reason: Unknown
% 2.74/1.87 % (12048)Termination phase: Saturation
% 2.74/1.87
% 2.74/1.87 % (12048)Memory used [KB]: 7931
% 2.74/1.87 % (12048)Time elapsed: 0.223 s
% 2.74/1.87 % (12048)Instructions burned: 712 (million)
% 2.74/1.87 % (12048)------------------------------
% 2.74/1.87 % (12048)------------------------------
% 2.74/1.87 % (12065)Instruction limit reached!
% 2.74/1.87 % (12065)------------------------------
% 2.74/1.87 % (12065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.87 % (12065)Termination reason: Unknown
% 2.74/1.87 % (12065)Termination phase: Saturation
% 2.74/1.87
% 2.74/1.87 % (12065)Memory used [KB]: 6908
% 2.74/1.87 % (12065)Time elapsed: 0.027 s
% 2.74/1.87 % (12065)Instructions burned: 86 (million)
% 2.74/1.87 % (12065)------------------------------
% 2.74/1.87 % (12065)------------------------------
% 2.74/1.88 % (12067)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_11704 for (2997ds/39Mi)
% 2.74/1.88 % (12068)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_11704 for (2996ds/448Mi)
% 2.74/1.89 % (12066)Instruction limit reached!
% 2.74/1.89 % (12066)------------------------------
% 2.74/1.89 % (12066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.89 % (12066)Termination reason: Unknown
% 2.74/1.89 % (12066)Termination phase: Saturation
% 2.74/1.89
% 2.74/1.89 % (12066)Memory used [KB]: 7036
% 2.74/1.89 % (12066)Time elapsed: 0.037 s
% 2.74/1.89 % (12066)Instructions burned: 108 (million)
% 2.74/1.89 % (12066)------------------------------
% 2.74/1.89 % (12066)------------------------------
% 2.74/1.89 % (12067)Instruction limit reached!
% 2.74/1.89 % (12067)------------------------------
% 2.74/1.89 % (12067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.89 % (12067)Termination reason: Unknown
% 2.74/1.89 % (12067)Termination phase: shuffling
% 2.74/1.89
% 2.74/1.89 % (12067)Memory used [KB]: 2174
% 2.74/1.89 % (12067)Time elapsed: 0.012 s
% 2.74/1.89 % (12067)Instructions burned: 39 (million)
% 2.74/1.89 % (12067)------------------------------
% 2.74/1.89 % (12067)------------------------------
% 2.74/1.90 % (12069)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_11704 for (2996ds/46Mi)
% 2.74/1.90 % (12070)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_11704 for (2996ds/98Mi)
% 2.74/1.91 % (12069)Instruction limit reached!
% 2.74/1.91 % (12069)------------------------------
% 2.74/1.91 % (12069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.91 % (12069)Termination reason: Unknown
% 2.74/1.91 % (12069)Termination phase: Preprocessing 3
% 2.74/1.91
% 2.74/1.91 % (12069)Memory used [KB]: 2174
% 2.74/1.91 % (12069)Time elapsed: 0.016 s
% 2.74/1.91 % (12069)Instructions burned: 48 (million)
% 2.74/1.91 % (12069)------------------------------
% 2.74/1.91 % (12069)------------------------------
% 2.74/1.92 % (12071)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_11704 for (2996ds/507Mi)
% 2.74/1.93 % (12070)Instruction limit reached!
% 2.74/1.93 % (12070)------------------------------
% 2.74/1.93 % (12070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.93 % (12070)Termination reason: Unknown
% 2.74/1.93 % (12070)Termination phase: Property scanning
% 2.74/1.93
% 2.74/1.93 % (12070)Memory used [KB]: 2430
% 2.74/1.93 % (12070)Time elapsed: 0.028 s
% 2.74/1.93 % (12070)Instructions burned: 101 (million)
% 2.74/1.93 % (12070)------------------------------
% 2.74/1.93 % (12070)------------------------------
% 2.74/1.93 % (12050)Instruction limit reached!
% 2.74/1.93 % (12050)------------------------------
% 2.74/1.93 % (12050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.93 % (12050)Termination reason: Unknown
% 2.74/1.93 % (12050)Termination phase: Saturation
% 2.74/1.93
% 2.74/1.93 % (12050)Memory used [KB]: 8315
% 2.74/1.93 % (12050)Time elapsed: 0.271 s
% 2.74/1.93 % (12050)Instructions burned: 904 (million)
% 2.74/1.93 % (12050)------------------------------
% 2.74/1.93 % (12050)------------------------------
% 2.74/1.94 % (12072)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_11704 for (2996ds/149Mi)
% 2.74/1.94 % (12073)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_11704 for (2996ds/39Mi)
% 2.74/1.95 % (12073)Instruction limit reached!
% 2.74/1.95 % (12073)------------------------------
% 2.74/1.95 % (12073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.95 % (12073)Termination reason: Unknown
% 2.74/1.95 % (12073)Termination phase: Preprocessing 3
% 2.74/1.95
% 2.74/1.95 % (12073)Memory used [KB]: 2174
% 2.74/1.95 % (12073)Time elapsed: 0.014 s
% 2.74/1.95 % (12073)Instructions burned: 41 (million)
% 2.74/1.95 % (12073)------------------------------
% 2.74/1.95 % (12073)------------------------------
% 2.74/1.96 % (12074)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_11704 for (2996ds/6Mi)
% 2.74/1.96 % (12055)Instruction limit reached!
% 2.74/1.96 % (12055)------------------------------
% 2.74/1.96 % (12055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.96 % (12055)Termination reason: Unknown
% 2.74/1.96 % (12055)Termination phase: Saturation
% 2.74/1.96
% 2.74/1.96 % (12055)Memory used [KB]: 8315
% 2.74/1.96 % (12055)Time elapsed: 0.275 s
% 2.74/1.96 % (12055)Instructions burned: 780 (million)
% 2.74/1.96 % (12055)------------------------------
% 2.74/1.96 % (12055)------------------------------
% 2.74/1.96 % (12074)Instruction limit reached!
% 2.74/1.96 % (12074)------------------------------
% 2.74/1.96 % (12074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.96 % (12074)Termination reason: Unknown
% 2.74/1.96 % (12074)Termination phase: shuffling
% 2.74/1.96
% 2.74/1.96 % (12074)Memory used [KB]: 1535
% 2.74/1.96 % (12074)Time elapsed: 0.003 s
% 2.74/1.96 % (12074)Instructions burned: 7 (million)
% 2.74/1.96 % (12074)------------------------------
% 2.74/1.96 % (12074)------------------------------
% 2.74/1.97 % (12075)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/1087Mi)
% 2.74/1.97 % (12076)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/47Mi)
% 2.74/1.98 % (12072)Instruction limit reached!
% 2.74/1.98 % (12072)------------------------------
% 2.74/1.98 % (12072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.98 % (12072)Termination reason: Unknown
% 2.74/1.98 % (12072)Termination phase: Saturation
% 2.74/1.98
% 2.74/1.98 % (12072)Memory used [KB]: 7164
% 2.74/1.98 % (12072)Time elapsed: 0.046 s
% 2.74/1.98 % (12072)Instructions burned: 149 (million)
% 2.74/1.98 % (12072)------------------------------
% 2.74/1.98 % (12072)------------------------------
% 2.74/1.99 % (12076)Instruction limit reached!
% 2.74/1.99 % (12076)------------------------------
% 2.74/1.99 % (12076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.99 % (12076)Termination reason: Unknown
% 2.74/1.99 % (12076)Termination phase: Preprocessing 3
% 2.74/1.99
% 2.74/1.99 % (12076)Memory used [KB]: 2302
% 2.74/1.99 % (12076)Time elapsed: 0.016 s
% 2.74/1.99 % (12076)Instructions burned: 47 (million)
% 2.74/1.99 % (12076)------------------------------
% 2.74/1.99 % (12076)------------------------------
% 2.74/1.99 % (12077)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/44Mi)
% 2.74/2.00 % (12078)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/432Mi)
% 2.74/2.00 % (12077)Instruction limit reached!
% 2.74/2.00 % (12077)------------------------------
% 2.74/2.00 % (12077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/2.00 % (12077)Termination reason: Unknown
% 2.74/2.00 % (12077)Termination phase: Property scanning
% 2.74/2.00
% 2.74/2.00 % (12077)Memory used [KB]: 2302
% 2.74/2.00 % (12077)Time elapsed: 0.013 s
% 2.74/2.00 % (12077)Instructions burned: 44 (million)
% 2.74/2.00 % (12077)------------------------------
% 2.74/2.00 % (12077)------------------------------
% 2.74/2.01 % (12057)Instruction limit reached!
% 2.74/2.01 % (12057)------------------------------
% 2.74/2.01 % (12057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/2.01 % (12057)Termination reason: Unknown
% 2.74/2.01 % (12057)Termination phase: Saturation
% 2.74/2.01
% 2.74/2.01 % (12057)Memory used [KB]: 7803
% 2.74/2.01 % (12057)Time elapsed: 0.300 s
% 2.74/2.01 % (12057)Instructions burned: 881 (million)
% 2.74/2.01 % (12057)------------------------------
% 2.74/2.01 % (12057)------------------------------
% 2.74/2.01 % (12039)Instruction limit reached!
% 2.74/2.01 % (12039)------------------------------
% 2.74/2.01 % (12039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/2.01 % (12039)Termination reason: Unknown
% 2.74/2.01 % (12039)Termination phase: Saturation
% 2.74/2.01
% 2.74/2.01 % (12039)Memory used [KB]: 10106
% 2.74/2.01 % (12039)Time elapsed: 0.385 s
% 2.74/2.01 % (12039)Instructions burned: 1041 (million)
% 2.74/2.01 % (12039)------------------------------
% 2.74/2.01 % (12039)------------------------------
% 2.74/2.01 % (12079)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/62Mi)
% 5.33/2.02 % (12080)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/31Mi)
% 5.33/2.02 % (12068)Instruction limit reached!
% 5.33/2.02 % (12068)------------------------------
% 5.33/2.02 % (12068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.02 % (12068)Termination reason: Unknown
% 5.33/2.02 % (12068)Termination phase: Saturation
% 5.33/2.02
% 5.33/2.02 % (12068)Memory used [KB]: 8059
% 5.33/2.02 % (12068)Time elapsed: 0.138 s
% 5.33/2.02 % (12068)Instructions burned: 450 (million)
% 5.33/2.02 % (12068)------------------------------
% 5.33/2.02 % (12068)------------------------------
% 5.33/2.03 % (12080)Instruction limit reached!
% 5.33/2.03 % (12080)------------------------------
% 5.33/2.03 % (12080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.03 % (12080)Termination reason: Unknown
% 5.33/2.03 % (12080)Termination phase: Preprocessing 1
% 5.33/2.03
% 5.33/2.03 % (12080)Memory used [KB]: 1918
% 5.33/2.03 % (12080)Time elapsed: 0.012 s
% 5.33/2.03 % (12080)Instructions burned: 33 (million)
% 5.33/2.03 % (12080)------------------------------
% 5.33/2.03 % (12080)------------------------------
% 5.33/2.03 % (12079)Instruction limit reached!
% 5.33/2.03 % (12079)------------------------------
% 5.33/2.03 % (12079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.03 % (12079)Termination reason: Unknown
% 5.33/2.03 % (12079)Termination phase: Property scanning
% 5.33/2.03
% 5.33/2.03 % (12079)Memory used [KB]: 2302
% 5.33/2.03 % (12079)Time elapsed: 0.018 s
% 5.33/2.03 % (12079)Instructions burned: 63 (million)
% 5.33/2.03 % (12079)------------------------------
% 5.33/2.03 % (12079)------------------------------
% 5.33/2.03 % (12081)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/96Mi)
% 5.33/2.03 % (12082)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/453Mi)
% 5.33/2.04 % (12083)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/71Mi)
% 5.33/2.04 % (12084)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/83Mi)
% 5.33/2.06 % (12083)Instruction limit reached!
% 5.33/2.06 % (12083)------------------------------
% 5.33/2.06 % (12083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.06 % (12083)Termination reason: Unknown
% 5.33/2.06 % (12083)Termination phase: Property scanning
% 5.33/2.06
% 5.33/2.06 % (12083)Memory used [KB]: 2430
% 5.33/2.06 % (12083)Time elapsed: 0.022 s
% 5.33/2.06 % (12083)Instructions burned: 71 (million)
% 5.33/2.06 % (12083)------------------------------
% 5.33/2.06 % (12083)------------------------------
% 5.33/2.06 % (12084)Instruction limit reached!
% 5.33/2.06 % (12084)------------------------------
% 5.33/2.06 % (12084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.06 % (12084)Termination reason: Unknown
% 5.33/2.06 % (12084)Termination phase: Saturation
% 5.33/2.06
% 5.33/2.06 % (12084)Memory used [KB]: 6780
% 5.33/2.06 % (12084)Time elapsed: 0.027 s
% 5.33/2.06 % (12084)Instructions burned: 84 (million)
% 5.33/2.06 % (12084)------------------------------
% 5.33/2.06 % (12084)------------------------------
% 5.33/2.07 % (12085)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/11Mi)
% 5.33/2.07 % (12085)Instruction limit reached!
% 5.33/2.07 % (12085)------------------------------
% 5.33/2.07 % (12085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.07 % (12085)Termination reason: Unknown
% 5.33/2.07 % (12085)Termination phase: shuffling
% 5.33/2.07
% 5.33/2.07 % (12085)Memory used [KB]: 1663
% 5.33/2.07 % (12085)Time elapsed: 0.005 s
% 5.33/2.07 % (12085)Instructions burned: 13 (million)
% 5.33/2.07 % (12085)------------------------------
% 5.33/2.07 % (12085)------------------------------
% 5.33/2.07 % (12086)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/41Mi)
% 5.33/2.08 % (12071)Instruction limit reached!
% 5.33/2.08 % (12071)------------------------------
% 5.33/2.08 % (12071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.08 % (12071)Termination reason: Unknown
% 5.33/2.08 % (12071)Termination phase: Saturation
% 5.33/2.08
% 5.33/2.08 % (12071)Memory used [KB]: 7931
% 5.33/2.08 % (12071)Time elapsed: 0.158 s
% 5.33/2.08 % (12071)Instructions burned: 509 (million)
% 5.33/2.08 % (12071)------------------------------
% 5.33/2.08 % (12071)------------------------------
% 5.33/2.08 % (12087)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11704 for (2995ds/6Mi)
% 5.33/2.08 % (12081)Instruction limit reached!
% 5.33/2.08 % (12081)------------------------------
% 5.33/2.08 % (12081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.08 % (12081)Termination reason: Unknown
% 5.33/2.08 % (12081)Termination phase: Saturation
% 5.33/2.08
% 5.33/2.08 % (12081)Memory used [KB]: 6908
% 5.33/2.08 % (12081)Time elapsed: 0.055 s
% 5.33/2.08 % (12081)Instructions burned: 96 (million)
% 5.33/2.08 % (12081)------------------------------
% 5.33/2.08 % (12081)------------------------------
% 5.33/2.08 % (12087)Instruction limit reached!
% 5.33/2.08 % (12087)------------------------------
% 5.33/2.08 % (12087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.08 % (12087)Termination reason: Unknown
% 5.33/2.08 % (12087)Termination phase: shuffling
% 5.33/2.08
% 5.33/2.08 % (12087)Memory used [KB]: 1535
% 5.33/2.08 % (12087)Time elapsed: 0.003 s
% 5.33/2.08 % (12087)Instructions burned: 6 (million)
% 5.33/2.08 % (12087)------------------------------
% 5.33/2.08 % (12087)------------------------------
% 5.33/2.08 % (12086)Instruction limit reached!
% 5.33/2.08 % (12086)------------------------------
% 5.33/2.08 % (12086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.08 % (12086)Termination reason: Unknown
% 5.33/2.08 % (12086)Termination phase: Property scanning
% 5.33/2.08
% 5.33/2.08 % (12086)Memory used [KB]: 2302
% 5.33/2.08 % (12086)Time elapsed: 0.013 s
% 5.33/2.08 % (12086)Instructions burned: 43 (million)
% 5.33/2.08 % (12086)------------------------------
% 5.33/2.08 % (12086)------------------------------
% 5.33/2.09 % (12088)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_11704 for (2994ds/150Mi)
% 5.33/2.09 % (12089)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_11704 for (2994ds/343Mi)
% 5.33/2.09 % (12091)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_11704 for (2994ds/253Mi)
% 5.33/2.10 % (12090)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_11704 for (2994ds/109Mi)
% 6.26/2.13 % (12090)Instruction limit reached!
% 6.26/2.13 % (12090)------------------------------
% 6.26/2.13 % (12090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.13 % (12090)Termination reason: Unknown
% 6.26/2.13 % (12090)Termination phase: Saturation
% 6.26/2.13
% 6.26/2.13 % (12090)Memory used [KB]: 7164
% 6.26/2.13 % (12090)Time elapsed: 0.037 s
% 6.26/2.13 % (12090)Instructions burned: 110 (million)
% 6.26/2.13 % (12090)------------------------------
% 6.26/2.13 % (12090)------------------------------
% 6.26/2.13 % (12088)Instruction limit reached!
% 6.26/2.13 % (12088)------------------------------
% 6.26/2.13 % (12088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.13 % (12088)Termination reason: Unknown
% 6.26/2.13 % (12088)Termination phase: Saturation
% 6.26/2.13
% 6.26/2.13 % (12088)Memory used [KB]: 7547
% 6.26/2.13 % (12088)Time elapsed: 0.048 s
% 6.26/2.13 % (12088)Instructions burned: 152 (million)
% 6.26/2.13 % (12088)------------------------------
% 6.26/2.13 % (12088)------------------------------
% 6.26/2.13 % (12078)Instruction limit reached!
% 6.26/2.13 % (12078)------------------------------
% 6.26/2.13 % (12078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.13 % (12078)Termination reason: Unknown
% 6.26/2.13 % (12078)Termination phase: Saturation
% 6.26/2.13
% 6.26/2.13 % (12078)Memory used [KB]: 4349
% 6.26/2.13 % (12078)Time elapsed: 0.139 s
% 6.26/2.13 % (12078)Instructions burned: 434 (million)
% 6.26/2.13 % (12078)------------------------------
% 6.26/2.13 % (12078)------------------------------
% 6.26/2.14 % (12092)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_11704 for (2994ds/140Mi)
% 6.26/2.14 % (12093)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_11704 for (2994ds/614Mi)
% 6.26/2.14 % (12094)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_11704 for (2994ds/202Mi)
% 6.26/2.16 % (12082)Instruction limit reached!
% 6.26/2.16 % (12082)------------------------------
% 6.26/2.16 % (12082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.16 % (12082)Termination reason: Unknown
% 6.26/2.16 % (12082)Termination phase: Saturation
% 6.26/2.16
% 6.26/2.16 % (12082)Memory used [KB]: 8187
% 6.26/2.16 % (12082)Time elapsed: 0.136 s
% 6.26/2.16 % (12082)Instructions burned: 454 (million)
% 6.26/2.16 % (12082)------------------------------
% 6.26/2.16 % (12082)------------------------------
% 6.26/2.17 % (12095)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_11704 for (2993ds/339Mi)
% 6.26/2.18 % (12091)Instruction limit reached!
% 6.26/2.18 % (12091)------------------------------
% 6.26/2.18 % (12091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.18 % (12091)Termination reason: Unknown
% 6.26/2.18 % (12091)Termination phase: Saturation
% 6.26/2.18
% 6.26/2.18 % (12091)Memory used [KB]: 7547
% 6.26/2.18 % (12091)Time elapsed: 0.082 s
% 6.26/2.18 % (12091)Instructions burned: 255 (million)
% 6.26/2.18 % (12091)------------------------------
% 6.26/2.18 % (12091)------------------------------
% 6.26/2.18 % (12096)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_11704 for (2993ds/283Mi)
% 6.26/2.19 % (12092)Instruction limit reached!
% 6.26/2.19 % (12092)------------------------------
% 6.26/2.19 % (12092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.19 % (12092)Termination reason: Unknown
% 6.26/2.19 % (12092)Termination phase: Saturation
% 6.26/2.19
% 6.26/2.19 % (12092)Memory used [KB]: 7036
% 6.26/2.19 % (12092)Time elapsed: 0.049 s
% 6.26/2.19 % (12092)Instructions burned: 141 (million)
% 6.26/2.19 % (12092)------------------------------
% 6.26/2.19 % (12092)------------------------------
% 6.76/2.20 % (12097)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_11704 for (2993ds/134Mi)
% 6.76/2.20 % (12089)Instruction limit reached!
% 6.76/2.20 % (12089)------------------------------
% 6.76/2.20 % (12089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.20 % (12089)Termination reason: Unknown
% 6.76/2.20 % (12089)Termination phase: Saturation
% 6.76/2.20
% 6.76/2.20 % (12089)Memory used [KB]: 7547
% 6.76/2.20 % (12089)Time elapsed: 0.113 s
% 6.76/2.20 % (12089)Instructions burned: 345 (million)
% 6.76/2.20 % (12089)------------------------------
% 6.76/2.20 % (12089)------------------------------
% 6.76/2.21 % (12094)Instruction limit reached!
% 6.76/2.21 % (12094)------------------------------
% 6.76/2.21 % (12094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.21 % (12094)Termination reason: Unknown
% 6.76/2.21 % (12094)Termination phase: Saturation
% 6.76/2.21
% 6.76/2.21 % (12094)Memory used [KB]: 7164
% 6.76/2.21 % (12094)Time elapsed: 0.066 s
% 6.76/2.21 % (12094)Instructions burned: 204 (million)
% 6.76/2.21 % (12094)------------------------------
% 6.76/2.21 % (12094)------------------------------
% 6.76/2.21 % (12098)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_11704 for (2993ds/298Mi)
% 6.76/2.22 % (12099)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_11704 for (2993ds/192Mi)
% 6.76/2.24 % (12097)Instruction limit reached!
% 6.76/2.24 % (12097)------------------------------
% 6.76/2.24 % (12097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.24 % (12097)Termination reason: Unknown
% 6.76/2.24 % (12097)Termination phase: Saturation
% 6.76/2.24
% 6.76/2.24 % (12097)Memory used [KB]: 7291
% 6.76/2.24 % (12097)Time elapsed: 0.046 s
% 6.76/2.24 % (12097)Instructions burned: 134 (million)
% 6.76/2.24 % (12097)------------------------------
% 6.76/2.24 % (12097)------------------------------
% 6.76/2.26 % (12100)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_11704 for (2993ds/258Mi)
% 6.76/2.27 % (12096)Instruction limit reached!
% 6.76/2.27 % (12096)------------------------------
% 6.76/2.27 % (12096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.27 % (12096)Termination reason: Unknown
% 6.76/2.27 % (12096)Termination phase: Saturation
% 6.76/2.27
% 6.76/2.27 % (12096)Memory used [KB]: 8059
% 6.76/2.27 % (12096)Time elapsed: 0.090 s
% 6.76/2.27 % (12096)Instructions burned: 283 (million)
% 6.76/2.27 % (12096)------------------------------
% 6.76/2.27 % (12096)------------------------------
% 6.76/2.28 % (12099)Instruction limit reached!
% 6.76/2.28 % (12099)------------------------------
% 6.76/2.28 % (12099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.28 % (12099)Termination reason: Unknown
% 6.76/2.28 % (12099)Termination phase: Saturation
% 6.76/2.28
% 6.76/2.28 % (12099)Memory used [KB]: 8187
% 6.76/2.28 % (12099)Time elapsed: 0.060 s
% 6.76/2.28 % (12099)Instructions burned: 192 (million)
% 6.76/2.28 % (12099)------------------------------
% 6.76/2.28 % (12099)------------------------------
% 6.76/2.28 % (12095)Instruction limit reached!
% 6.76/2.28 % (12095)------------------------------
% 6.76/2.28 % (12095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.28 % (12095)Termination reason: Unknown
% 6.76/2.28 % (12095)Termination phase: Saturation
% 6.76/2.28
% 6.76/2.28 % (12095)Memory used [KB]: 7931
% 6.76/2.28 % (12095)Time elapsed: 0.106 s
% 6.76/2.28 % (12095)Instructions burned: 339 (million)
% 6.76/2.28 % (12095)------------------------------
% 6.76/2.28 % (12095)------------------------------
% 6.76/2.28 % (12101)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/90Mi)
% 6.76/2.29 % (12102)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/231Mi)
% 6.76/2.29 % (12103)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/458Mi)
% 7.41/2.30 % (12098)Instruction limit reached!
% 7.41/2.30 % (12098)------------------------------
% 7.41/2.30 % (12098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.30 % (12098)Termination reason: Unknown
% 7.41/2.30 % (12098)Termination phase: Saturation
% 7.41/2.30
% 7.41/2.30 % (12098)Memory used [KB]: 8187
% 7.41/2.30 % (12098)Time elapsed: 0.086 s
% 7.41/2.30 % (12098)Instructions burned: 300 (million)
% 7.41/2.30 % (12098)------------------------------
% 7.41/2.30 % (12098)------------------------------
% 7.41/2.31 % (12104)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/31Mi)
% 7.41/2.31 % (12101)Instruction limit reached!
% 7.41/2.31 % (12101)------------------------------
% 7.41/2.31 % (12101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.31 % (12101)Termination reason: Unknown
% 7.41/2.31 % (12101)Termination phase: Saturation
% 7.41/2.31
% 7.41/2.31 % (12101)Memory used [KB]: 6908
% 7.41/2.31 % (12101)Time elapsed: 0.028 s
% 7.41/2.31 % (12101)Instructions burned: 92 (million)
% 7.41/2.31 % (12101)------------------------------
% 7.41/2.31 % (12101)------------------------------
% 7.41/2.31 % (12075)Instruction limit reached!
% 7.41/2.31 % (12075)------------------------------
% 7.41/2.31 % (12075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.31 % (12075)Termination reason: Unknown
% 7.41/2.31 % (12075)Termination phase: Saturation
% 7.41/2.31
% 7.41/2.31 % (12075)Memory used [KB]: 8059
% 7.41/2.31 % (12075)Time elapsed: 0.342 s
% 7.41/2.31 % (12075)Instructions burned: 1087 (million)
% 7.41/2.31 % (12075)------------------------------
% 7.41/2.31 % (12075)------------------------------
% 7.41/2.32 % (12104)Instruction limit reached!
% 7.41/2.32 % (12104)------------------------------
% 7.41/2.32 % (12104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.32 % (12104)Termination reason: Unknown
% 7.41/2.32 % (12104)Termination phase: Preprocessing 1
% 7.41/2.32
% 7.41/2.32 % (12104)Memory used [KB]: 1918
% 7.41/2.32 % (12104)Time elapsed: 0.011 s
% 7.41/2.32 % (12104)Instructions burned: 33 (million)
% 7.41/2.32 % (12104)------------------------------
% 7.41/2.32 % (12104)------------------------------
% 7.41/2.32 % (12105)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/297Mi)
% 7.41/2.32 % (12106)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/987Mi)
% 7.41/2.33 % (12107)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/182Mi)
% 7.41/2.33 % (12093)Instruction limit reached!
% 7.41/2.33 % (12093)------------------------------
% 7.41/2.33 % (12093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.33 % (12093)Termination reason: Unknown
% 7.41/2.33 % (12093)Termination phase: Saturation
% 7.41/2.33
% 7.41/2.33 % (12093)Memory used [KB]: 8699
% 7.41/2.33 % (12093)Time elapsed: 0.191 s
% 7.41/2.33 % (12093)Instructions burned: 615 (million)
% 7.41/2.33 % (12093)------------------------------
% 7.41/2.33 % (12093)------------------------------
% 7.41/2.34 % (12100)Instruction limit reached!
% 7.41/2.34 % (12100)------------------------------
% 7.41/2.34 % (12100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.34 % (12100)Termination reason: Unknown
% 7.41/2.34 % (12100)Termination phase: Saturation
% 7.41/2.34
% 7.41/2.34 % (12100)Memory used [KB]: 7675
% 7.41/2.34 % (12100)Time elapsed: 0.087 s
% 7.41/2.34 % (12100)Instructions burned: 260 (million)
% 7.41/2.34 % (12100)------------------------------
% 7.41/2.34 % (12100)------------------------------
% 7.41/2.34 % (12108)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/182Mi)
% 7.41/2.35 % (12102)Instruction limit reached!
% 7.41/2.35 % (12102)------------------------------
% 7.41/2.35 % (12102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.35 % (12102)Termination reason: Unknown
% 7.41/2.35 % (12102)Termination phase: Saturation
% 7.41/2.35
% 7.41/2.35 % (12102)Memory used [KB]: 7164
% 7.41/2.35 % (12102)Time elapsed: 0.063 s
% 7.41/2.35 % (12102)Instructions burned: 231 (million)
% 7.41/2.35 % (12102)------------------------------
% 7.41/2.35 % (12102)------------------------------
% 7.41/2.35 % (12109)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/154Mi)
% 7.41/2.36 % (12110)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_11704 for (2992ds/79Mi)
% 7.41/2.38 % (12110)Instruction limit reached!
% 7.41/2.38 % (12110)------------------------------
% 7.41/2.38 % (12110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.38 % (12110)Termination reason: Unknown
% 7.41/2.38 % (12110)Termination phase: Property scanning
% 7.41/2.38
% 7.41/2.38 % (12110)Memory used [KB]: 2430
% 7.41/2.38 % (12110)Time elapsed: 0.024 s
% 7.41/2.38 % (12110)Instructions burned: 79 (million)
% 7.41/2.38 % (12110)------------------------------
% 7.41/2.38 % (12110)------------------------------
% 7.41/2.38 % (12107)Instruction limit reached!
% 7.41/2.38 % (12107)------------------------------
% 7.41/2.38 % (12107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.38 % (12107)Termination reason: Unknown
% 7.41/2.38 % (12107)Termination phase: Saturation
% 7.41/2.38
% 7.41/2.38 % (12107)Memory used [KB]: 7419
% 7.41/2.38 % (12107)Time elapsed: 0.057 s
% 7.41/2.38 % (12107)Instructions burned: 184 (million)
% 7.41/2.38 % (12107)------------------------------
% 7.41/2.38 % (12107)------------------------------
% 7.41/2.39 % (12111)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_11704 for (2991ds/216Mi)
% 7.41/2.39 % (12112)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_11704 for (2991ds/114Mi)
% 7.41/2.39 % (12103)First to succeed.
% 7.41/2.40 % (12103)Refutation found. Thanks to Tanya!
% 7.41/2.40 % SZS status Theorem for DTF2THF_11704
% 7.41/2.40 % SZS output start Proof for DTF2THF_11704
% 7.41/2.40 thf(type_def_5, type, complex: $tType).
% 7.41/2.40 thf(type_def_7, type, set: ($tType) > $tType).
% 7.41/2.40 thf(type_def_8, type, formal_Power_fps: ($tType) > $tType).
% 7.41/2.40 thf(type_def_9, type, nat: $tType).
% 7.41/2.40 thf(type_def_10, type, real: $tType).
% 7.41/2.40 thf(func_def_0, type, formal_Power_fps: ($tType) > $tType).
% 7.41/2.40 thf(func_def_1, type, complex: $tType).
% 7.41/2.40 thf(func_def_2, type, real: $tType).
% 7.41/2.40 thf(func_def_3, type, set: ($tType) > $tType).
% 7.41/2.40 thf(func_def_4, type, nat: $tType).
% 7.41/2.40 thf(func_def_5, type, finite_finite: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_6, type, ring_1: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_7, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_8, type, semiring_1: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_9, type, semiring_0: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_10, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_11, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_12, type, group_add: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_13, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_14, type, type: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_15, type, countable: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_16, type, one: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_17, type, zero: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_18, type, field: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_19, type, times: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_20, type, ord: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_21, type, neg_numeral: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_22, type, order: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_23, type, mult_zero: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_24, type, ln: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_25, type, monoid_mult: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_26, type, linorder: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_27, type, preorder: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_28, type, ordered_ring: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_29, type, zero_neq_one: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_30, type, field_char_0: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_31, type, semigroup_mult: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_32, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_33, type, linordered_idom: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_34, type, linordered_ring: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_35, type, ordered_semiring: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_36, type, comm_monoid_mult: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_37, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_38, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_39, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_40, type, topological_t0_space: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_41, type, topological_t1_space: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_42, type, linord581940658strict: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_43, type, ring_11004092258visors: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_44, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_45, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_46, type, real_V758409581_field: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_47, type, topolo2133971006pology: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_48, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_49, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_50, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_51, type, topolo2135403230pology: !>[X0: $tType]:($o)).
% 7.41/2.40 thf(func_def_52, type, comple372758642hic_on: (complex > complex) > set @ complex > $o).
% 7.41/2.40 thf(func_def_53, type, deriv: !>[X0: $tType]:((X0 > X0) > X0 > X0)).
% 7.41/2.40 thf(func_def_54, type, formal_Power_fps_tan: !>[X0: $tType]:(X0 > formal_Power_fps @ X0)).
% 7.41/2.40 thf(func_def_55, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 7.41/2.40 thf(func_def_56, type, id: !>[X0: $tType]:(X0 > X0)).
% 7.41/2.40 thf(func_def_57, type, one_one: !>[X0: $tType]:(X0)).
% 7.41/2.40 thf(func_def_58, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 7.41/2.40 thf(func_def_59, type, zero_zero: !>[X0: $tType]:(X0)).
% 7.41/2.40 thf(func_def_60, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 7.41/2.40 thf(func_def_61, type, compow: !>[X0: $tType]:(nat > X0 > X0)).
% 7.41/2.40 thf(func_def_62, type, funpow: !>[X0: $tType]:(nat > (X0 > X0) > X0 > X0)).
% 7.41/2.40 thf(func_def_63, type, neg_numeral_dbl_inc: !>[X0: $tType]:(X0 > X0)).
% 7.41/2.40 thf(func_def_64, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 7.41/2.40 thf(func_def_65, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 7.41/2.40 thf(func_def_66, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 7.41/2.40 thf(func_def_67, type, topolo1751647064n_open: !>[X0: $tType]:(set @ X0 > $o)).
% 7.41/2.40 thf(func_def_68, type, topolo1099314120nected: !>[X0: $tType]:(set @ X0 > $o)).
% 7.41/2.40 thf(func_def_69, type, arcosh: !>[X0: $tType]:(X0 > X0)).
% 7.41/2.40 thf(func_def_70, type, arsinh: !>[X0: $tType]:(X0 > X0)).
% 7.41/2.40 thf(func_def_71, type, artanh: !>[X0: $tType]:(X0 > X0)).
% 7.41/2.40 thf(func_def_72, type, ln_ln: !>[X0: $tType]:(X0 > X0)).
% 7.41/2.40 thf(func_def_73, type, transitive_relpowp: !>[X0: $tType]:(nat > (X0 > X0 > $o) > X0 > X0 > $o)).
% 7.41/2.40 thf(func_def_74, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 7.41/2.40 thf(func_def_75, type, s: set @ complex).
% 7.41/2.40 thf(func_def_76, type, t: set @ complex).
% 7.41/2.40 thf(func_def_77, type, f: complex > complex).
% 7.41/2.40 thf(func_def_78, type, g: complex > complex).
% 7.41/2.40 thf(func_def_79, type, w: complex).
% 7.41/2.40 thf(func_def_94, type, sP0: ((nat > real) > nat > real) > ((nat > real) > $o) > (nat > $o) > $o).
% 7.41/2.40 thf(func_def_95, type, sK1: complex > (complex > complex) > nat).
% 7.41/2.40 thf(func_def_96, type, sK2: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0)).
% 7.41/2.40 thf(func_def_97, type, sK3: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0)).
% 7.41/2.40 thf(func_def_98, type, sK4: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 7.41/2.40 thf(func_def_99, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_100, type, sK6: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X0)).
% 7.41/2.40 thf(func_def_101, type, sK7: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 7.41/2.40 thf(func_def_102, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_103, type, sK9: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > nat > X0)).
% 7.41/2.40 thf(func_def_104, type, sK10: nat > (nat > $o) > nat).
% 7.41/2.40 thf(func_def_105, type, sK11: (nat > $o) > nat).
% 7.41/2.40 thf(func_def_106, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 7.41/2.40 thf(func_def_107, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 7.41/2.40 thf(func_def_108, type, sK14: (complex > complex) > set @ complex > (complex > complex) > complex).
% 7.41/2.40 thf(func_def_109, type, sK15: (complex > complex) > set @ complex > (complex > complex) > complex).
% 7.41/2.40 thf(func_def_110, type, sK16: !>[X0: $tType]:(set @ X0 > X0)).
% 7.41/2.40 thf(func_def_111, type, sK17: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > set @ X0 > set @ X1)).
% 7.41/2.40 thf(func_def_112, type, sK18: !>[X0: $tType]:(X0 > nat > set @ X0)).
% 7.41/2.40 thf(func_def_113, type, sK19: !>[X0: $tType]:(set @ X0 > X0 > nat)).
% 7.41/2.40 thf(func_def_114, type, sK20: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 7.41/2.40 thf(func_def_115, type, sK21: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 7.41/2.40 thf(func_def_116, type, sK22: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_117, type, sK23: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_118, type, sK24: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > X1) > set @ X0 > X0)).
% 7.41/2.40 thf(func_def_119, type, sK25: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_120, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 7.41/2.40 thf(func_def_121, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_122, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_123, type, sK29: (complex > complex) > set @ complex > (complex > complex) > complex).
% 7.41/2.40 thf(func_def_124, type, sK30: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 7.41/2.40 thf(func_def_125, type, sK31: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 7.41/2.40 thf(func_def_126, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 7.41/2.40 thf(func_def_127, type, sK33: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 7.41/2.40 thf(func_def_128, type, sK34: ((nat > real) > nat > real) > ((nat > real) > $o) > (nat > $o) > (nat > real) > nat > nat).
% 7.41/2.40 thf(func_def_129, type, sK35: (nat > $o) > ((nat > real) > $o) > nat > real).
% 7.41/2.40 thf(func_def_130, type, sK36: (nat > $o) > ((nat > real) > $o) > nat).
% 7.41/2.40 thf(func_def_131, type, sK37: ((nat > real) > nat > real) > ((nat > real) > $o) > nat > real).
% 7.41/2.40 thf(func_def_132, type, sK38: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 7.41/2.40 thf(func_def_133, type, sK39: (complex > complex) > set @ complex > (complex > complex) > complex).
% 7.41/2.40 thf(func_def_134, type, sK40: (complex > complex) > (complex > complex) > set @ complex > complex).
% 7.41/2.40 thf(func_def_136, type, sK42: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > set @ X0 > X1)).
% 7.41/2.40 thf(func_def_137, type, sK43: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > set @ X0 > set @ X1)).
% 7.41/2.40 thf(func_def_138, type, sK44: !>[X0: $tType]:((X0 > X0) > X0)).
% 7.41/2.40 thf(func_def_139, type, sK45: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 7.41/2.40 thf(func_def_140, type, sK46: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 7.41/2.40 thf(func_def_141, type, sK47: !>[X0: $tType]:(X0 > X0 > set @ X0)).
% 7.41/2.40 thf(func_def_142, type, sK48: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > X0 > X1)).
% 7.41/2.40 thf(func_def_143, type, sK49: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_144, type, sK50: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > X0)).
% 7.41/2.40 thf(func_def_145, type, sK51: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > X1)).
% 7.41/2.40 thf(func_def_146, type, sK52: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > X0)).
% 7.41/2.40 thf(func_def_147, type, sK53: !>[X0: $tType, X1: $tType]:(set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1)).
% 7.41/2.40 thf(func_def_148, type, sK54: !>[X0: $tType, X1: $tType]:(set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X0)).
% 7.41/2.40 thf(func_def_149, type, ph55: !>[X0: $tType]:(X0)).
% 7.41/2.40 thf(f2511,plain,(
% 7.41/2.40 $false),
% 7.41/2.40 inference(subsumption_resolution,[status(thm)],[f2510,f1776])).
% 7.41/2.40 thf(f1776,plain,(
% 7.41/2.40 (real_V758409581_field @ complex = $true)),
% 7.41/2.40 inference(cnf_transformation,[status(thm)],[f874])).
% 7.41/2.40 thf(f874,plain,(
% 7.41/2.40 (real_V758409581_field @ complex = $true)),
% 7.41/2.40 inference(fool_elimination,[status(thm)],[f873])).
% 7.41/2.40 thf(f873,plain,(
% 7.41/2.40 real_V758409581_field @ complex),
% 7.41/2.40 inference(rectify,[status(thm)],[f380])).
% 7.41/2.40 thf(f380,axiom,(
% 7.41/2.40 real_V758409581_field @ complex),
% 7.41/2.40 file('/export/starexec/sandbox/tmp/tmp.opwukp64f0/DTF2THF_11704.p',tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__field_81)).
% 7.41/2.40 thf(f2510,plain,(
% 7.41/2.40 (real_V758409581_field @ complex != $true)),
% 7.41/2.40 inference(trivial_inequality_removal,[status(thm)],[f2509])).
% 7.41/2.40 thf(f2509,plain,(
% 7.41/2.40 (real_V758409581_field @ complex != $true) | (one_one @ complex != one_one @ complex)),
% 7.41/2.40 inference(superposition,[status(thm)],[f2014,f2506])).
% 7.41/2.40 thf(f2506,plain,(
% 7.41/2.40 ( ! [X0 : $tType,X1 : X0] : ((one_one @ X0 = (deriv @ X0 @ (^[Y0 : X0]: (Y0)) @ X1)) | (real_V758409581_field @ X0 != $true)) )),
% 7.41/2.40 inference(beta_eta_normalization,[status(thm)],[f2505])).
% 7.41/2.40 thf(f2505,plain,(
% 7.41/2.40 ( ! [X0 : $tType,X1 : X0] : ((real_V758409581_field @ X0 != $true) | ((deriv @ X0 @ (^[Y0 : X0]: (Y0)) @ X1) = ((^[Y0 : X0]: (one_one @ X0)) @ X1))) )),
% 7.41/2.40 inference(argument_congruence,[status(thm)],[f1994])).
% 7.41/2.40 thf(f1994,plain,(
% 7.41/2.40 ( ! [X0 : $tType] : (((deriv @ X0 @ (^[Y0 : X0]: (Y0))) = (^[Y0 : X0]: (one_one @ X0))) | (real_V758409581_field @ X0 != $true)) )),
% 7.41/2.40 inference(definition_unfolding,[status(thm)],[f1708,f1559])).
% 7.41/2.40 thf(f1559,plain,(
% 7.41/2.40 ( ! [X0 : $tType] : ((id @ X0 = (^[Y0 : X0]: (Y0)))) )),
% 7.41/2.40 inference(cnf_transformation,[status(thm)],[f1068])).
% 7.41/2.40 thf(f1068,plain,(
% 7.41/2.40 ! [X0 : $tType] : (id @ X0 = (^[Y0 : X0]: (Y0)))),
% 7.41/2.40 inference(fool_elimination,[status(thm)],[f1067])).
% 7.41/2.40 thf(f1067,plain,(
% 7.41/2.40 ! [X0 : $tType] : (id @ X0 = (^[X1 : X0] : (X1)))),
% 7.41/2.40 inference(rectify,[status(thm)],[f5])).
% 7.41/2.40 thf(f5,axiom,(
% 7.41/2.40 ! [X0 : $tType] : (id @ X0 = (^[X5 : X0] : (X5)))),
% 7.41/2.40 file('/export/starexec/sandbox/tmp/tmp.opwukp64f0/DTF2THF_11704.p',fact_4_id__def)).
% 7.41/2.40 thf(f1708,plain,(
% 7.41/2.40 ( ! [X0 : $tType] : ((real_V758409581_field @ X0 != $true) | ((deriv @ X0 @ id @ X0) = (^[Y0 : X0]: (one_one @ X0)))) )),
% 7.41/2.40 inference(cnf_transformation,[status(thm)],[f1300])).
% 7.41/2.40 thf(f1300,plain,(
% 7.41/2.40 ! [X0 : $tType] : ((real_V758409581_field @ X0 != $true) | ((deriv @ X0 @ id @ X0) = (^[Y0 : X0]: (one_one @ X0))))),
% 7.41/2.40 inference(ennf_transformation,[status(thm)],[f684])).
% 7.41/2.40 thf(f684,plain,(
% 7.41/2.40 ! [X0 : $tType] : ((real_V758409581_field @ X0 = $true) => ((deriv @ X0 @ id @ X0) = (^[Y0 : X0]: (one_one @ X0))))),
% 7.41/2.40 inference(fool_elimination,[status(thm)],[f683])).
% 7.41/2.40 thf(f683,plain,(
% 7.41/2.40 ! [X0 : $tType] : (real_V758409581_field @ X0 => ((^[X1 : X0] : (one_one @ X0)) = (deriv @ X0 @ id @ X0)))),
% 7.41/2.40 inference(rectify,[status(thm)],[f3])).
% 7.41/2.40 thf(f3,axiom,(
% 7.41/2.40 ! [X0 : $tType] : (real_V758409581_field @ X0 => ((^[X4 : X0] : (one_one @ X0)) = (deriv @ X0 @ id @ X0)))),
% 7.41/2.40 file('/export/starexec/sandbox/tmp/tmp.opwukp64f0/DTF2THF_11704.p',fact_2_deriv__id)).
% 7.41/2.40 thf(f2014,plain,(
% 7.41/2.40 (one_one @ complex != (deriv @ complex @ (^[Y0 : complex]: (Y0)) @ w))),
% 7.41/2.40 inference(definition_unfolding,[status(thm)],[f1899,f1559])).
% 7.41/2.40 thf(f1899,plain,(
% 7.41/2.40 ((deriv @ complex @ id @ complex @ w) != one_one @ complex)),
% 7.41/2.40 inference(cnf_transformation,[status(thm)],[f1171])).
% 7.41/2.40 thf(f1171,plain,(
% 7.41/2.40 ((deriv @ complex @ id @ complex @ w) != one_one @ complex)),
% 7.41/2.40 inference(flattening,[status(thm)],[f421])).
% 7.41/2.40 thf(f421,negated_conjecture,(
% 7.41/2.40 ~((deriv @ complex @ id @ complex @ w) = one_one @ complex)),
% 7.41/2.40 inference(negated_conjecture,[status(cth)],[f420])).
% 7.41/2.40 thf(f420,conjecture,(
% 7.41/2.40 ((deriv @ complex @ id @ complex @ w) = one_one @ complex)),
% 7.41/2.40 file('/export/starexec/sandbox/tmp/tmp.opwukp64f0/DTF2THF_11704.p',conj_0)).
% 7.41/2.40 % SZS output end Proof for DTF2THF_11704
% 7.41/2.40 % (12103)------------------------------
% 7.41/2.40 % (12103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.40 % (12103)Termination reason: Refutation
% 7.41/2.40
% 7.41/2.40 % (12103)Memory used [KB]: 7931
% 7.41/2.40 % (12103)Time elapsed: 0.107 s
% 7.41/2.40 % (12103)Instructions burned: 329 (million)
% 7.41/2.40 % (12103)------------------------------
% 7.41/2.40 % (12103)------------------------------
% 7.41/2.40 % (12027)Success in time 0.83 s
%------------------------------------------------------------------------------